RFT ESSENTIALS OF PRESSURE

INTERPRETATION TEST

ESSENTIALS OF PRESSURE TEST INTERPRETATION

RFT ESSENTIALS OF PRESSURE TEST

INTERPRETATION

TABLE OF CONTENTS

TABLE OF CONTENTS

1. INTRODUCTION. 13 III. INTERPRETATION 29

II. THE PRINCIPLE OF RFT MEASUREMENTS. 17

11.1. THERFTTOOL.. ....................... 17

1.1. Capabilities ................................. 17 1.2. Limitations.. ................................ 19

11.2. CALIBRATIONS AND ACCURACY ___ ____ __. ._ ..__ ___ __ __. __ 19

11.3. HIGH PRECISION QUARTZ PRESSURE GAUGE __ ___ ___. ._. __ 19

3.1. Principle of Measurement .._______ _____ 20 3.2. Comparison with Conventional

Gauges.. _. _. 20 3.3. Quartz Gauge Pressure Correction __. 20

11.4. APPLICATIONS OF RFK PRESSUREMEASUREMENTS 21

Introduction ___.____ __.. . .._. .._____ __ .___ 21 4.1. Analysis of Hydrostatic and

Reservoir Pressure Profiles _. 21 4.2. Application of the Quartz Gauge to

Fluid Density Measurements __ ___ __ ._ __ 25

111.1. QUALITATIVE INTERPRETATION _.

1.1. Pretest validity ___ __. ..______ ____ __. _. 1.2. Permeability Indication in Valid

Pretests ___ ____ ._ __ __.

111.2. QUANTITATIVE INTERPRETATION..

Introduction ___ _____ ___ ____ .__ .__ __ ___ __

111.3. DRAWDOWN ANALYSIS ____ __. _.

3.1. Analytical Study .____ ___. _.. 3.2. Spherical Flow Skin-Effect. .__ ___ _. __. _. 3.3. Upper Limit of Measurable

Drawdown Rate ..______ ___ _. 3.4. Factors Affecting the Drawdown __ ___ 3.5. Radius of influence for Drawdown

111.4. BUILD-UP ANALYSIS

4.1. Spherical Build-up ._ ___ ___ ._ __. 4.2. Cylindrical Build-up _.,,_.,_______________ 4.3. Radius of Influence for Build-up... __. 4.4. Depth of Investigation _______....___.____ 4.5. Upper Limit of Measurable

Permeability from Build-up. 4.6. Build-up Analysis versus Drawdown

Analysis

29

29

30

31 31

32

32 33

34 3.5 35

35

36 37 39 40

40

41

9

4.7. Influence of impermeable bed boundaries ___ _. ___ ___ ____ ______. _.. 41

4.8. Influence of the invaded zone 43

111.5. SPECIFIC PROBLEMS ASSOCIATED WITH RFT RESPONSE _____ ___. ____. __ ____ _. _, .._ ___ 44

5.1. Relationship between sand-face water pressures measured by the RFT and phase pressure in a virgin reservoir.. 44

5.2. Suuerchargine . . 47 5.3

111.6.

Aiemow:..: 51

QUICKLOOK INTERPRETATION FROM BUILD-UP.. 54

6.1. Determination of Quicklook Permeability. 54

6.2. Quicklook permeability from build-up in limited drawdown tests. ._ ___ _.____ __. ___ ____ ____ ___ 56

6.3. Field example __ _____ ______ ___ ___ ____. ___ ___ 56

IV. mWITHCSU _________.____............. 61

V. SPECIAL APPLICATIONS OF THE RF-r. .

V.I. RFT TESTING IN TIGHT RESERVOIRS..

1.1. Statement of the problem ____......._.__ 1.2. Conduct of an RFI job in a tight

reselwxr .

V.2. RFT TESTING IN NATURALLY FRACHJRED RESERVOIRS _____ __

2.1. Generalities ___________ ______. ._ __ ______ 2.2. Theoretical pressure response 2.3. Field example ___.... .___ ___ ____ __ ___. ___ 2.4. A note on the limit of resolution of

the method. _... ., .__ ____ _______ __ _.__

69

69

69

70

71

71 73 74

75

I. INTRODUCTION

I. INTRODUCTION

The Repeat Formation Tester (RFT) is an open hole wireline instrument primarily used for measuring vertical pressure distribution in a reservoir, as well as for recovering formation fluid samples.

The point by point reservoir pressure measurement technique is used to determine the gradients of both hydrostatic pressure of the mud column in the borehole before the tool is set or after the tool is retracted, and the formation pressure when the tool is set.

In exploration and delineation wells, where depletion has not yet affected the original pressure distribution of the reservoir, the pressure profile may be interpreted essentially in terms of fluid densities and contacts (i.e. OWC, GOC).

During infill drilling the RFT pressures allow definition of vertical and horizontal communication and/or boundaries. Used in conjunction with other information (e.g. Production Logging) RFf pressures may be interpreted in terms of horizontal and, in particular, vertical trans- missibilities.

However, the Repeat Formation Tester is also a device capable of providing an estimate of formation permeability through the interpretation of pretest pressure data recorded during drawdown and build-up. This book will discuss the RFT pretest. For information on recovery analysis please refer to “ The Essentials of Wireline Formation Tester “, March 1976 Edition.

13

II. THE PRINCIPLE OF RFT MEASUREMENTS

II. THE PRINCIPLE OF RFT MEASUREMENTS

U-l. THE RFl. TOOL

1.1. Capabilities

The Repeat Formation Tester tool has been designed to :

- Measure formation pressures and

- Collect reservoir fluid samples.

Depth accuracy can be controlled by correlating a Gamma Ray curve or an SP curve with the Open Hole logs.

Once downhole, the RFf can be set as many times as desired under normal operating conditions. This device is capable of high precision pressure measurements, and it can retrieve two fluid samples per trip in the hole.

The tool can be set at any desired depth independent of mud pressure. Even at very shallow depths it still has enough setting force to provide a good seal with the formation through the packer.

Two pretest chambers, automatically activated every time the tool is set, withdraw 10 cc of formation fluid each. Chamber-l has a lower flowrate than chamber-2 These rates of fluid withdrawal vary with tool and downhole conditions but they are in the neighbourhood of 50 cc/min and 125 cc/min respectively, giving a flowrate ratio of about 2.5. These pretest samples are not saved. FIG. II-I: RFr in closed and open positions.

17

RFT essentials of ~xxzssure test Interpretation

When the tool is set, a packer moves out one side and back up pistons move out on the opposite side, as seen in Fig. II-l. The body of the tool is held away from the borehole wall to reduce the chances of differential sticking.

Fig. II-2 shows the RFT pretest and sampling principle. A filter in the flowline probe prevents sand entry into the tool and a piston cleans the filter when the tool is retracted. Thus flowline plugging is substantially reduced. A strain gauge pressure transducer located in the flowline monitors the pressure during the test. The pressure is continuously recorded at surface in both analogue and digital form, giving pressure drawdown data and subsequent buildup data whenever the pretest (or sampling) is concluded.

FIG. 11-2: m pretest and sampling principle.

A typical pressure recording is shown in Fig. II-3 which shows both analog and digital pressure curves as standard log presentation. The “motor speed” may be presented on the log also, if desired. This motor drives the hydraulic pump which sets and retracts the RFT. The speed curve of the motor can be used for identifying various stages in the tool’s set and retract cycles. Initially, in Figure U-3, the pressure is that of the mud column. When the tool is set, the pressure rises slightly because of the compression of the mudcake by the packer. Then the

FIG. 11-3: Typical pressure recording during a pretest.

probe piston retracts and the pressure drops due to the resulting flowline volume expansion and communication with the formation. When the piston stops, the pressure builds up again because the packer is still continuing to compress the mudcake until the tool is fully set. Next the pressure drops as the first 10 cc pretest piston begins moving at a constant rate. This time is denoted as to. After about 15 seconds the first pretest piston reaches the end of

18

its travel. At this time, tl, the second piston begins moving at a rate 2.5 times faster than the first piston movement, consequently the pressure drops further. When both pretest chambers are full, at time t,,the pressure builds up towards a final pressure. The running time used for pressure analysis, At, is counted starting at tz.

Analysis of the build-up curve may yield permeability and reservoir pressure as with conventional drill stem and production pressure tests. Finally, after the tool is retracted, the mud column pressure is again measured.

1.2. Limitations

Unlike its predecessor, the Formation Interval Tester, the RFI is limited to measuring formation pressure and to retrieving formation samples in open holes only.

Minimum hole size required is 6 inches and maximum hole size is 14s4 inches. Maximum mud pressure rating is 20,OCQ psi, and maximum mud temperature is 350°F. Standard sizes for the sample chambers are l-gallon and 23’4 -gallon, but &gallon and 12-gallon chambers are also available.

II.2. CALIBRATION AND ACCURACY

The RFI’ pressure measurement is considerably more accurate than that obtained with previous wireline techniques. However, the absolute accuracy of the pressure measurement depends on the calibration technique. As the gauge and the tool are temperature sensitive, a good calibration must be applied in order to achieve the greatest possible XC”G3CY.

The standard gauge used in the RFI is a strain gauge. Using a c< dead weight * tester for calibrating the gauge and applying temperature corrections, the RFT system accuracy is better than 0.41% of full scale (i.e. 41 psi for a 10 Ooo psi gauge).

The greatest accuracy is attained by placing both the

II. The principle of RFT measurements

gauge and the downhole electronics in a temperature-controlled oven and calibrating with a dead-weight tester for a series of different temperatures. The utimate accuracy thus obtained is a maximum error of 13 psi for a 10 000 psi gauge (0.13 % of full scale). The resolution of the presently used system is 1 psi. A new telemetry system (telemetry B) is presently being introduced which allows improving the resolution to 0.1 psi. Similarly, the repeatability will be improved to 0.4. psi, as compared to 3 psi with the present measurement system.

Gauge calibration data are recorded on a graph for future reference to correct log readings to true pressure as a function of temperature. A typical gauge master calibration is shown in Figure H-4, where the influence of gauge hysteresis is also shown on the calibration curves.

FIG. 11-4: Example of Strain gauge field master calibration.

U-3 HIGH PRECISION QUARTZ PRESSURE GAUGE

For special formation pressure studies where absolute accuracy is very important, the RFT can be run with a high precision quartz gauge (such as the one manufactured by Hewlett Packard). These gauges have an accuracy typically of the order of:

0.5 psi, if the temperature is known to a 1 OC XC”GXY 1 psi, if the temperature is known to a 10 “C accuracy 5 psi, if the temperature is known to a 20 “C accuracy

19

RFT essenti of pressure test interpretation

Gauge resolution is 0.01 psi for a 1 second time constant compared to 1 psi with the standard RFI gauge.

3.1. principle of Measurement

The high precision quartz gauge consists of two quartz controlled crystal oscillators basically sensitive to pressure and temperature. One quartz crystal acts as a sensor to the fluid pressure and temperature, the other acts as a reference with the following specifications :

1) The temperature effect on both crystals is identical in a condition of equilibrium.

2) The crystals form a matched pair when calibrated.

3) The reference crystal is placed in a vacuum (not exposed to pressure).

3.2. Comparison with Conventional Gauges

The advantages of the quartz gauge compared to conventional gauges are its high accuracy, good repeatability, high resolution, positive depth control, high data density, and output type (quartz clock with printout).

Unfortunately the quartz gauge takes a long time to stabilize before it reaches the true pressure. Depending on the accuracy to be achieved, stabilization times have been observed to last up to 20 minutes for both pressure and temperature

*changes. The pressure accuracy is also very dependent on good temperature data.

3.3. Quartz Gauge Pressure Correction

Due to the fact that the quartz gauge is located lower than the strain gauge in the RFT (see Fig. II-S), the pressure read from the quartz gauge must be depth-corrected to the pressure reference level (with is the RFT strain gauge level). The following expression is used:

Corrected pressure = quartz gauge reading minus pmud mln”s ~2~~~

where pza, is the hydrostatic head due to the 3.47 ft column of DC 200 (a silicone agent used to protect the gauge from mud) and pmud is the pressure due to the 1.33’col”mn of mud. pza, = 1.44 psi at 77OF and 1 atmosphere and must be corrected for downhole pressure and temperature “sing Fig. 11.6.

FLUID 1.27’ BEING

STRAIN GAUGE

TO TWO CHAMBERS

3.47

-

i

-SILICONE OIL DC200

n

QUARTZ GAUGE

FIG. U-5: Quartz gauge location in the RFT.

It should be noted here that the strain gauge is usually calibrated in psig (gauge pressure measured with respect to atmospheric pressure) while the quartz gage may be calibrated in psia (absolute pressure, with respect to zero). This difference (around 14.7 psi) must be taken into account when doing detailed comparisons.

20

FIG. U-6: Pressure of Column of DC 200 in HPA-A Adapter corrected for temperature and pressure.

U-4 APPLICATIONS OF RFT PRESSURE MEASUREMENTS

lUbdUCtiOIt

Besides the retrieval of formation fluid samples and the measurement of formation pressures, the RFT has found many applications in the field of reservoir engineering :

- In exploration of appraisal wells in unproduced fields, it is known that fornmtion pressures must conform to gravity-capillary equilibrium established over geologic times. Thus the conduct of the RFT survey and the interpretation of the data is governed by the constraint that the formation pressures lie on straight-line fluid gradients and the main objective of the testing is

II. The principle of RFT measurements

to delineate these gradients (water, oil and gas) and their intersections.

- In development (in-Iill) wells, the observed formation pressures may already be affected by either partial depletion or possibly water injection. Thus the new development well is used as an observation location at which the current state of the reservoir can be measured on a vertically distributed basis. The measured pressure profile reflects the response of the reservoir to production/injection and it is axiomatic that the pressure information may not be interpretated in terms of reservoir structure and fluid distribution without knowledge of the production which has taken place. Reservoir simulation may often be the only possible approach to interpret RFK data on a field-wide basis. Such simulations may be considerably enhanced by history-matching to layer pressures and layer production rather than surface rates. This subject is beyond the scope of this book and will be treated in separate publications.

4.1. Analysis of Hydrostatic and Reservoir Pressure Profiles

As previously noted, the design of the RFT allows an unlimited number of pressure measurments during one trip into the borehole. At each measurement point three different pieces of information are recorded :

- The hydrostatic pressure (within the mud column)

- The shut-in (formation) pressure

- The pressure transient induced by the withdrawal of 20 cm3 of formation fluid.

Analysis of the hydrostatic pressure

As described earlier, the pressure within the borehole is routinely recorded before and after each setting cycle. Comparison of both pressures allows an easy verification of the stability of the measuring system. Stability may be improved by keeping the tool stationary for a few minutes before setting it. Then pressures before and after the pre-test should not differ by more than one or two psi.

This is subject to the previso that the mud level in the

21

RG. 11.7: Hydrostatic and reservoir pressure profiles in a well of the Triassic Province

22

II. The principle of RFT measurements

borehole remain constant throughout ‘the recording (50 C”I of mud column correspond to a pressure difference of about 1 psi).

On the typical recording of Fig. 11-3, the pressure readings immediately before setting and after retracting the tool are identical : 7 039 psi (7 OOII + 0 + 30 + 9). This is indicative of a well stabilized measurement system.

The hydrostatic pressure which is thus obtained should be continuously plotted against depth while the RFT operation proceeds. Such a plot should show a pressure gradient corresponding to the actual density of the mud.

I” order to convert the pressure gradient measurement of psi/m into a metric mud density (g/cm’) for this example, one uses the simple relation :

FInid density (glrn3) = P*~ww gradient @i/m) 1.422 (4.1.1)

To calculate the gradient, care should be taken to “se true vertical depths rather than logged depths.

Abrupt variations of this gradient may be indicative of “on-stabilized pressure recordings. Gradual changes may be due to either a drop of the mud level (the pressure decreases with time) or to segregation of the mud with heavy particles settling towards the bottom of the hole. This is well illustrated on Fig. II-7 which shows the hydrostatic pressure profile in a well.

The analysis of the pressures measured above 2 700 m shows a gradient of 2.11 psi/m corresponding to a mud density of 1.48 g/cm’. Note that the mud pressure measured at 2 700 m is about 5 780 psi, giving a total gradient of 2.14 psi/m or an average mud density of 1.50 g/c”?. The agreement behveen these two values is good, indicating that the mud column is quite homogeneous between surface and 2 700 m.

However, below 2 700 m, the pressure gradient increases progressively until it reaches a value corresponding to a mud density of 2.79 g/cm’ just above the bottom of the hole. This is probably due to the settling of mud weighting material. But such an increase might also be indicative of the presence of a cc trip slug D) a heavy mixture of mud pumped

downhole just before pulling the drill pipe to minimize the risk of blow-out.

A plot of formation pressure (either read directly or derived from build-up plots) against depth can give a large amount of valuable information to the reservoir engineer.

The pressure gradient can be interpreted in terms of formation fluid density, “sing equation (4.1.1). The approach is similar to the one described above for the hydrostatic pressure and it gives an indication of the nature of the formation fluids (gas, oil, or water) as well as the positions of the interfaces between different phases (gas-oil contact, oil-water contact).

It should be noted that the intercept of the pressure gradients, corresponding for instance to oil and water, is representative of the so-called free water level; it may thus be somewhat below the 100 per cent water level, as indicated by logs, due to capillary pressure effects. This is shown schematically on Fig. 11-S. In the transition zone, both oil (or gas) and water may be mobile; hence the pressure distribution will be somewhere between the gradient for oil (or gas) and water.

t

\

FIG. II-8 : RF’I free water level compared to CPI water level.

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The above is, of course, strictly valid only for reservoirs whose pressure distribution has not been affected by depletion. If after some depletion and pressure drop the pressure gradient is still uniform and parallel to the original fluid gradient, then depletion can be considered as being uniform and vertical pressure communication within the reservoir (either direct or through the aquifer) must be good.

Conversely, if depletion is not uniform, this will be indicated by the fact that the pressure no longer follows a unique gradient. Various situations are depicted on Fig. 11-9. Permeability barriers within the water zone may limit the efficiency of the natural water drive or that of water injection. Bypassed oil will be easily identified by its pressure remaining at, or close to,. the original pres&re.

RFf esentiaIs of pressure test interpretation

0.63 g/cm’, again in good agreement with the expected value for oil. Hence the gas-oil contact can safely be put at 2 717 m. This is confirmed by the open hole log interpretation reproduced on the left side of Fig. 11-7.

The oil-water contact is less easy to see since the formation is not thick enough to establish a reliable gradient.

However, the four lower measurements in zone D fall on a straight line with an apparent gradient corresponding to 1.12 g/cm’. Pressures above 2 750 m were taken in a transition zone and exhibit an intermediate gradient of around 0.8 g/cm3. Again this can be confirmed by the open hole log information. Thus the nature of the formation fluids and interfaces can be positively identified with the RF-I-.

As far as the uniformity of the depletion is concerned, the pressure distribution is easily interpreted. This well was drilled in early 1979 into a reservoir which has been producing since 1966.

Zone C, with its fluid gradients which can be clearly identified, has been uniformly depleted and good vertical communication can be expected (in fact, it is the uniform pressure distribution which identifies zone C as a reservoir unit). However, it seems that a shalier streak visible &I the open hole interpretation might impede somewhat the communication between the main body of zone C and its lower part (called zone c’ on Fig. U-7).

FIG. II-Y: Effect of depletion on the reservoir pressure pdile.

We have already studied the hydrostatic pressure profile shown on Fig. 11-7. Looking now at the formation pressure profile, we can interpret it as follows : zone C shows a very distinct gradient change at 2 717 m. The fluid density above can be calculated to be 0.17 g/cm3 which fits closely with what one would expect for gas at this depth.

The gradient below corresponds to a fluid density of

Fig. II-10 shows a similar application in a gas field where three zones are producing through the same tubing. The hydrostatic pressure measurements fall on a single well-defined pressure gradient indicating a homogeneous mud of 1.62 g/cm) density, in excellent agreement with the surface data of 1.61 g/cm3. The formation pressure plot indicates a large gradient change within zone C at 2 223 m ; the density above (0.25 g/cm3) fits dosely with the expected gas density; the gradient below corresponds to the density of the reservoir salt saturated water (1.17 p/cm’). As far as depletion is concerned, zones B and C show uniform depletion. Therefore, a good vertical communication exists between these hvo reservoirs. On the contrary the slightly higher pressure of zone A would indicate an imperfect communication with zones B and C.

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The higher pressures exhibited by zones A and B clearly identify them as being separate reservoir units

FIG. H-10: Pressure profile in a gas well of the M’Zab basin in Algeria.

unconnected with each other or with zone C. The higher pressure of zone A together with its low water saturation production, and its pressure remains probably close to the original reservoir pressure. (But note that the presence of small cc breaks z as indicated on logs does not necessarily mean the presence of a vor5cal permeability barrier. Compare for example on Fig. II-7 the shale at 2 670 m with the shale at 2 600 m).

Zone D which is partly depleted has been perforated in all nearby wells. It has a good permeability and hence shows the highest depletion (lowest pressure).

II. The principle of RFT measurements

Its communication with the water zone E (and hence probably the aquifer) is not perfect, as shown by the difference in absolute pressures. Should water injection be needed for pressure support, this should therefore preferably not be attempted in zone E.

The application of FST pressure measurements to reservoir management can of course be much enhanced by comparing pressure variation from well to well. The principle is rather straightforward: continuous resenroir layers will be identified by uniform reservoir pressure distribution. Disconti- nuities will be indicative of faults or other permeability barriers. It should be remembered that true vertical depths must be used for this approach.

4.2. Application of the Quartz Gauge to Fluid Density Measurements

Due to the improved resolution of the Quartz Gauge, it is possible to determine formation fluid density in relatively thin beds. If, as in Figure II-11 a crossplot

hl 442 hm

FIG. 11-11: Plot of mud pressure versus Formation pressure.

of formation (P,) and hydrostatic (P,) pressures are made in a bed with vertical communication, a line whose slope depends on the formation fluid density is obtained. Assuming static equilibrium, it follows that :

PO - pn = p&h and

pti - P,, = p&h

25

thus :

&yy Pti -

where p, and pm are respectively the densities of oil and mud

Now pm (the mud density) may be obtained by measuring the hydrostatic gradient over a distance h :

Pm2 -Pm’ = p gh

m

The advantage in using the Quartz Gauge to determine fluid density in this manner is best illustrated through an example. Let us take the theoretical situation described in Fig. 11-12. Theoretically the slope of the line should be :

If the pressures were measured with a strain gauge whose resolution can be taken as 1 psi, Ap,fAp, could be anything from 7/S to 3112. Thus the ernx could be as much as 75 %. This error would be drastically decreased to 6 % if these pressures were measured with a quartz gauge (resolution of

0.01 psi), as the slope would have been between 5.02/9.98 and 4.9W10.02.

FIG. II-12 : Them&al example of a Pressure versus depth diagram to illustrate gauge resolution importance in the determination of Pressure gradient.

Note however that using more than two pressure measurements would, of course, enhance the statistical accuracy of the gradient determination both for the conventional strain gauge as well as for the quartz gauge.

26

III. INTERPRETATION

III. INTERPRETATION

III.1 QUALITATIVE INTERPRETATION

The analog prestest pressure cmve as it appears on Track I is helpful in determining the validity of the pretest for further analysis. When the pretest is valid it will be used to consider whether or not to take a sample. Under certain conditions, a valid pretest can also be analysed in terms of formation permeability and pressure.

1.1. Pretest Validity

Fig. III-1 shows a number of tests in which seal failures of different kinds have occurred. Fig. III-la is a total seal failure with the gauge reading the hydrostatic value of the mud column. An explanation for this would be that the tool was set in a portion of the hole where the diameter was too large. If the pump motor revolution curve is recorded on the same track one will notice the opening and closing of the pretest chambers from that curve. Fig. III-lb shows partial seal (or probe plugging) obtained before final seal failure. In Fig. 111-1~ there is some indication of seal at the beginning but later the mud leaks around the packer. That this is in fact a seal failure is shown by the build-up pressure curve, which a builds-up B back to the hydrostatic value

Partial probe plugging during pretest as shown in Fig. III-ld is indicated by erratic drawdown.

FIG. III-i (a. b, c) : Typical RFT pretest records during seal failures.

Fig. III-1 e shows a more significant case of plugging in this case during the first pretest ; nevertheless in Fig. III-ld and e the build-up data are still usable for further analysis. Shown in Fig. III-lf is the case

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FIG. III-1 (d, e, f) : Typical RF7 pretest records showing probe plugging.

h

FIG. III-1 (g, h): Typical RFT pretest records in tight formation and when gas is present in the Bowline.

where complete plugging occurs during the second pretest. Complete plugging at the beginning of the

RFT essentials of pressure test interpretation

first pretest (fig. 111.lg) might be mistaken for a test in a tight formation.

If gas is trapped in the flowline, the pressure profile will look as shown in Fig. III-lh. Due to the expansion of gas in the system, the pressure drops with the piston motion. Consequently, the flow into the pretest chambers is not at a constant rate and permeability cannot be derived from drawdown.

1.2. Permeability Indication in Valid Pretests

Qualitatively, the analog pretest pressure protile gives an excellent quicklook estimation of the formation permeability in the vicinity of the probe. More quantitative permeability evaluation is possible, as will be explained in a later chapter of this book.

Fig. III-2a is an example of good permeability, above 100 md; Fig. III-2b is an indication of moderate permeability of about 10 md. Fig. 111-2~ suggests low permeability, of the order of 1 md, while Fig. III-2d shows a very low pretest flowing pressure, indicative of a permeability of the order of 0.1 md or less. The limit is the dry test or total plugging as in Fig. III-l%

ABOUT 10 md b

30

III. Interpretation

ABOUT O.,md d

FIG. III-2 (a, b, c, d): Typical RFT pretest recording under various conditions of formation permeability.

in which the pretest flowing pressure remains near zero or even drops below zero to a negative value. This negative reading may be explained by temperature effect.

Theoretically the lowest possible pressure which the RFT can measure is the vapour pressure of the fluid within the pretest system (usually mud or filtrate). This vapour pressure is a function of temperature and can be obtained from appropriate handbooks. For 250 “F for example (absolute) vapour pressure for water is 30 psia. Readings below the vapour pressure and, in particular, negative readings, can only be explained by a combination of temperature effect (which is shown on the gauge calibration chart) and gauge error (which depends on the calibration method used - see chapter 11-2).

III-2 QUANTITATIVE INTERPRETATION

Introduction

During the pretest, the formation fluid is withdrawn through the RFI probe into the pretest chambers. This generates a localized Bow in the formation

whose pattern is essentially spherical in character, as illustrated in Fig. 111-3. Hence the analysis of the dynamic pressure response of the pretest is based on the theory of spherical flow of a slightly compressible fluid in a homogeneous medium.

/

PRESSURE DISTURBANCE

RFT

%be

I-- BORE HOLE AXIS

FIG. 111-3: Spherical flow model

This drawdown pressure depends on the effective permeability of the formation to the flowing fluid, which is usually mud filtrate from the invaded zone.

At the end of the drawdown period when the pretest chambers are full, the pressure disturbance continues to advance in a similar pattern due to fluid flowing from the undisturbed part of the formation towards the low pressure area in the vicinity of the RFI probe. This period is termed the build-up period. The pressure measured at the probe continues to build-up until it reaches equalization, which is usually that of the original formation pressure. The time required for this build-up is essentially a function of the formation permeability of the uninvaded formation to the mobile phase of the formation fluid.

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Thus there at two different approaches to derive the formation permeability from the pretest :

1) From the drawdown;

2) From the build-up

III-3 DRAWDOWN ANALYSIS

3.1. Analytical Study

As a consequence of the spherical nature of the fluid flow which implies that most of the fluid movement takes place in a small volume immediately surrounding the probe, steady state conditions are usually obtained very quickly during the drawdown period and the resulting pressure drop can be described as follows :

APP,, = C &$ (1 -$) (3.1.1)

where A p.. is the drawdown pressure, C is the flowshape factor, q is the flow rate, p is the viscosity of the flowing fluid, rP is the effective probe radius*, r. is the outer radius of the pressure disturbance, and kd is the permeability that affects the pressure drawdown.

The effective probe radius, rP, can be considered as much smaller than the outer radius of the pressure disturbance, re, and consequently the equation can be simplified to:

k,=C x 271 Ap rP

(3.1.2)

Since the RFT probe enters the formation form the borehole, the flow pattern cannot be exactly spherical; this deviation from an exactly spherical flow pattern is expressed by the flow shape factor, C,

* Note the u effective * probe radius for spherical flow is smaller than the actual probe radius. Carslaw and Jaeger (s Conduction of Heat in Sotidsn) have determined the equivalent spherical radius of a disc (for the Row into a half-space) to be given by 2 times its actual value divided by n. This updates the previously assumed (Mu&at) value of r,Q

and is illustrated in Fig. 111-4. Depending on well diameter, the actual flow will lie somewhere between the limiting cases of spherical flow for an infinitely small borehole where C is 0.5, and hemispherical flow for a very large borehole where C is 1. The exact value of this flowshape factor has no significance in itself but only as part of the total proportionality constant which is given by:

c

RFT essentials of pressure test interpretation

2n rD

/

@ ‘/ / \

c * 1.0 HEMISPHERICAL

FLOW

\I -.- /\

c = .5 SPHERICAL FLOW

F’IG. 111-4: Flow shape factor for various flow pattern.

Detailed computer simulations of three-dimensional steady-state flow into the probe set in a g-inch borehole have been made in order to derive the actual flow geometry and to solve for the proportionality constant. Using this simulator- derived constant we can write the permeability

32

equation for the standard probe-packer configuration in its final form as:

k, = 5660 2 APP,,

(3.1.3)

where

kd = drawdown permeability (md) 4 = flowrate (c&x) k = viscosity of flowing fluid, usually mud filtrate

(cp) Apss = drawdown pressure (psi)

The flowrate, q, can be derived by dividing the volume of the pretest chamber by the corresponding flowing time. One computation can be made for each stage of the drawdown. At very low permeabilities, the achml Bowrate is difficult to estimate since it is not determined by the rate of the pretest piston displacement, but by the formation permeability i.e. the ability of the formation to produce 20 cc of formation fluid.

For the “Large Diamenter Probe ” or the “Fast Acting Probe” the proportionality constant to be used is 2395 and for the “Large Area Packer” it is equal to 1107.

The limitation of the application of the drawdown method is two-fold:

- At very high permeabilities, the drawdown pressure is too small to be measured accurately with the strain gauge, which has a 1 psi resolution. This limitation may, to some extent, be reduced by using high resolution quartz gauges.

- At very low permeabilities, the pressure may drop below the bubble point (or vapour pressure). Gas (or vapaur) is liberated and the flow-rate of the liquid withdrawn from the formation is less than the volumetric displacement of the pretest pistons (see also chapter 3.3.).

Eample :

An example of drawdown analysis of pretest using data recorded on Fig. II-3 gives:

p, = 2050 psi ql = 1005.4 = 0.65 c&x p2 = 4470 psi q2 = 1016.1 = 1.64 cdsec

As this well was drilled using oil-base mud, CL = 0.25

III. Interpretation

cp is taken as the in-situ viscosity. The drawdown permeabilities can then be calculated as:

kd, = 5660 0.65 x o.25 = o.45 *d 2050

k, = 5660 1.64 x 0.25 = 0,52 md 4.470

In this example there is a good agreement between the two values of the drawdown permeabilities.

3.2. Spherical Flow Skin-Effect

The probe only penetrates a very short distance into the formation and its aperture is located in the thin annular region of formation around the wellbore which is affected by mud solid invasion. Since the steady-state fIowing pressure registered at the probe is essentially determined by the permeability in the vicinity of the probe, the properties of this altered zone strongly influences the drawdown behaviour. In addition, localised changes in permeability may be induced by the act of introducing the probe into the formation. It is possible to envisage either compaction and fines plugging causing permeability impairment, or local fracturing resulting in an increase in effective permeability near the probe.

@i - P), = APP, = s (3.2.1)

Theses ideas may be quantified by introducing the

do

concept of a spherical flow skin factor, denoted S,, which accounts for the additional pressure drop due to the altered zone in the vicinity of the probe. In an infinite isotropic formation steady-state drawdown is described by this equation:

where both the numerator and the denominator of equation 3.1-2 have been multiplied by two.

In the case where there is formation alteration near probe, this equation is written in the form:

(P, - P),, = & (2C + SJ dP

in which :

s, = !kh 4rrk,r, 4P

(3.2.2.)

33

where Ap,,,. = incremental pressure drop due to alteration.

In RFI units this equation becomes:

1170 qu (P, - P),, = 7 w + SJ (32.3)

*P where :

s = Aprlrinki*p 1170 qp

When the medium is anisotropic, it is suggested that the isotropic permeability k be replaced by k,, the equivalent spherical permeability from build-up analysis.

In practical situations the spherical flow skin factor, S,, can only be obtained by measuring (pi - p)= at the end of a flow period, determining the permeability of the unaltered zone from build-up analysis, and using the equation:

(Pi - P),, = F (2C + SJ IP

to calculate S,.

3.3. Upper Limit of Measurable Drawdown Rate

The maximum inflow rate, e,,,,,, at which fluid can flow to the RFI probe from the formation without having the system pressure fall below that fluid’s bubble point pressure (at reservoir temperature) is :

RFT essentials of pressure test interpretation

pretest system will be drawn to the bubble point of the sampled fluid (water, for example) and flashing of that fluid will occur in the chambers. The analog pressure record then has the characteristic form illustrated in Fig. 111.5. This phenomenon occurs in very low permeability formation or if there is plugging or formation damage near the probe giving a large spherical skin factor, S,.

FIG. 111-5: Record limited drawdown test.

For the following typical parameter values and standard probe size:

p = 0.5 cp s, = 0

pb = 15 psi (at 250“ F) pi = 4 000 psi

the maximum inflow rate becomes q,,,,, = 1.4 kd, Hence drawdown permeabilities of less than around 1 md yield maximum inflow rates less than the second piston displacement rate.

emax = k,*, (P. - ~b)

1170 w (2C + S,) (3.3.1)

where :

kd = spherical drawdown permeability

‘P = effective probe radius - in cm pi = formation pressure - in psi pb = bubble point pressure of filtrate P = filtrate viscosity - in cp c = sow shape factor S, = Spherical flow skin factor

in md

in psi

In a case where the first piston displacement rate also exceeds qs.max, the pressure in the chambers rapidly falls to pb at which point vapourization commences. The probe inflow rate and chamber pressure now remain essentially constant at qs,max and p,, respectively until a cumulative volume of 20 cc of filtrate has entered the system. This fill up time, Tr, in Fig. III-5 depends on the value of q5.max and is longer than the period of piston motion T2. Flashing of water continues until the second piston stops at time Tz ; from Tz until Tr the water vapour condenses as incoming filtrate refills the pretest system with liquid.

The displacement rate of the first piston is approximately 0.67 cc/set and for the second piston is 1.67 cc/sex. If one of these rates exceeds q,,,,, the

It is apparent from the pressure response that when flashing occurs, the flowrate does not follow the two-rate process but essentially remains constant, I.e. :

q,.,,, is also = V,/Tr

where

34

V, = total piston displacement volume (20 cc)

Tr = fill-up time (set).

3.4. Factors Affecting the Drawdown

a. Radius of investigation

The fluid flow through the RFT probe is essentially spherical, and it can be demonstrated that almost all of the pressure drop occurs very near the probe. About 50 percent of the pressure drop occurs within one probe radius (0.55 cm).

Thus the drawdown is affected by the condition of the formation very close to the probe, which may differ significantly from the conditions deeper within the formation.

Some of the very fine solid particles suspended in the drilling mud may pass through the mudcake formed on the borehole wall and penetrate into the formation, blocking pore constrictions. The clay contained in the formation can also be de-stabilized close to the well-bore because of the ionic imbalance between mud filtrate and formation water, thus impeding the flow of fluids in the pores. The damaged zone caused by these effects will affect the drawdown, leading to an under-estimation of the permeability.

In soft formations, the area immediately surrounding the probe may become compacted, thus leading

0.2

0.1

0

s, Water Iot”ra?tlon. ‘ractlon s.. rmngr

FIG. 111-6: Relationship between absolute and effective permeabilities.

again to a pessimistic permeability evaluation. On the other hand, in hard, brittle formations, the penetrating probe may cause localized miniature fracturing and therefore lead to an over-estimation of permeability.

b. Water saturation

The relative permeabilities of the formation change with the water saturation. The total effective permeability in the invaded zone at saturation close to irreducible oil saturation may be considerably less than the absolute permeability, as illustrated in Fig. 111-6.

3.5. Radius of influence for Drawdown

During a period of flow into a point sink, the region of the formation affected by the fluid withdrawal expands radially outwards. The extent of propagation of the flow disturbance is given by the equation :

rlnf = (A&c) 1’2 (3.5.1)

which gives an estimate of the dimension of the spherical region around the sink and is termed the radius of inlluence. This is the spherical equivalent of the formula :

r, = (4kt/‘&C,)1” (3.5.2)

so commonly encountered in radial cylindrical flow.

rLni in RFT units is given by :

Lf (3.5.3)

III-4 BUILD-UP ANALYSIS

When, during the pretest, the two pretest chambers are full, the formation fluid stops flowing through the probe. The pressure increase propagates spherically and continues to do so until at least one impermeable barrier is reached. At this stage the spherical flow pattern is altered, and, in the case of two parallel boundaries, the spherical propagation becomes radial and cylindrical. This phenomenon is illustrated in Fig. III-7a and b.

3s

FIG. III-7a: Spherical propagation of pressure disturbance.

FIG. III-7b : Cylindrical propagation of Pressure disturbance.

During this period of outward propagation the pressure gradient near the probe rapidly approaches zero. All the flow therefore takes place deeper into the formation, and conditions near the probe have no effect on the pressure history during the later stages of the build-up.

For this reason, the build-up analysis may be used to obtain information about the undamaged part of the reservoir immediately surrounding the well.

As mentioned in the previous chapter, the pretest flowrates q, and q, may be considered constant over

the respective flow periods, provided the probe pressure during drawdown does not fall below the bubble point of the fluid being sampled giving rise to gas liberation in the piston chambers. The analysis of the build-up pressure response is accordingly based on a Iwo-rate drawdown and neglects compressibility (storage) effects in the prestest sampling system.

4.1. Spherical Build-up

The probe pressure response during build-up is obtained by superposition of the two single drawdown responses, and calculations based on spherical flow in an infinite homogeneous medium lead to the expression:

P, - P, = 8 x 106 9,~ ( ‘l$KJv2

k, 1,2 x f,(At) (4.1.1)

in which :

where :

Pi = R = 41 =

q2 =

Ir =

9 =

c, =

k,=

T1 =

Tz =

At =

initial formation pressure - in psi probe pressure (spherical buildup) - in psi flowrate during the first sampling period - in cdsec flowrate during the second sampling rate - in cdsec viscosity of fluid in uncontaminated formation -incp porosity of formation - in fraction of the total volume total compressibility of fluid in unconta- minated formation - in psi-’ isotropic spherical build-up permeability - in md sampling time related to q1 - in seconds or minutes sampling time related to qz - in seconds or minutes elapsed time after shut-in - in seconds or minutes (see figure U-3).

A plot of p.. the observed pressure during build-up, verstls f,, the spherical time function, on a

36

III. Interpretation

linear-linear grid graph as shown in Fig. III-8 will ideally result in a straight line of slope m. Extrapolation of this straight line to fS (At) = 0, i.e. infinite time, yields the static formation pressure pi. The equation of this straight line can be written as :

where p, = m.f, (At) + pi

“I= 8 x 104 q+ (@&,)“*

k ,n (psi/secl’2)

T -

/

3 7 i

-

/

-

F’IG. 111-8: Pressure plot in the case of a spherical flow.

From the slope, m, of the spherical build-up plot, the isotropic permeability k, can be determined as:

k, = 1856 ,J (z) “’ (‘NJ,)“” (4.1.2)

Example :

Fig. III-8 shows the build-up plot obtained using the data recorded on Fig. 11-3. Taking q1 = 0.65 cc/set

and q2 = 1.64 cc&c as already computed, the points plot on a straight line, confirming the spherical flow hypothesis. On the contrary, the radial (cylindrical) hypothesis cannot be retained as the corresponding points do not form a straight line. The slope of the straight line is computed as 12.5 psisec -In. The permeability k, is obtained using the following values :

C, = 1.5X10+ psi? (m-situ total compressiblity p = 0.25 cp (in-situ oil viscosity) @ = 0.08 (porosity from open hole logs)

This results in k, = 0.69 md. The permeability from drawdown which was derived previously is k, = 0.52 md.

In the above example the well was drilled with oil base mud; consequently the formation damage should be negligible and the fluid viscosities and relative permeabilities in invaded and non-invaded zones should be similar.

The spherical pressure propagation is affected by both horizontal and vertical permeabilities of the formation. This is given by the following relation :

k =k’“k 2’3 = A’” k I 1 r (4.1.3)

where k, is spherical permeability and A the anisotropy here defined as k&.

It should be noted that the anisotropy may vary greatly as a function of the investigated volume since it is a combination of a microscopic anisotropy due to the sedimentary texture of the rock and a macroscopic anisotropy due to the reservoir heterogeneity (layering).

4.2. Cylindrical Build-up

As mentioned earlier, the spherical flow pattern changes to a radial-cylindrical flow pattern when it reaches the upper and lower impermeable boundaries. In relatively thin beds this phenomenon is quite significant, the build-up is affected only by the horizontal permeability.

The build-up equation is given by:

p. - p = 2687 2 x f (At) I c k,h ’

(4.2.1)

37

RFT essentii3I.5 of pressure test interpretation

in which:

f, (At) = log T, + T, + At + 25 log ___

T, + At

T, + At % At

where :

Pi = initial formation pressure in psi P, = probe pressure (cylindrical build-up) in psi q, = llo;e;te during the first sampling period - in

q, = Bowrate during second sampling period - in c&x

P = viscosity of fluid in uncontaminated formation - in cp

k, = cylindrical build-up permeability - in md h = the distance between the two impermeable

boundaries - in cm T, = sampling time related to q, - in seconds OT

minutes Tz = sampling time related to q, - in seconds or

minutes At = elapsed time after shut-in - in seconds or

minutes

Pressure readings from the log are plotted versus the cylindrical time function f, (At), as illustrated in Fig. III-lo. If the pressure propagation is cylindrical, the pressure versus cylindrical time function plot is then ideally a straight line which intersects the line f (At) = 0, i.e. infinite time, at the static formation pressure.

Example :

An example of a pretest performed in a thin streak close to the upper boundary of the reservoir is shown in Fig. W-9, the pressure data are plotted on Fig. III-10 versus both spherical and cylindrical time function.

The points fall on a straight line, confirming the cylindrical flow hypothesis. On the contrary, the line corresponding to the spherical time function is curved.

From the pressure record we get T, = 15.45, Tz = 5.65, and therefore q, = 0.65 c&x and q2 = 1.8 cc&c. From the pressure plot, the slope, m, can be determined, m = 220 psi/cycle.

FIG. III-9 : Pretest recording of a cylindrical flow example.

38

/ I

4

06

me

/ .

/ -

- - FTG. III-IO: Pressure plot in the case of a cylindrical Row (from the data of fig. 111-9).

The permeable bed of thickness h may be estimated from the open hole logs, in this example h = 40 cm (1.3 ft). The hydrocarbon in-situ viscosity is equal to 0.30 cp. Knowing these parameters k, may be calculated from equation 4.2-l giving k, = 0.06 md.

4.3. Radius of Inlluence for B&up

So far the analysis considers that the reservoir is homogeneous. Since reservoirs are not homogeneous and since changes in the build-up slope associated with permeability variation are often observed, it is therefore important to relate the observed pressure response to what is happening in the formation. A simplified analysis of the build-up based on a single rate drawdown of flowrate, q, and duration, T, will be considered.

The pressure behaviour in the formation during spherical build-up is illustrated in Fig. III-U. Since the pressure gradient is specified as zero at the probe and at infinity, it must pass through a maximum value at some intermediate position.

FIG. III-11 : Pressure behaviour in the formation during spherical build-up.

The slope of the build-up curve at any time is largely influenced by the permeability of the zone through which most of the flow is taking place at that time. The slope will largely be unaffected by the permeability in the negligible flow regions as long as these regions have sufficient permeability to allow pressure communication.

Thii can be quantified by defining the radius rmar at which q attains a maximum value, and the inner radius, I,,,~“, at which q attains some small value, say 2 % of the total flow. The following equation can be derived :

L” = ,.,,Jg x m x ($)I”

(4.3.1)

rmax = 0.0205~ x i/T=T x (&)‘”

(4.3.2)

39

4.4. Depth of Investigation

The build-up permeability computed from the slope of a build-up plot represents a value averaged over the region in which flow has occurred but with progressively less weight being given to late time data. It is obviously important to establish what volume of rock has significantly contributed to the calculated k value. Although theoretically the build-up can be prolonged indefinitely, eventually the changes in observed probe pressure become so small that no more information on flow properties can be gained. Hence the depth of investigation is closely related to the gauge resolution.

The question of depth of investigation arises because reservoir formations are heterogeneous, and permeability variation with position is commonplace. Hence the concept of depth of investigation can be identified with the problem of the detection of permeability changes at some distance from the probe. The easiest change in permeability to quantify is of course the case where an impermeable boundary is encountered. The mean value of bed thickness, h, in terms of RFT variable is:

h = 1.2 ( 4rr (p- z*, ,,) I” (4.4.1)

where :

h = bed thickness in ft = probe flow rate in cc/set

; = duration of flow period = T1 + Tz Pi = initial formation pressure in psi p* = final build-up pressure at infinite close-in time $ = formation porosity C, = total system compressibility A = kJkr is the anisotropy If the influence of a boundary at a distance h/Z from the probe is to be detectable, the pressure gauge resolution 6p must be smaller than the observable pressure effect (pi-p*). The radius of investigation, ri, may be equated with h/2. Accordingly the relation between depth of investigation and pressure gauge

resolution becomes :

ri = 0.6 ( &) 1’3 (4.4.2)

Note that the depth of investigation for the RFI does not depend on permeability.

RFT essentials of pressure test interpretation

4.5. Upper Lit of Measurable Permeability from Build-up

An important issue concerning the measurement of formation permeability from a pretest build-up is the relation between the maximum permeability which can be detected with any accuracy and the resolution of the pressure gauge. Obviously the earlier in the build-up the pressure recordings are taken the larger the observable pressure changes ; this is particularly important in a rapidly reacting environment in which the product @PC, which controls the rate of response in real time, is very small such as in a water zone. However there is a practical limit as to how early in the build-up an analysis is feasible.

Analysis of field data has shown that for a total pretest flowing time of 20 seconds the straight line section on a spherical build-up plot may begin at 6 seconds after shut-in, in some observed cases this means that t/T may reach as high as 1.3. The analytical solution in RFT units for this value of t/T is given by the spherical build-up equation:

!!c!!$f (&) 1’2= 0.95 x 10s (4.5.1)

where :

k = spherical permeability q = probe flow rate in cdsec P = tluid viscosity in cp $ = formation porosity C, = total system compressibility in psi? T = total probe flow time in set

The Ap value which is equal to (Pi - P,) represents the observable drawdown at the beginning of the build-up. In order to obtain reasonable accuracy in the determination of the slope of the spherical build plot it is necessary that the gauge resolution, bp, be of an order of magnitude less than this initial drawdown, i.e. 6p = 0.1 Ap. Hence the relation between gauge resolution and measurable permeability becomes :

F (&) I’*= 7.56 x l@ (4.5.2)

the maximum permeability k,,,, may be written in the form:

&, = 390

From the point of view of upper detectable permeability, it is obviously better to withdraw the sample as rapidly as possible.

The value t/T, that is the time it takes for the build-up to attain linear spherical behaviour, is a function of the following influences :

- Storage-due to compressibility of fluid in pretest sampling system. A total volume of fluid in the sampling system, more exactly pretest chambers and flow line, of approximately 60 cc is compressible. As the pressure builds-up a small flow from the formation is required to sustain the compression, causing after-flow into the probe, consequently causing an appreciable dynamic pressure drop distorting the pressure build-up response. At early shut-in times the pressure does not build up as rapidly as in an ideal system and hence initial data fall below the later straight line segment where after-flow effects have become negligible. The problem of after-flow is compounded by any reduction in permeability in the vicinity of the probe-spherical skin effect - which will increase the dynamic pressure drop associated with the continuing flow into the probe.

- Borehok effect - upon shut-in there is a rapid transition from hemispherical to spherical build-up but early time data will show some deviation from pure spherical behaviour. Since the actual steady-state pressure drop during drawdown is greater than in spherical flow, the initial build-up data will lie below the extrapolation of the straight line portion of the build-up plot representative of true spherical flow. This effect is superimposed on the influence of sampling system storage.

- Dynamics of prtxw~-t~ mea.wrenzent system - these problems arise particularly with the high precision quartz gauge which, when subjected to a step change in pressure, exhibits a response with a settling time of several minutes. Although the isothermal resolution of the quartz gauge is 0.01 psi, it cannot be taken advantage of in transient pretest conditions, and this gauge does not allow the measurable permeability range to be significantly extended. However the quartz gauge greatly improves the accuracy of the absolute value of the final build-up pressure and this feature is of considerable benefit.

III. Interpretation

4.6. Build-up Analysis versus Drawdown Analysis

In general the analysis of pressure build-up is much more accurate than the analysis of drawdown. The drawdown is significantly influenced by the skin effect (local damage in the immediate vicinity of the probe).

On the other hand some limiting factors have to be considered in the build-up analysis such as:

- In formations of medium to high permeability, generally above a few millidarcies, the build-up occurs too rapidly to be analysed quantitatively.

- The possibility of spherical and/or cylindrical propagation occurring complicates the inter- pretation. In the first case, knowledge of porosity and compressibility is necessary; in the second case the bed thickness has to be estimated. The spherical analysis yields a permeability which requires the knowledge of anisotropy if it is to be translated into horizontal permeability.

4.7. InIluence of impermeable bed boundaries

It has been demonstrated that the pressure disturbance created by the flow into the RET probe initially propagates quasi-spherically outwards and upwards and the pressure build-up following the pretest will fall on a straight line when plotted against the appropriate time function as shown on Fig. 111-8. The slope of such a build-up can be used to determine the spherical permeability of the formation.

If on the other hand the spherical propagation of the pressure disturbance is limited vertically by impermeable bed boundaries then the mode of pressure propagation changes. In practice the RFT probe could be set close to a single boundary or placed at some location between two boundaries.

The simplified case where the probe is situated midway between two impermeable boundaries has been considered for the analysis of the radial-cylindrical Bow behaviour. This corresponds to the classical well test analysis and allows the

41

determination of the permeability-thickness product k,,h as explained eadier.

Actually both models are limiting cases of a number of practical possibilities. We shall consider here the eventuality of the probe being set:

1) Far enough away from one or two boundaries so that aftetiow effects have time to die out before boundary effects are felt,

2) Close enough so that the boundary (or boundaries) are within the radius of investigation of the test.

If these conditions are fulfilled, then one could except to be able to detect the change in pressure propagation mode by observing pressure build up behaviour.

The theoretical basis of this has been treated in some detail in Ref. 1, in this book we only want to look at the conclusions :

- in the case of only one boundary affecting the build-up this will result in an apparent upswing of the spherical plot, the late-time asymptote of this upswing is another straight line of double the slope of the non-bounded case.

- in the case of two boundaries affecting the build-up a similar upswing wiU occur on the spherical plot. When plotting this pressures against a cylindrical time function the points will fall on a straight line thus confirming radial-cylindrical propagation mode.

In principle these features could be used to establish whether one or hvo boundaries arc interfering with the tool response. However in practice pressure gauge resolution will limit the ability to discriminate between late-time straight lines on radial and spherical plots. Under favourable circumstances however such features may actually be observed and interpreted in terms of apparent bed thickness. A numerical example of this technique is presented under III-5.2.b (Field example).

The procedure is based on the simultaneous observation of build-up on both a spherical and a cylindrical time function plot: At early times the spherical plot is linear and the cylindrical plot concave downwards (see Figs. III-10 and 111-g). At

RFT essentials of pressure test interpretation

late times the cylindrical plot is linear and the spherical plot concave upwards. The linear portion of the spherical plot extrapolates to a lower pressure than the linear portion of the cylindrical plot. Both plots have to be examined to see whether they present the characteristic behaviour as shown on Figs. III-10 and III.8 since it is easy otherwise to confuse the late stage of a true spherical build-up with a straight line on a Homer-type plot, as has often been done in the past. Radial-cylindrical (Homer-type) flow can only be presumed when both plots have the requisite characteristic shape.

The slope of the early-time straight portion of the spherical plot is found and multiplied by 1.03 (to correct for quasi-spherical behaviour). The spherical permeability can then be calculated in the usual way (Equ. 4.1.2.), the extrapolation of this straight line gives p*. the extrapolation of the linear portion of the cylindrical plot gives pi, its slope can be interpreted in terms of k,h. (see Fig. III 12).

If we assume for the moment that the anisotropy A = k& is known then we can solve in principle for the three unknowns h, k,, k, by using the three equations :

h = 1.2 ( 4rr (p- -=& k,wc) “3 (4.7.1)

kh = 2687 %! m

(4.1.3)

where V = q, T, + qr Tz

Analytical and numerical analyses have also led to a relationship between the time of the observed build-up change t* and the distance of the boundaries. The corresponding equation is:

h = (As)“z (0.02956 - 0.007378 $) (4.7.2)

where A t* = t* - T (T = flowing time)

Actually these equations are not independent and it is impossible to solve for k, k, and k, when A is unknown (or for A, k, and k, when h is unknown). Information from other logs (h) or core analysis (A) must be used to solve for this.

42

III. Interpretation

Thus a value of c h B may be derived from either the the well bore i.e. water and oil (exceptions are pressure match (eq. 4.7.1.) or time match (eq. 4.7.2) water-zones, and oil-zones if drilled with oil-base and compared with the permeability thickness mud). In the case of the pretest very little fluid is

FIG. III-12 : Typical spherical plot and the different time domains

product derived from (4.2.1.), provided and independent estimate of anisotropy is available. Comparison of the different CC h>> values allows verification of the consistency of the data. Such an approach can give interesting results when permeabilities are favourable (up to a few millidarcies with the present RFT design) and support from other sources (logs, cores) is available.

withdrawn and no perceptible change in the saturation profile will result.

Hence the following simplified model may be adopted :

- Only water is mobile in the invaded zone with Q = k. kyw where k’& is the relative permeability to water at S,, (typlcally around 0.3 in a water-wet rock).

4.8. Iufluence of the invaded zone

So far tbe analysis of the pressure build-up has been based on single-phase flow theory. In practice there are often two mobile fluids present in the vicinity of

- In the non-invaded zone only oil is mobile with k: = k.Qo where kFo is the relative permeability to oil at connate water saturation (close to 1). Note that it is only these end-point permeabilities which may be detected with the RFI (see Fig. 111-6).

43

This model was studied using a two-dimensional finite-element numerical simulation. The results of this study are detailed in Ref. 1 and have shown that almost identical spherical build-ups can arise from either the effect of impermeable boundaries or due to radial discontinuity with the invaded zone having a higher mobility than the non invaded zone (provided the build-up has a radius of influence larger than the radius of the invaded zone).

Thus the familiar problem of non-uniqueness arises in which the observed response can be attributed to more than one possible cause. Therefore the depth of invasion must be determined separately to see if any observed change in slope can be ascribed to composite fluid behaviour. If the deviations cannot be explained on this basis, then the presence of impermeable streaks may be considered. Thus it is possible to consider the detection of barriers only if one the following conditions applies:

1) The test has been run in a water zone,

2) The test has been run in an oil zone and oil-base mud has been used,

3) The depth of filtrate invasion is greater than the radius of influence in water,

4) The mobility in the invaded zone is close to the mobility in the virgin reservoir,

5) The depth of invasion is small and the whole build-up essentially occurs in the non-invaded zone.

III-5 SPECIFIC PROBLEMS ASSOCIATED WITH RFT RESPONSE

5.1. Relationship between sand-face water pressures measured by the RFT and phase pressure in a virgin reservoir

In an oil or gas reservoir drilled with mud, the fluid in the vicinity of the well-bore consists of two phases, mud filtrate and oil or gas. Their pressures are different because of capillary pressure effects and therefore it is important to assess exactly what is measured by the RFT. In a homogeneous water-wet reservoir with an oil-water contact the variation of

Rm essentials of pressure test interpretation

saturation and phase pressure from the water zone through the capillary transition zone into the oil is as shown in Fig. 111-13. In the transition zone the phase pressure difference is given by the capillary pressure which is a function of the wetting phase saturation :

P, = P, - P, = P, (SW)

which at hydrostatic equilibrium :

where : P, (SW) = Ap g h

Ap = pw - p. (pw and p0 being the phase densities) h = vertical height above free water level (FWL)

Note here that generally the free water level is not coincident with the oil-water contact. The OWC corresponds to the depth at which the oil saturation starts to increase from zero. The FWL is the depth at which the capillary pressure is zero. The OWC lies above the FWL by an amount depending on the capillary pressure, which in turn depends on formation parameters such as grain size, permeability, etc.

Provided the phase is continuous, the pressures in the respective phases are given by:

PO = P- - P&h Pw = P- - pwgh

On a depth-pressure diagram the intersection of the continuous phase pressure lines occurs at the free water level as shown in Fig. 111-13. In the water zone and in the oil zone, only the respective phase pressure (water or oil) is relevant. In the transition zone, both phase pressures need to be considered together.

In the oil zone the fluid loss from the mud causes an influx of water into the formation which displaces oil radially outwards. The coresponding near well-bore saturation distribution is illustrated in Fig. 111-14. The shape of this saturation profile changes with time and is determined by:

- Mud loss characteristics (e.g. overpressure and mud cake properties).

- Capillary imbibition of water into the formation. - Gravity drainage of filtrate.

To understand the problem it is important to realize that the aqueous phase is not in hydrostatic

FIG. III-13 : Pressure gradients around the water-oil contact.

equilibrium but is flowing under the influence of capillary, gravitational and viscous forces.

To demonstrate that in the oil zone the RFT measures the undisturbed formation oil pressure, pOf, a model is considered where the vertical permeability is assumed to be zero. Also it is proposed that the filtrate influx is radial and the oil displacement process is governed by viscous and capillary pressure forces. The mechanics of such an invasion process depend on the injection rate, fluid viscosities, formation permeability, relative permeability and imbibition capillary pressure as illustrated for a water-wet reservoir in Fig. 111.15.

Ideally, where capillary pressure is negligible and the mobility ratio is favourable the saturation profile follows the dotted line as in Fig. 111.14. However, in practice, there exists a continuous water saturation profile in which SW changes from 1 - Sor in the swept zone, where the oil has been left trapped as a residual discontinuous phase, to Swc, the virgin formation saturation. The corresponding pressure

profile for the case of low displacement rate is also illustrated in Fig. III-14. Since the oil displacement rate is low, the oil phase is virtually at uniform pressure, pO. equal to pOf.

It can be seen that as the water saturation approaches 1 - Sor in the swept zone the water phase pressure becomes indistinguishable from the oil phase pressure. Hence the water phase pressure at the sandface, p+ which is measured by the RFT, is identical to the oil phase pressure in the reservoir, pOf. This analysis applies both to the oil zone and to the capillary transition zone, providing the oil phase is continuous. Hence the RFI pressure data in the transition zone will follow the oil gradient line.

Another model can now be considered, in which the capillary pressure is negligible and in which there is a sharp interface between the invaded water and the oil, caused by filtrate in the formation slumping downwards under the influence of what is known as gravity drainage, as illustrated in Fig. 111.16. Its extent depends on the vertical permeability and on

45

FIG. 111-14: Saturation and pressure profiles during filtrate invasion.

the phase density difference p,,, - p,,. (This drainage is continuous unless interrupted by an impermeable barrier). In the reservoir, the oil phase is at hydrostatic equilibrium :

& = p. - p. g D = constant

where :

& = oil phase potential D = vertical depth measured from any reference

the water phase potential is written as:

Vw = pw - ~w g D

(which exhibits a downward flow vertical gradient). At any depth the pressure in the two phases must be equal since capillary pressure is assumed negligible. Considering the two levels as in Fig. 111-16, it follows that :

p’ = p1 Y 0 pz = pz Y 0 P: - pi = pZ - pf = PO gAD (since the oil column is static)

The potential difference AI$ in the water phase is given by:

AQ=V’-$=p&&+pPwgAD=(p,-pp,)gAD

46

III. Interpretation

I +. FIG. III-15 : Relative permeability and capillary pressure functions.

Thus :

$I’ - $ = ApADg

This driving force sustains the drainage of water downwards. The flux is determined by AQ. the water viscosity and the vertical permeability. The important point is that the water phase is not at hydrostatic equilibrium (g - & = p,,,gAD). The pressure and its gradient measured in the flowing water column are equal to those in the adjacent static oil column, and therefore the sand-face pressure measured by the RR will be equal to the static oil pressure.

Capillary pressure effects may have to be examined more closely when dealing with water-gas contacts (large vettability contrast) and low permeabilities. This is under investigation. In more general terms, the RFT pressure is equal to the pressure of the continuous fluid phase in the undisturbed region of

the formation. This statement applies to oil or water-wet reservoirs, as we11 as to transition zones created by capillary forces above water contacts. The only exception is when the formation pressure is supercharged due to mud filtrate influx.

5.2. supercharging

a. Theory

As a consequence of mud filtrate invasion in the immediate vicinity of the well-bore, the formation may exhibit pressures higher than the actual formation pressure. This is known as supercharging. This effect should not be confused with intrinsic formation overpressures.

When the well is drilled, all permeable zones are locally overpressured by the invading filtrate ; this overpressure dissipates when the mud cake is built, and invasion becomes negligible. However, in low permeability formations this overpressure still exists at the time of the RFT measurement.

RG. 111-16: Gravity drainage of filtrate.

47

The presence of supercharging in a zone may help predict future production problems in heterogeneous formations.

There are three kinds of mud filtrate invasion ; the initial spurt loss leading to a rapid build-up of mudcake ; the dynamic filtration which occurs when the mud cake attains an equilibrium thickness, and the static filtration which takes place after circulation of the mud has stopped. Ferguson and Klotz studied mud loss in an oil well model. Typical results of these tests are presented in Fig. III-17 for the dynamic filtration and Fig. III-18 for the static filtration. The static filtration rate for the mud is given by:

0.217 ’ = (AtI + 15.5)1’2

where :

q = Ruid loss in cc/min/lOO cm*

RFT essentials of pressure test interpretation

At, = time from termination of circulation - hrs

Note that the standard API filter loss test is not representative of down-hole conditions and cannot be used to predict filtration rates in the well.

Following the observations of Ferguson and Klotz, the supercharging effect can be adequately modelled assuming constant influx rates of both dynamic and static filtration. From the analytical solution of the diffusivity equation, the amount of excess pressure, Ap’, can be determined.

Using the principle of superposition, the excess pressure at a time At, after circulation is stopped, is given by:

Ap1 = 44.62

k + log At, - 3.23 + log 2 %.G~; >

where :

Ap’ = excess pressure - in psi q,., = equilibrium dynamic filtration rate in

q,,* = equilibrium static liltration rate in cdminlcm k, = radial permeability in md P = fluid viscosity in cp C, = total compressibility in psi-’ Lv = well bore radius in ft T,,, = duration of circulation in hrs At, = time after circulation is stopped - in hrs

The above equation is based on single-phase flow in an infinite reservoir.

An example of supercharging in a typical case is given below :

q,,, = 0.066 cdmin/cm ql,* = 0.033 cc/min/cm

These influx rates correspond to double those given by Ferguson and Klotz since their data was taken at 75O F, whereas at a more realistic reservoir temperature of 150” F the viscosity of water is approximately half that at 7S’ F.

k, = 0.34 md

FIG. III-17 FIG. III-18.: Mud fluid loss.

48

III. Interpretation

*w = 0.34 ft At, = 14 hn TI,, = 20 hrs $I = 0.12

For these parameter values, the overpressure derived from the above equation is:

Ap’ = 14.2 psi

In this case the supercharging is already quite significant. It can become much more important if the permeability is low and filtration rates are high.

The variation of excess pressure, Ap’, with formation permeability and mud static filtration rate (on a per unit basis) is illustrated in Fig. III-19 which refers to an 8-inch borehole, assuming a 12-hour dynamic filtration followed by 12-hour static filtration at half the dynamic rate.

FIG. III-19 : Excess pressure due to filtrate influx into an infinite reservoir.

It is apparent that the excess pressure Ap’ depends on both formation permeability and filtration rate.

Since the overpressure, Ap’, varies with time. build-up plots which reflect the sum Ap’ + P, (the

dynamic pressure change associated with spherical build-up), will in principle be influenced by mud filtrate invasion.

The variation of Ap’ with time is given approximately by:

d (API) ~ = 44.62 y + & in Psi/hr dt I 1

For the same parameter values given above, this corresponds to 0.0016 psi/min which is quite insignificant and could not be detected on a build-up plot.

For comparison, the rate of increase of the probe pressure in the absence of supercharging, for a single rate drawdown is given by:

d (p,) 8 x lo4 w (‘WY” L

dt k3” 2

Taking typical values of these parameters for a pretest in a 0.34 md formation (q = Icc/sec, p = 0.7

FIG. 111.20: Effect of supercharging on spherical build-up.

49

cp, Ct = 33X l@psi?, k = 0.34 md, t = 50 set, T = 20 set), this gives a pressure buildup rate of 117 psilmin.

Hence the effect of supercharging on build-up is simply to increase the pressure by a iixed amount, Ap’, and the slope of the build-up plot is not altered. This is illustrated in Fig. 111-20. Supercharging therefore does not affect permeability estimation from build-up plots.

b. Field Example

An example of supercharging effect is shown in Fig. 111-21, where a series of tests were taken in a gas reservoir. The data points lie on a straight line except for points A and B. The gradient of 0.453 psi/m or 0.138 psi/ft corresponds to an in-situ gas density of 0.319 p/cc. Test A at 3626 m shows an overpressure of 28 psi registered after a build-up of 12 minutes duration, indicating a very low permeability at this point (less than lC+ md).

RFf essentials of px?sswe test i”terpretati0”

permeability analysis ; however, the observed overpressure is certainly associated with a layer of extremely low permeability and supercharging is the obvious explanation for this anomaly. The open-hole logs indicated that the location of test A corresponded to a shaly streak.

Test B shows an overpressure of about 10 psi and the build-up took approximately 2 minutes to stabilize. The spherical plot of this build-up is shown in Fig. III-22a, with a slope of 123 psilsec’” giving a spherical permeability, k, of 0.17 md. The late time data fall on a straight line on a radial cylindrical plot, with a slope of 46.6 psiilog cycle giving a radial permeability-thickness product of krh of 0.4 md-ft.

FIG. III-22 a: Field example test B. Spherical plot showing probable presence of an impermeable bed boundary.

From Fig. III-22a the late time deviation from spherical behaviour commences at about At* = 30 set (i.e. t = 50 sex), and the extrapolated pressure p* is 8 psi less than the static pressure pi. The thickness, h, from the pressure match equation:

V. A I

l/3 h = 1.2

4n (pi - p*) oc, (4.7.1)

with A = k,/k, = formation anisotropy

is 2.4 ft assummg A = 1, whIe the corresponding value of h from the time match equation:

FIG. 111-21: Field example supercharging effect on a pressure versus depth plot.

h = [+!?k]“‘( 0.02956 - 0.007378 5) (4.7.2)

The pretest pressure response at A indicated the presence of gas in the tool, which precludes a proper

is 3.6 ft. Taking for h an average value of 2.8 ft, the radial permeability corresponding to the krh product of 0.4 md-ft derived from the cylindrical plot of Fig. III-22b is k, = 0.14 md. Since A = kJk, has been assumed equal to unity in this case the spherical and

50

62&a

t

1.

F’IG. 111-2.2 b : Test B - Radial cylindrical plot of late time data.

radial permeabilities should be equal. Hence the four methods of interpretation (III,, m,,, pi-p*, and At’) are reasonably consistent.

However if the formation is highly anisotropic e.g. A = 0.01, the values of h from the pressure and time match equations are 0.51 ft and 0.68 ft respectively. Taking 0.59 fi as an average, the radial permeability is now 0.68 md, whereas the value of k, from k, = k, .A’” is 0.79 md. The results are still consistent, but the formation has a much higher horizontal permeability. The important point is that the RFI cannot in itself resolve the question of anisotropy, and it should be emphasized that spherical permeabilities are, in general, considerably less than radial permeabilities.

The observed overpressure is associated with low permeability rock. Of the 37 tests, (in addition to B) three allowed a permeability calculation from build-up slope; the pressure and permeability (drawdown and bluid-up) data for all tests is given in Table III-I. The three build-ups, each of approximately 30 sec. duration, gave permeabilities of 0.96 md, 1.23 md and 0.61 md respectively, and none of these three tests showed any evidence of overpressure.

Thus it may be concluded that in this well supercharging will not become signihcant at spherical permeabilities above 0.5 md. This threshold value is fairly typical for a large number of analysed field data. Notable exceptions have been observed in wells drilled with oilbase mud where build-up with up to 12

III. Interpretation

minutes (k, = 0.03 md) duration did not exhibit any overpressure. The important point is that the spherical build-up plot becomes the diagnostic tool for determining the possible occurrence of overpressure. Pressure tests exhibiting very low spherical permeabilities may be in error due to supercharging.

Also included in Table I are the drawdown permeabilities computed from the equation :

k,=5660% b

(3.1.3)

for both flow periods (denoted kt and kz respectively). It can be seen that the average drawdown permeability is consistently higher than that from the build-up by a factor of 5 to 12, implying a negative spherical skin factor, indicating that the formation may be slightly fractured as the probe enters the formation.

5.3. Afterliow

a. Theory

The compressibility of the volume of fluid contained in the portion of the tool flowline system ccmummicating with the formation e.g. connecting lines, pressure gauge bellows and pretest chambers, has an important effect on the dynamics of the Rm pretest response. When the second pretest piston stops, fluid flow from the formation persists in order to sustain the compression of fluid up to reservoir pressure. This is known as afterflow. It causes the pressure build-up response at early time to be anomalous, falling considerably below the later straight line section of a spherical plot. The effect of the aftetiow is illustrated in Fig. 111-23, where the idealized flowrate schedule based on the piston displacement, denoted q, is compared to the actual sandface flowrate, q,, at the probe. Note that q. always lags behind q.

An analysis of the dynamics associated with the capacity of the RFI fluid system gives a quantitative estimate of the duration of the afterilow, based on a very simple model. A time constant, is defined, such that :

T= 1170 v (2C + S,) v, c,

k’P

51

RFT essentials of pressure test interpretation

VERTICAL RESERVOIR PERMiABILIlY FRL)ll DEPTH PRESSURE DRAWDOWN

0 P k k i k i 1 2 1.2 5

(ml (psi) (md) (md) hd) (md)

3484 6236 3488 6236 3492 6238 3497 6241 3505 6242 3508 6245 3515 6247 3521 6251 3527 6252 3532 6255 3537 6257 3542 6260 3547 6263 3550.5 6265 3554.5 6266 3559 6267 3564 6270 3568 6272 3570 6276 3580 6276 3585 6279 3589.5 6282 3593 6284 3596.5 6286 3601 6286 3606 6289 3615.5 6292 3619 6295 3623 6297 3626 A 6327' 3630 6300 3635.5 6303 3640.5 6304 3644 6306 3652 6311 3653.5 6312 3656 B 6320'

10.6 9.2

1::: 7.7

10.9 GAS GAS

23.8 GAS

9.9 GAS GAS

2.7 3.4

56:: 29.3 25.4 12.8 UNSATISFACTORY UNSATISFACTORY 21.3 24.4

i:: 4.5 5.3 GAS

13.0 10.5 20.1 23.0 12.6 17.9

3::: 3:::

19:9 i-i

3.5

1::: GAS

12.5 13.5 UNSATISFACTORY

5z.i 3.3

23:3 43.0 28.9

45.7 2.4 2.6

23.8

9.9

3.1 6.7 5.2

52-I 19.1

DRAWDOWN DMWDOWN

22.9 4.7 5.8

11.8 21.0 15.3 4.4

31.5

63:: 19.7

13.0 DRAWDOWN

5:-z 26:1 45.7

2.5

0.96 1.23

0.61

0.17

Arithmetic Average Drawdown Permeability = 16 md.

TABLE III-I: Comparison of drawdown permeabilities and build-up pxmeabilities.

52

Ct = compressibility of the fluid V, = total volume withdrawn

(flowline + chambers)

‘P = probe radius C = flowshape factor S, = skin factor

For the standard RFI probe without skin effect this becomes :

T = 5660 p V,CJ(k,rJ

The product of system volume and compressibility, V,CI, is known as the storage constant, Cs.

P, - P, = (P, - P,“) - (T+)

where p, = pp at t = to, and the afterflow is given by the equation :

-2% q=$e T

where : At = t - P, and Q = spat t = P

Also : $= h, cl4 - Pzl

1170 p (2C + S,)

The above equation shows that after&w will decline

III. Interpretation

exponentially with the time constant t as defined above.

In order to have an idea of the dynamics of afteriIow, it is useful to consider some typical values for the parameters in the expression of the time constant. For a pretest the volnme V, of fluid within the RFI system is 60 cc, i.e. pretest chambers plus flowlines. Using the standard probe proportionality constant of 5f560 and k = 0.5 cp, C, = 3 lp as fluid characteristics, we get :

0.509

k

After&w can be considered to have decayed to a negligible amount after eight time constants. Therefore the duration of the after&xv can be written as : Taft = 4/k. For a permeability of 1 md, the expected afterflow duration is then 4 sec. This figure gives an estimate of the minimum shut-in time required before a spherical plot becomes linear.

Note that when a quartz gauge is used, the active volume within the system is increased to 110 cc.

The above analysis is based on the assumption that the system is liquid-filled and that the compressibility could be taken as that of filtrate. A small quantity of gas in the system will appreciably increase the time constant since the effective compressibility is increased. Hence the beginning of the straight line on spherical plot will occur later if gas is trapped in the system.

b. Presence of gar in the system

When the pretest flow system is completely filled with water, i.e. CI = 3X1@ psi-‘, afterflow is not a serious problem. However, if gas is trapped in the active volume, the overall system compressibility V,C, (V,C, = V,C, + V&a for a liquid-gas mixture) increases considerably since gas compressibility C, is high. In this event afterflow will be of much longer duration, and care must be taken in choosing the straight line section of a spherical build-up plot for permeability analysis.

The best indication of the presence of gas is the shape of the drawdown response which is also influenced by storage effects. If the drawdown does not exhibit rapid attainment of the steady-state condition, then gas is probably present and the ensuing build-up will also suffer from prolonged afterflow. The influence

53

of system storage on drawdown is illustrated in Fig. III-23 where the probe flowrate is shown to lag behind the piston displacement rate, due to the expansion of the fluid in the active volume when the pressure is falling. The time needed for the drawdown pressure drop to reach steady-state condition will be controlled by this process. The volume of fluid in the sampling system is greater than that contained in the small region of formation around the probe over with the steady-state formation pressure drop occurs. Hence the drawdown pressure drop should reach the steady-state after a period of 8 r since the difference between the probe flowrate and the piston displacement has the same dynamics as afterflow.

If the drawdown pressure drop does not reach the steady-state in a period of less than 8 T, (z calculated using water compressibility), then gas is probably present in the system. Note that since the first piston is in motion for twice as long as the second, there is a better chance of attaining steady-state condition daring the lint drawdown period. Conversely, if the permeability based on the second drawdown is larger than that calculated from the first drawdown, then steady-state may not have been reached. However, formation cleanup would also result in the second drawdown permeability being greater than the first. Therefore great attention should be paid to the nature of the drawdown beheviour before a build-up is analysed for permeability.

RFT essentials of pressure test interpretation

III-6 QUICKLOOK INTERPRETATION FROM BUILD-UP

6.1. Determination of Quicklook Permeability

As an alternative to a fall analysis of the build-up on a spherical plot, the overall time taken for the pressure to stabilize may be used as a << quicklook B permeability indicator. This quantity is synonymous with the duration of observable build-up, denoted Tab, as illustrated in Fig. 111-24. For a single-rate drawdown of flow period T, the concept of observable build-up is given by the equation :

1 1 dp k”*

vm c 8 x 1Oa w (U&)“*

(6.1.1)

where Sp is the pressure gauge resolution. The actual duration of observable build-up for a particular pretest may be estimated from the digital pressure record; a convenient definition of Tab is the time measured from the initiation of first piston motion until the shut-in pressure p. attains the value pi-6p, where pi is the final stabilized value. Fig. III-25 illustrates the determination of Tab.

FIG. 111.24: The concept of the duration of observable build-up on a single-rate spherical plot.

F’IG. 111-2.5: Determination of the actual duration of observable build-up Tab from a pressure - Time record.

54

The << quicklook >x permeability computed from the estimation of Tab is denoted $ in order to distinguish it from k, derived from the slope of a spherical build-up plot. Solving for & the equation for a standard pretest becomes:

& = [8 x 1W qv (@&J1” ] 2’3

Note here that a single drawdown formula is used for l& This hypothesis is validated since in low permeability tests where the above method applies, the drawdown rate is controlled by the permeability of the formation near the probe and not by the piston displacement.

In this equation, q is taken as V,K*, and T as Tz + Tt. For the following typical parameter values:

I$=025 T2+T,=20sec C, = 3 X l@ psi-’

w = 0.5 Cp q = 1 cc/xc dp = 1 psi

the relation between Tab and & is given in Table 111-2.

Obviously Tab cannot be measured with the same precision as the build-up slope, m,, and hence the quicklook permeability is subject to some uncertainty. However, the build-up duration, Tab. is evident from the pretest pressure record and it is fairly easy to determine when Tab has been reached while monitoring the test.

The excess pressure due to supercharging, Ap’, is inversely proportional to the permeability. The values of this reciprocal permeability, Ilk,, are also given in Table III-Z. A plot of 14 against T ob as illustrated in Fig. 111-26, shows that the degree of supercharging is directly proportional to the duration of the observable build-up, To,,. Hence Tab turns out to be an excellent criterion on which to assess the probability of a particular pretest being supercharged. The reciprocal permeability, l%, is referred to as the supercharg- ing index, SI. It is rare for supercharging to be observed at values of SI less than 3 corresponding to Tab of less than 2 minutes.

The linear relation between lk and Tab which is illustrated in Fig. III-26 has the form:

1 - = 0.0256 T,, - 0.3 iz

However, for values of Tab greater than 100 sen, the approximate relation :

In. Interpretation

is sufficiently accurate and particularly useful for obtaining rapid estimates of spherical permeability or supercharging index from Tab. For build-ups longer than 2 minutes, Tab is inversely proportional to &.

FIG. 111-26: Supercharging index, l/1;,, as a function of observable build-up time, Tab, for a standard pretest.

TOb

(set) (ml) bl&

30 2.20 0.45

60 0.80 1.26

120 0.36 2.80

180 0.23 4.34

240 0.17 5.87

360 0.11 8.94

600 0.066 15.07

TABLE III-Z: Relation between the duration of observable build-up, Toh, and spherical permeability, &, for a standard pretest with a gauge of 1 psi resolution.

55

When quicklook build-up permeabilities, based on T ob estimates, are compared with the corresponding values derived from the slope of a spherical plot, it is found that in most pretests & is approximately twice the value of $, i.e. :

Hence the quicklook formuIa appears to overpredict the permeability by a factor of 2 when the standard strain gauge (1 psi resolution) is used. The difference will be smaller for gauges with better resolution.

For build-ups longer than 2 minutes, the terminal pressure recorded is frequently on the order of 1 psi less than the true formation pressure, pi extrapolated on a spherical plot. Hence the observable build-up time measured directly on the chart corresponds to a 6p of around 2 psi rather than equal to the gauge resolution of 1 psi. The correction factor of 2 given above allows for this discrepancy and is based on a survey of many pretests in which both & and k, were measured.

On this basis a quicklook estimate of the build-up slope spherical permeability, h, may be obtained for a standard pretest from the approximate equation :

k,=$ (6.1.4) Ob

Suffice it to say that application of Eqn. 6.1-3 or Eqn. 6.1-4 (or of a relation with a different constant of proportionality) will depend on the resolution of the particular gauge in use and on how well Tab is <<picked, from the pressure recording.

This is illustrated in 6.3 with a field example.

6.2. Quicklook permeability from build-up in limited drawdown tests

In the case -of a standard pretest the quicklook formula for k, in terms of Tab is eqn. 6-l-2.

In the case of a pretest, where the flowrate is determined by the formation deliverability rather than the piston movement, the quicklook formula

RFT essentials of pressure test interpretation

requires Tz = Tf and q = V,Rf where Tf is the chamber fill-up time. In this event both Tf and Tab must be obtained from the pressure record, as illustrated in Fig. 111-25. The quicklook perme- ability now becomes :

In most common pretests Tz is essentially constant and there is a unique relation between permeability, ic, and Tab. However, with limited drawdown rate, the quicklook permeability depends on both Tab and Tf. Since pretests which exhibit significant supercharging are often also of the limited drawdown rate type, it is important to use the correct equation for &. Incidentally this is also the main reason for adopting a quicklook formula based on an average drawdown rate. If some of the pretests show limited rate behaviour, only the reciprocal permeability l&, should be employed as the supercharging quality control parameter.

In order to appreciate the extent of the possible supercharging, the following approximate relation has been derived from examination of a limited number of supercharged pretests.

lip’ = 4SI = * = f k s

It should be emphasized that this equation only gives an order of magnitude estimate of Ap’. The actual value of the proportionality constant depends on the particular mud-fluid loss character- istics and other factors.

6.3. Field example

A typical pressure record for a standard pretest is shown in Fig. 111-27, with a final pressure of 2028 psi. Following the practical definition of the observabIe build-up duration, To,, is read as 210 sec. It is clearly seen from the digital recording that for times longer than 210 set the gauge resolution prevents the build-up from being

56

III. Interpretation

FIG. 111-27: Field example - Determination of the quicklook permeability &.

observed. The quicklook permeability for Toh = 210 set is:

& = 0.2 md

based on:

p = 0.5 cp, @ = 0.25, T, = 19.7 set and Ct = 3 x lo-6 ps-1.

The spherical build-up plot of this test was made for T1 = 14.5 set and T2 = 19.7 set, both values being read from the record. The build-up exhibits a classic straight line response of slope - 493.6 psi/s.@ giving spherical permeability of:

k, = 0.105 md

Thus the quicklook permeability, k,, is very nearly double the permeability, k,, determined from the build-up slope. The final, stabilized, extrapolated pressure on the plot is 2028.4 psi whereas the terminal value on the log is around 2027.5 psi. This difference together with the subjective nature of choosing Tab. accounts for the discrepancy. However, it is worth noting that this factor of two is obtained in many similar pretests (low drawdown rate). This tends to show that the quicklook permeability is a meaningful quantity, which has the advantage of being easily computed from rapid examination of the build-up profile.

57

IV. RFT WITH CSU

IV. RFT WITH CSU

Many advantages can be offered by the application of the Cyber Service Unit* to oil field technology. The RFT also takes part in this through the introduction of sofhvare which enables the user to make easier and more accurate analyses of pressure or sample formation tests, either in real time or in playback mode at the well-site.

1) The RFT “Quicklook” program processes the RFT field data tape. Outputs include:

- Build-up plots

- Build-up slope computations

- Extrapolated pressure determination

- Permeability computations (drawdown and build-up)

- Test summaries.

A playback of a pressure test is given in Fig. IV-l. The playback pressure outputs from the field data tape are presented both in analog and digital formats with numerical display. The numbers correspond to the pressure value at the line touching the top edge of the figures. Pressure from the high precision quartz gauge is presented on the third track in a similar way to the strain gauge pressure, except that the pressure value has hvo decimal figures which are in correspondence with the digital pressure output. The numerical

* Mark of Schlumberger.

FIG. IV-l : Playback of an RFT test using the CSU RFT Quicklook program.

elapsed time output is also displayed in addition to the pressure outputs. A blown-up profile, as shown in Fig. IV-2 may give a better idea of what

61

XlYIi ETIM YlXli SBP

Xf”W IDEll YFWI *Drn

FIG. IV-2 : Pressure versus time plot using the CSU RFT Quicklook pmgram.

is happening during the pretest. The sequence from the setting of the packer until the build-up is reached, as mentioned earlier in chapter II-l, can thus be seen clearly.

Build-up plots of pressure against a Homer time function (HTF) or against a Spherical time function (STF’) may be generated. These plots can

351111.

3000.

2500.

FIG. IV-3: Spherical plot produced with the CSU.

FIG. IV-5: CSU build-up sunmnry Spherical plot.

FIG. IV-6: CSU build-up summary Homer plot.

be used to verify the quality of a test and to assist in the best determination of build-up slope and final build-up pressure. Fig. IV-3 shows the spherical build-up plot of the data from Fig. IV-I.

The cylindrical or Homer time function plot of the same data is given in Fig. W-4. A straight line can

62

IV. RFT with csu

be overlain on the build-up plot for accurate slope determination.

Finally, build-up summaries of both spherical and cylindrical build-up plots can be obtained on the same film. Examples of these build-up summaries are given in Figs. IV-5 and IV-6.

2) The RFT “Real Time” program makes it possible to better monitor the test while it is being

NAME DESCRIPTION

HTF Homer Time Function HPGD HP Gauge Digital Pressure

LORD Line Ordinate LABS Line Abscissa LSLO Line Slope

LLPL Line Left Plot Limit LRPL Line Right Plot Limit LTPL Line Top Plot Limit LBPL Line Bottom Plot Limit

FTN Formation Test Number TSI Test Sample Identifier MTD Measured Test Depth BTFS Build-upTime Plot

(Homer or Spherical) OGS Oil or Gas Selection PGS Pressure Gauge Select

TFI $%$r%z?on Time CFF Compressibility of Formation Fluid FFV Formation Fluid Viscosity PHI Porosity C2V Chamber 2 Volume PTP Pressure at TP Elapsed Time HPRE Hydrostatic Pressure FBS Final Build-up Slope FPRE Formation Pressure KD2 Permeability from Drawdown KIB Permeability from Build-up KTP Permeability Thickness Product

SGP Strain Gauge Pressure PONE Pressure L’s Digit FHPG Fractional Pressure HP Gauge

performed. The objective is to generate the time function (cylindrical or spherical) and the build-up plot in real time, so as to facilitate the decision of whether to continue testing or not. Indeed, there would be no need to keep testing when the Homer region of a cylindrical plot has been reached, and rig time can be saved if it can be decided that all the requested parameters can be derived from the data already acquired.

However valid pretests take only a small amount of time (a few minutes at most) and little, if any time can be saved by stopping the build-up prematurely. As a rule, pretests should not be stopped before the pressure has reached a stabilized value unless the build-up time exeeds time limits set from supercharging or safety considerations.

FIG. IV-7: Real time CSU presentation of RR data.

FIG. IV-9~. FIG. IV-S: Real time spherical plot produced on CSU

c

L , / 6.8%) I I I .I

FIG. IV-9 a. FIG. IV-9d.

Better use of the real time plotting may be made during sample tests when large volumes of formation fluids are withdrawn and system storage becomes significant.

This program automatically determines the beginning and the end of the flow period, then computes at each time step the value of the selected time-function. The plot thus generated can be automatically and repetitively c< blown up )> so as to provide larger scale readings when times become too much compressed on a *Homer >) or spherical scale.

Fig. IV-7 shows an example of an RFT recorded FIG. IV-9b.

64

IV. RFT with csu

with the strain gauge. The corresponding real-time obtained, also in real time, each successive plot spherical plot is represented in Fig. W-8. being a x5 magnification of the last fifth of the Optionally, four build-up plots could have been plot, as shown in Fig. W-9, IV-9a, b, c, d.

65

V. SPECIAL APPLICATIONS OF THE RFT

V. SPECIAL APPLICATIONS OF THE RFT

V-l RFT TESTING IN TIGHT RESERVOIRS

1.1. Statement of the problem

In low permeability reservoirs, the determination of fluid gradients will often be hampered by the effect of supercharging, which creates abnormally high sand-face pressures caused by mud filtrate influx during and after drilling.

Supercharging has been covered in Chapter 111-5. A theoretical analysis, corroborated by many field examples, shows that in the case in which the layer under test is unbounded in the radial direction (and can be considered as infinite-acting), the excess pressure A p’ due to supercharging is, in a first order of approximation, inversely proportional to the radial permeability of the layer. For a typical water-base mud, the proportionality constant is of the order of 4.5, and one may write:

Ap’ = 4.5/k,

Thus supercharging will be observed whenever the layer radial permeability is low enough for Ap’ to be higher than the gauge resolution, 6 p. When testing with a 1 psi resolution gauge, supercharging will affect the results when radial permeabilities are of the order of 4.5 md or less.

When testing in tight formations a series of tests will

have the appearance shown in Fig. V-l if plotted on a pressure-depth diagram. The circles represent

x

PRESSURE -

FIG. V-l : Supercharging rejection criterion.

pretests in good permeability zones where supercharging is negligible, but scattered to some extent because of errors in both pressure and depth. The crosses represent pretests in low permeability zones where supercharging causes the points to lie to the right of the gradient by an amount equal to Ap’. When using the RFI in a tight reservoir, a necessary step in finding the fluid gradient is the elimination of supercharged tests. This can be done using a pressure-depth diagram such as the one used in Fig. V-l

69

1.2. Conduct of an RFT job in a tight IWtZVOir

First, it is essential at the well-site to plot all data on a pressure-depth diagram as soon as it is obtained. This plot will be the basic document from which it will be decided whether or not enough tests have been made, and from which the gradients will be drawn once supercharged tests are rejected.

Second, it is advisable to label each point on the diagram (see Fig. V-2) with the corresponding value of the supercharged index, SI, which has been defined in Chapter III-6 as the reciprocal of the quicklook permeability 14. It has been shown how k, can be derived from the observable build-up time To,,, itself read directly from the pressure record.

One may write : SI = T,,,/ZO, and in reservoirs where there are enough tests in good permeability zones to categorically establish the fluid gradient, it is easy to spot supercharged tests as lying to the right of the uniform scatter band. In this way a cut-off value of SI (or Toh) may be determined, below which supercharging is negligible. Note however that this cut-off value depends on local conditions, particularly mud fluid loss characteristics.

Third, it is necessary to test as many zones as necessary for a reliable determination of the gradient. The objective is to try to obtain pretests in relatively high permeabilities (thus unaffected by supercharging) and which are sufficiently separated in depth so as to accurately define the fluid gradient.

The approach is to search for maximum permeability zones during the course of the survey. In that line of action, pretests which exhibit long build-up times are not useful since they are most likely supercharged. When this happens, it is better to terminate the test and to take a new one at about the same depth or elsewhere in an attempt to find good permeability zones, of course together with the help of open-hole logs.

In some cases it might be impossible, even after extensive searching, to obtain non-supercharged tests to allow an accurate definition of the fluid gradient. When this is the case, A p’ must be considered as an effective error in the determination of the true formation pressure pi, which is added to the experimental error associated with pressure

measurements. The points lying inside the uniform scatter band, if defined, will all be subject to some degree of supercharging, and the measured gradient

RFT essential.5 of pressure test interpretation

TVD

I

FW

FIG. V-2: Recommended procedure for fluid contacts determinations.

will lie somewhat to the right of the true fluid gradient because of this bias, as shown in Fig. V-l. In extreme cases, the determination of a fluid gradient, which is subject to errors in pressure measurements, in depth measurement, in the number and quality of the data points, and in the depth range over which data points are available, cannot be made with any XC”*aCy.

Good use may be made of a relationship such as A p’ = C/k, where the proportionality constant may be determined empirically (or taken as 4.5 as shown previously). Plotting the observed overpressure (measured from an assumed “best-fit” pressure gradient) against the inverse of permeability (from To,, or drawdown or build-up) one should observe a reasonably coherent straight-line relationship if the pressure gradient is chosen correctly (both in absolute value and in slope). Conversely a non-typical trend and/or a large scatter will result.

70

V. Special applications of the RFT

V-2 RFT TESTING IN NATURALLY FRACTURED RESERVOIRS

2.1. Generalities

The Repeat Formation Tester has important applications in naturally fractured reservoirs composed of a highly permeable fracture network and low permeability blocks whose average dimension is controlled by the fracture density. The fraction of the total porosity contained within the

MATRIX BLOCKS

5 -----_

> -----_

_) ------_

‘7 -----__

5 SW 1

s,

fracture system is small and open-hole logs respond to the fluids in the matrix blocks. However the reservoir produces the fluid(s) present in the fracture system and it frequently occurs that the fluid content of matrix and fractures are quite different. Hence logs may give an erroneous view of what the reservoir will actually produce.

In order to understand the complex production mechanism of a naturally fractured reservoir it is necessary to consider the original oil accumulation process. In many fractured reservoirs the matrix and fracture system are initially filled with water and oil

FlG. V-3: Diagramatic representation of saturation and pressure distributions in a naturally fractured reservoir.

71

RFT essentials of pressure test hlterpn?tation

migrates upward through the fracture system. The situation then arises where the matrix blocks containing water are surrounded by oil in the fracture system. Due to the density difference between the phases water is displaced from the blocks and is replaced by oil until a gravity-capillary equilibrium is reached as shown in Figure V-3. Since the matrix block originally contained water it is water-wet and the drainage capillary pressure curve is appropriate. This means that the lower portion of each block will remain saturated with water to a level which depends on the threshold capillary pressure and the density difference between oil and water. Above this level the oil saturation in the block increases upward and if the block is large enough the irreducible water saturation may be attained. The important point is that the logs will register this water held in each block by capillary forces but initially the reservoir will produce only the fluid in the fracture system, i.e. oil. Evidently the size of the blocks has an important effect on how much oil has accumulated in the reservoir. If the average block size is small very little oil will have migrated into the blocks and vice-versa. Blocks smaller than a certain critical size will contain no oil at all since the hydrostatic head over the block due to the density difference is less than the threshold displacement pressure. As a fractured reservoir is produced gas is liberated which migrates upward to form a secondary gas cap. Also water may enter the

fracture system either from aquifer expansion or water injection. Thus the GOC and OWC in the fracture system as well as the saturation in the blocks will change as the reservoir is produced. A detailed analysis (Ref. 2) has led to the conclusion that within each matrix block (if large enough for sufficient tests to be made) the RFI gradients will correspond to the mobile continuous phase within the block. However, the overall pressure gradient will be determined by the fluid in the fracture system e.g. :

- if oil is present in the fractures the overall gradient will correspond to the oil density as shown in Figure V-3, since at the base of each block the local water phase pressure is equal to the oil phase pressure in the fracture at that level.

- conversely, if water is present in the fractures a water gradient will be observed.

It is apparent that RFT pressure data can give much insight into the producing mechanism of fractured reservoirs. This capability may be enhanced by the analysis of the build-up response. The environment for this is favourable since most naturally fractured reservoirs have low permeability and pressure build-ups after pretest may be observed effectively. This analysis will primarily result in the determination of the matrix permeability using the techniques described under 111-4. This is not as easily

EQUIVALENT SPHERCAL SYSTEM

FIG. V-4 : Naturally fractured reservoir model.

72

V. Special applications of the RET

accessible from conventional well testing. Under favourable circumstances one other most important parameter may be derived: the size of the matrix block. This is discussed below.

2.2. Theoretical pressure response

It is possible to develop a simplified model of the pressure build-up response of the RFT in a naturally fractured reservoir, by making use of the constant pressure outer boundary analytical solution to the spherical diffusivity equation. Such a model assumes a matrix made up of parallelepiped blocks separated by the fracture network. In the context of the RFT pretest, it is sufficient to consider a single matrix block crossed by the borehole, surrounded by a constant pressure fracture system. It is assumed that the probe is set in the centre of the matrix block, and that the fracture network pressure remains undisturbed by the withdrawal of the pretest chamber fluid. It is also convenient to regard the matrix block as spherical in shape, since the analytical solution to this problem for a cubic block would require a complicated superposition in order to generate the constant pressure boundary condition.

Fig. V-4 shows the model envisaged, and the equivalent spherical system used to obtain the solution to the problem.

The build-up response was analyzed using the flowrate schedule in Fig V-5, where a single rate drawdown q of duration T was adopted. The results obtained are shown in Fig. V-6. One aft&low effects have died out, the pressure vs time diagram shows a straight line which reflects the infinite-acting behaviour of the matrix block. The slope m of this straight line is given by:

m = 7.999~104 qp (@p C,)‘” I ky psi. see-’

where k, is the matrix spherical equivalent permeability, which is related to vertical permeability k, and to horizontal permeability k, by:

k, = (k,. k,z)‘”

At shot-in time At* (corresponding to total elapsed time t*) the diagram starts to deviate from a straight line, and tends to level off to the fracture network

pi . . . . . . . . . . .._ . .._............................ -

PWSSURE YP*

L!r---

%s

!

F’IG. V-5 : Single flowrate schedule used for the naturally fractured reservoir model solution.

I

I LINEAR SPHERICAL

I BUILD-UP

I 7E”FL~

3

2 n i

f,(T,t)=&. +

FIG. V-6: Typical spherical build-up in a naturally fractured reservoir.

pressure pi. This levelling off is the effect of the constant boundary pressure condition existing in the fractures.

73

The straight line segment of slope m can be extrapolated to a pressure p*, which is higher than reservoir pressure pi. Both the shut-in time A t*, at which deviation from linear behaviour occurs, and the pressure difference, p’ -pi. reflect the radius of the spherical system envisaged, i.e. the average size hb (hb = 2r,) in which the RFI probe is set.

The next step, in order to quantify the determination of hb either by a pressure match (p* - pi) or by a time match (A t*) equation, is to develop suitable correlations for the above two quantities, as functions of hb under various sets of environmental conditions (namely T and q). The results, obtained in each case by least squares regression method, can be written as:

a. Pressure match

The average block size hb is given by the quadratic equation: (2301.9xD’) h,* + (C - 115.1 D) hb - 0.3 = 0, with

c= 4n @* - p,) UC, ‘/3

qT 1

p* = is the extrapolated pressure in psi pi = is the reservoir pressure in psi $I = is the matrix porosity (decimal fraction) C, = is the matrix fluid compressibility in psi’

FIG. V-7: Field example of a fractured reservoir.

4 = is the flow rate in CC/SW T = is the flow time in set

b. Time match

The average block size h, is given by the equation :

h, =

where At* is the shut-in time at which deviation from linear behaviour occurs, and where t* is the corresponding total elapsed time (t* = T + At*).

2.3. Field example

The test shown in Fig. V-7 was taken in a fractured reservoir, using one pretest chamber (qT = 10 cc) only. Fig. V-8 shows the spherical plot, where as

FIG. V-8: Field example of a fractured reservoir - Spherical build-up.

expected, deviation from a straight line build-up is obvious. Fig. V-9 is a magnified section of the late time build-up for this test, from which the slope is computed as :

m = 208 psi.sec-’

Relevant data for this test are:

= 0.5 cp il, = 0.3 C, = 3X10-6 psi-’ T = 12 set qT = 10 cc from which q = 0.833 cc&c

Using the formula:

k, is computed as:

k, = 0.23 md

Extrapolated pressure is read as: p* = 5930 PSI Meanwhile reservoir pressure is read as: pi = 5926 PSI

Coefficients C and D as defined above in 2-3 are computed as :

c = 0.017 D = O.OQO41

and the quadratic equation giving hb is: 0.00038 h,’ - 0.030 hh - 0.3 = 0

giving hg = 88 cm

FiG. V-9 : Field example of a fractured reservoir enlarged spherical plot.

V. Special applications of the RFI’

b. Time match

The elapsed time at which boundary effects start to show up is read as:

t* = 47 set, giving At* = 47 - 12 = 35 sec.

The time match formula defined in 2-3 above gives then :

The values of hp and 8 check reasonably well, considering the various uncertainties in the determination of all the parameters involved. Also it should be considered that the pressure match is essentially sensitive to the volume of the matrix block while the time match is sensitive to the distance from the constant pressure boundary. Both should strictly speaking only agree if the matrix block is actually a sphere with the probe set in the centre as postulated in the analytical solution.

Such a measurement is only of value if supported statistically. In this example s observed x best block sizes varied between 2 and 4 feet which corresponded to expectations. However, the limitations of this method to detect larger block sizes must be considered, as explained below.

2.4. A note on the limit of resolution of the method

Boundary effects will not be observed on a spherical build-up plot if the difference between the extrapolated pressure p* and the reservoir pressure pi is less than the gauge resolution (1 psi for the standard strain gauge). Therefore a block larger in size than a maximum limit will give a pretest response identical to that of an unbounded reservoir, because the build-up will be indistinguishable from an infinite-acting response.

The actual maximum measurable block size, h,, is an independent function of all the parameters proper to the test considered : v, @, etc. However, an order of magnitude can be obtained by making use of the matching equations in the test studied above in 2-4.

a. Pressure match

The value of hz is obtained by substitution of the

RET essediaIs of pressure test interpretation

value of the gauge resolution to the difference p* - Pi-

Setting p* - p1 = I psi, with all other parameters unchanged, gives :

k = 103 cm

b. Time match

The value of &, is obtained by assuming that the build-up keeps following a linear response until the recorded pressure equals p* less the value of the gauge resolution.

In the subject example, the recorded pressure equals p” less I psi, or 5929 psi at elapsed time t* = 135 set

(At* = 125 sex). Setting these values in the time match equation, with all other parameters unchanged, gives :

lg = 180 cm

Values of & and & are rather different this time, which again can be explained by the many uncertainties surrounding the parameters used. However this is irrelevant for the purpose of this study, which is illustrated by one example only. The important conclusion here is that in general, due to the limitation in the range of application of quantitative methods with the RFT (formation of around or less than 1 md), fractured blocks of a size a little mcxe than 100 cm, say generally above 200 cm, will not be seen as such, and will give a build-up response identical to those observed in unbounded reservoirs.

76

M-081 022

1 ATL-Marketing 1

Nov. 1981