phd proposal_ reoverable reserves

8/22/2019 PhD Proposal_ Reoverable Reserves

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Analysis of Layered Gas Reservoir Performance Using

a Quasi-Analytical Solution for Rate and Pressure Behavior

Objectives

The overall objectives of this research are:

1. To provide a quasi-analytical solution for the depletion (i.e., boundary-dominated

flow) performance of wells produced at a common production pressure in a layered

gas reservoir. This scenario is that of a "layered, no crossflow" case, and as such, we

duplicate the numerical simulations given by Fetkovich, et al.1 using our quasi-

analytical approach as a validation.

2. To use the analytical liquid flow solutions and the quasi-analytical gas flow solutions

as mechanisms for characterizing the performance of layered gas reservoirsin parti-

cular, cases of commingled production (no crossflow in the reservoir). The methods

derived from these solutions will be used to estimate:

The total original gas-in-place (G).

The moveable (or recoverable) reserves in each layer (EURj), The permeability ratio (2-layer case), The total flow capacity (kh product), and The productivity index for individual layers (Jgj).

3. To investigate the sensitivity of individual layer properties on the depletion perfor-

mance of layered reservoirs. The reservoir properties to be investigated include:

The permeability ratio (2-layer case), Skin factors for individual layers, Reservoir layer volumes, and The effect of drawdown (i.e., the magnitude of the wellbore flowing pressure)

__________________________________________________

This proposal follows the style and format of the SPE Journal.

Deliverables


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The expected deliverables of this work are:

1. Presentation of a single-layer, quasi-analytical solution for the depletion performance

of gas wells produced at constant bottomhole pressure. This solution will be used to

develop rate and cumulative production relations for wells in a layered gas reservoirs(with no crossflow in the reservoir).

2. Investigation of the sensitivity of individual layer properties on the depletion

performance behavior for a layered reservoir system. This study includes:

The permeability ratio (2-layer case), Skin factors for individual layers,

Reservoir layer volumes, and

The effect of drawdown (i.e.,pwf).

3. Development of analysis techniques for commingled production data from layeredgas reservoirsin particular, the following techniques are provided:

a. Modifiedp/zversus Gp analysis plot for layered (no crossflow) systems,

b. Type curve analysis approach for the analysis of rate-time data from layered (no

crossflow) gas reservoir systems (this includes the generation of new productionperformance type curves for layered gas reservoirs),

c. Direct extrapolation technique for the estimated ultimate recovery (EUR).

4. Application/validation of these new analysis techniques using both field and synthetic

data (the synthetic cases are generated using a commercial reservoir simulation

program).

Present Status of the Question

Decline Curve Analysis for Single Layer Reservoir Systems:

Decline curves and decline type curves are the primary mechanisms for the analysis and

prediction of oil and gas production in the petroleum industry. This is not an overstatement of

the value of decline curve methodologies however, we must recognize that decline curve

methods have evolved from simple (basically empirical) extrapolation techniques into very

comprehensive (and hence, complex) reservoir models. The pioneering work in this area was

provided by Arps,2 who presented empirical exponential and hyperbolic models for the purpose

of rate extrapolation. Interestingly, the exponential model is actually the rigorous solution for a

well producing a slightly compressible fluid from a closed reservoir (boundary-dominated flow

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prevails). In a similar fashion, the "hyperbolic" relations proposed by Arps have been shown to

be approximate solutions for both the dry gas and solution gas drive reservoir cases. This is not

a trivial issue the fact that the "empirical" Arps relations have an analytical (or semi-

analytical) basis means that these relations hold promise in providing representative predictions

of reservoir performance.

In 1973 Fetkovich3 presented the classic work on the topic of decline type curve analysis.

Fetkovich showed that the Arps exponential decline relation is the rigorous (exact) solution for a

well producing at a constant bottomhole pressure at pseudosteady-state flow conditions. The

exponential decline equation was used as a correlating function to establish the "dimensionless

decline variables" (tDd and qDd), where these variables were then used to develop the so-called

"Fetkovich" decline type curves. The "Fetkovich" type curve is unique in that it can be used for

both analysis and prediction. This type curve permits us to forecast well performance, but it also

allow us to estimate reservoir properties (i.e. flow capacity, kh, skin factor, s, fracture

half-length, etc), as well as the oil or gas in place. This classic work by Fetkovich is the

foundation for all modern work in production data analysis. The primary issue related to the

present work is the extension to multilayer reservoir cases. Fetkovich, et al.1 provide an

approach for the analysis/interpretation of multilayer gas reservoir performance, but we note that

neither the Fetkovich, et al. work (nor any subsequent work) has effectively addressed the use of

decline type curves for multilayer reservoir systems.

In 1985 Carter4 presented a new set of type curves developed exclusively for the analysis of gas

reservoir performance data. Carter used a finite-difference numerical model to generate a

sequence of decline type curves for gas wells produced at a constant bottomhole pressure. The

most significant contribution of this work was that Carter demonstrated that the constant pressure

behavior of a gas well is path-dependent (as we might expect), but that this path is uniquely

defined by the level of drawdown (i.e., the bottomhole pressure).

In short, Carter showed that a correlating parameter () depends only on the reservoir fluid

properties and presented a sequence of rate solutions for various cases of a constant wellbore

pressure. Carter's type curves provide a consistent (and rigorous) approach for the analysis of

production data from a gas well produced at a constant bottomhole pressure. However, these

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type curves have several limitations the approach is only valid for wells produced at a

constant bottomhole pressure, and we would like to have a more generalized approach where the

gas flowrate-time behavior can be correlated with the flowrate-time behavior predicted by a

liquid theory.

In 1987 Fraim and Wattenbarger5 developed a correlation of the gas and liquid flow solutions

using a "pseudotime" (or normalized time) function to account for changes in gas properties with

pressure and time. This significantly improved the use of the Fetkovich type curve for the

analysis and interpretation of gas well performance and essentially made the use of Carter's

type curves unnecessary. The Carter type curves remain popular because this approach is simple

and straightforward (comparatively) however, the Fraim-Wattenbarger approach is preferred

because of its ability to "correlate" gas and liquid solutions (a much more general approach).

The only significant issue related to the Fraim and Wattenbarger5 technique is the requirement of

an accurate estimate of gas-in-place (where G is used to "seed" the pseudotime calculation).

This most often results in an iterative procedure (based on G), but this is easily resolved in one or

two steps, and the iterative calculations are easily solved with modern computational tools. As a

practical note, it is not recommended that the iterative calculation procedure be performed

automatically, but rather, manual intervention is recommended (successive handanalyses will

yield a convergent solution, but an automated regression solution may not yield the mostrepresentative estimate of gas-in-place).

In 1986, Aminian, et. al.6 also developed a set of type curves base on a semi-analytical model for

gas flow behavior in a closed reservoir. These type curves are formulated in a "dimensionless"

format like the Fetkovich-style type curves, although the dimensionless variables are defined in

terms of gas reservoir variables. This work is similar to that proposed by Carter,6 but presented

in a less rigorous form (these decline type curves can be applied in a straightforward fashion, but

will not be as rigorous as the Fraim and Wattenbarger5 approach).

In 1991 Blasingame, et al.7 introduced constant pressure analog time and constant rate analog

time functions as mechanisms to analyze production data exhibiting variable-rate/variable

pressure drop behavior. This work provides a rigorous, straightforward approach for the analysis

of liquid or gas production data, and offers the option of using analogs for either constant rate of

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constant pressure (Fetkovich decline type curve format). As noted, these analog time functions

are formulated in terms of a pseudotime for the case of a gas reservoir, though the approach still

requires an iterative procedure for the gas-in-place. Blasingame, et al. provide verification of

this approach using simulated and field performance data for the oil (liquid) and gas well cases.

The approach was not specifically tied to the use of a decline type curve for the constant rate

analog case.

In 1993 Palacio and Blasingame8presented a new, unified method for the analysis of production

data (single phase oil or gas flow) using an appropriate pseudopressure-pseudotime trans-

formation and type curves analysis technique. This method is completely general, and should be

suitable for the analysis of all production data (excluding shut-ins and recompletions). The

approach uses a modified time function (which addresses both the variable-rate/variable pressure

issue, as well as the variation of gas properties with time).

Palacio and Blasingame also presented a "Fetkovich-Carter" type curve, which combines the

constant pressure gas flow solution and the Arps' decline curve stems on a single type curve.

The "rate-integral: and "rate integral-derivative" functions have been added to the "Fetkovich-

Carter" type curve, which improves the overall utility of this approach for scenarios of constant

pressure production. Although this work represents an improvement in the interpretation and

analysis of well performance data from gas reservoir systems, it remains limited to the single-layer case. An extension of the "Fetkovich-Carter" type curve to the case of a multilayered gas

reservoir would be useful.

Knowles9 (1999) presented a new approach for developing an approximate solution for

boundary-dominated gas flow in single-layer reservoirs. His approach was to use a straight line

approximation for the behavior of the ct product with thep/zprofile (i.e., the "first-order" poly-

nomial approximation). This approach yields a p/z-squared (i.e., (p/z)2) form of the stabilized

flow equation, which in turn provides the proper algebraic form for coupling the stabilized flow

equation directly with the gas material balance equation in order to yield an explicit analytic rate-

time gas equation.

Ansah, et al.10 (2000) presented a suite of semi-analytical relations for boundary-dominated gas

flow in single-layer reservoir systems that can be used for rate-time, rate-cumulative and p/z(gas

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material balance) predictions. Similar to Knowles, they also employed the "first-order" poly-

nomial approximation assumption for the behavior of the ct product with thep/zfunction. This

relation is (generally) limited to pressures below 5000-6000 psia, but the simplicity of the

relation gives rise to a number of potential applications (reserves prediction, production extrapo-

lations, etc.). Ansah, et al. present these solutions in terms of dimensionless variables and in the

form of type curve plots. Field-variable solutions can easily be derived from the dimensionless

solutions.

Doublet, et al11 presented a variety of oil field case analyses using the Fetkovich/McCray type

curve to estimate oil-in-place and moveable oil reservoir volumes, as well as the flow charac-

teristics of the reservoir. In this decline type curve analysis they use the "rate integral" and "rate

integral derivative" functions to analyze and interpret production rate and pressure data from oil

reservoir systems. This work provides a strong validation of the approach as well as the utility of

using decline type curve analysis for single-layer reservoir systems. An extension of this

approach for multilayer gas reservoir systems is needed and should be developed.

In the proposed work, we present a new, quasi-analytical flow solution for the depletion

performance of gas wells produced at constant bottomhole pressure in a layered reservoir. This

approach is quite simple, and borrows from the Knowles9 and Ansah, et al.10 work (the single-

layer approximate solution for gas systems is used for the multilayer reservoir case). We provide

new type curves in terms of rate-time, pressure-cumulative-production, and cumulative produc-

tion-time performance for layered gas reservoir. The type curves are applied and verified using

both field and synthetic well performance data.

Behavior of a Well Producing from a Layered Reservoir System: (No Crossflow)

Templaar-Lietz12 (1959) provided one of the earliest studies of layered reservoir behavior, where

they studied the effect of oil production rate on well performance in a two-layer reservoir (equal

layer thickness and steady-state flow). Lefkovits, et al.13

(1961) then modified the Templaar-

Lietz depletion equation to model a two-layer reservoir with unequal thickness. Lefkovits, et al.

presented an analytical solution for a two-layer system (without crossflow) their solution was

developed using the Laplace transform and they obtained an analytical inversion result.

Lefkovits, et al. found that differential depletion between layers exists only during transient flow,

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when the more permeable layer is depleted faster than the less permeable layer. It is relevant to

note that, for steady-state flow, both layers contribute equally to production.

Raghavan14 (1989) discussed the behavior of commingled wells in layered system, and suggested

methods to determine layer properties and well performance especially for reservoirs with

significant contrasts in reservoir properties. The primary conclusion of this study is that during

the transient flow period the rates from different reservoir layers are not constant, and, in short,

the rates are controlled by the kh-products of individual layers, the total flowrate, and the skin

factors for individual layers. At later times, when pseudosteady-state flow becomes established,

the layers contribute to production proportional to the pore volumes (Vp) of the individual layers.

Both Lefkovits et al.13 and Raghavan considered layered behavior from the perspective of well-

test analysis, rather than from the standpoint of long-term production performance. In addition,

neither Lefkovits et al, nor Raghavan considered the behavior of layered gas reservoir systems.

In 1991, Johnston and Lee15 presented new guidelines for analyzing production and pressure

transient test data from either multilayer reservoir systems. They used analytical solutions to

illustrate a variety of well performance cases for various multilayer well completions. Johnston

and Lee focused on identifying patterns of characteristic behavior and gave guidelines for inter-

preting well performance behavior in multilayer reservoir systems.

Gao and Lee16 (1993) presented a new approach which used pseudopressure and pseudotime

formulations to model the performance of commingled reservoirs with pressure dependent fluid

properties in each layer. They developed an analytical model (which used liquid flow solutions)

which was then compared to the results from a numerical model. Gao and Lee focused their

attention on the "short time" analysis of well test data, and did not consider long-term pro-

duction performance. We considered extending the Gao and Lee approach for the analysis/

modelling of long-term well performance, we be have instead elected to consider the develop-

ment of multilayer gas flow solutions using quasi-analytical gas flow solutions. We believe that

this approach will be more straightforward and robust.

Depletion Performance of a Layered Gas Reservoir System:

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Fetkovich, et al.1, applied a fully implicit, radial numerical model to generate rate/time and

pressure/cumulative production data for the case of a single gas well produced at a constant

wellbore pressure. All of their work pertained to single-phase gas flow in a two-layer gas

reservoir without crossflow (i.e., commingling of fluids is only permitted in the wellbore,

there is no crossflow in the reservoir).

For comparison, Fetkovich, et alalso investigated the case of two non-communicating layers

where each layer contained a single gas phase (this configuration was used to model annual 72-

hour shut-ins and 48-hour deliverability tests as well as long-term production). In addition, this

model was used to verify the results obtained from the proposed analysis approach ( i.e., a p/z

versus Gp approach for multilayered reservoir systems). Fetkovich, et al.1 noted that Arps

depletion-decline exponents ("b"-values) between 0.5 and 1 can be obtained with using the

"layered no crossflow" model. In contrast, for the case of a single homogeneous layer, the

maximum decline exponent (i.e., "b"-value) is 0.5 (ref. 3). The fundamental work by Fetkovich

(ref. 3) stated that when two liquid flow solutions are commingled ( i.e., added), the resulting rate

decline behavior is hyperbolic, (i.e., b 0 specifically for the case presented by Fetkovich,1

the resulting "b"-value was 0.2).

It is relevant to note that Fetkovich, et al.1 proved that the permeability contrast and layer volume

ratio can be inferred (or estimated) from the value of the decline exponent (b).1

It was observedthat if a gas well exhibits b>0.5, this behavior can indicate the presence of a layered reservoir

system, and in such systems the b-value can approach 1.0. This appears to be a unique

characteristic of a layered gas reservoir system. Fetkovich, et al.1 also showed that the shape of

thep/z-factor versus cumulative gas production plot is governed by the permeability contrast and

layer volume ratio, and that this behavior can (and should) be used to detect layering.

In summary, Fetkovich, et al.1 attempted to demonstrate the theory behind decline type curve

analysis for the single layer system as applied to the case of multiple layers, commingled at the

wellbore (the so-called "layered-no crossflow" case). Fetkovich1 provided a general result for

the case of production at a constant wellbore pressure that was derived as a combination of the

material balance equation and the pseudosteady-state flow equations (for gases and liquids).

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The second work (i.e., Fetkovich, et al.1) investigated the behavior of both rate-time and p/z-

cumulative production performance for a single well in a 2-layer gas reservoir, specifically for

the case of production at a constant bottomhole flowing pressure. As a comment, our proposed

work will integrate these investigations using a new semi-analytical solution for a single layer

gas reservoir to develop a solution for a multilayer gas reservoir.

McCoy, et al.17 continued the work of Fetkovich et al,1 and they included the effect of a poorly

stimulated layer on the overall depletion performance of a two-layer gas reservoir. The goal of

the work presented by McCoy, et al. was initially to reproduce the results of the Fetkovich et. al.1

study (ref. 1), then to investigate the effect of changing the skin on the lower permeability layer.

In a practical sense this situation would be presented by a "stimulation" treatment where the skin

factor in the low permeability layer is changed. McCoy, et al. found the controlling parameters

to be the layer volume ratio and the skin factor in the low permeability layer in particular,

these parameters control the overall recovery and the time dependency of recovery. The

conclusions of the McCoy, et al. study were focused on the dependency of recovery in the low

permeability layer, in particular on the skin factor for the low permeability layer. Their goal was

to demonstrate the value (i.e., increased recovery) that could (or should) be achieved when the

low permeability layer is stimulated.

Another investigation of layered gas reservoir performance was performed by Kuppe, et al.

18

Inthis work they developed a simple spreadsheet model to estimate original gas-in-place, the

productivity indices for each layer, and the recoverable reserves. The analysis approach is based

on a combined technique which use the gas material balance equation and the pseudosteady-state

relation for gas flow. This methodology was demonstrated for wells in the Cooper Basin

(Australia), where the production from multilayer gas reservoirs is commingled. Kuppe, et al

matched field performance data using a spreadsheet-based program which averages the

calculated p/z curves for the high and low permeability layers using an appropriate set of

"weighting" factors based on the productivity index. The purpose of the "weighting" factor is to

"adjust" the 2 computed p/ztrends into a single "average" p/ztrend, which is then compared to

the measured/observedp/ztrend.

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Procedure

The primary task of this work is to demonstrate the use of our proposed quasi-analytical solution

as part of a performance-based reservoir characterization. In particular, our goal is to provide a

representative analysis of a typical multilayer gas reservoir sequence (in our case, we will studythe Hugoton Field in Kansas (USA)). We will use production data, wellhead pressure data, and

annual shut-in pressure data obtained for individual wells. To achieve the objectives of this

research, we propose the following tasks:

1. Development of the quasi-analytical model for a layered gas reservoir system

produced at constant bottomhole pressure. The production is "commingled" at the

wellbore, there is no "crossflow" in the reservoir.

The pressure and flowrate models are given in dimensionless format as follows:

(example plots are also provided to illustrate characteristic behavior)

Dimensionless Wellbore Pressure for an Individual Layer: (pDj)

0)()0.5(1

1 =

+= wD

DdjDj p

tp ......................................................(1)

[ ]0)(

)exp(-)(1)(1

)exp(-)(1)(1p

tppp

tppppp wD

DdjwDwDwD

DdjwDwDwDwDD

+

++= .......(2)

)/(

)/(

ii

j

Djzp

zpp = ....................................................................................(3)

Dimensionless Wellbore Pressure for the Total System: (pD)

0)()0.5(1

1 =

+= wD

DdD p

tp ........................................................(4)

[ ]

[ ]0)(

)exp(-)(1)(1

)exp(-)(1)(1

+

++= wD

DdwDwDwD

DdwDwDwDwDD p

tppp

tppppp

.........(5)

)/(

)/(

iiD

zp

zpp = .....................................................................................(6)

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p/zversus Total Cumulative Gas Production: (pwD = 0.1 case)

Fig. 1 - p/zversus total cumulative gas production for a commingled gas well

produced at a constant wellbore pressure (pwD=(pwf/zw)/ (pi/zi) = 0.1),

with k1/k2 varying from 1x10-3 to 1x103.

Total Cumulative Gas Production versus time: (pwD = 0.1 case)

Fig. 2 - Total cumulative gas production versus production time for a

commingled gas well produced at a constant wellbore pressure

(pwD=(pwf/zw)/ (pi/zi) = 0.1), with k1/k2 varying from 1x10-3 to 1x103.

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Dimensionless p/z-difference function versus Dimensionless Total Cumulative Gas

Production: (pwD = 0.1 to 0.5)

Fig. 3 - p/z-function versus total cumulative gas production function for a

commingled gas well produced at a constant wellbore pressure

(pwD=(pwf/zw)/ (pi/zi) = 0.1-0.5), with k1/k2 varying from 1x10-3 to 1x103.

Dimensionless Decline Rate for an Individual Layer: (qDdj)

0)()0.5(1

1

2=

+= wD

Ddj

Ddj pt

q .....................................................(7)

[ ]0)(

)exp(-)(1)(1

)exp(-4

2

2

p

tppp

tppq wD

DdjwDwDwD

DdjwDwDDdj

+

= ....(8)

Dimensionless Decline Rate for the Total System: (qDd)

0)()0.5(1

1

12

=+

==

wD

j Ddj

Dd pt

qn

...........................................(9)

[ ]0)(

)exp(-)(1)(1

)exp(-4

2

2

+

= =

p

tppp

tppq wD

n

1j DdjwDwDwD

DdjwDwDDd

.(10)

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Type Curve for a Layered (No Crossflow) Gas Reservoir: (pwD=0.1 to 0.5)

Fig. 4- Dimensionless decline gas rate versus dimensionless decline time for a commingled

well produced at various constant wellbore pressures (pwD = (pwf/zwf)/ (pi/zi) = 0.1 to

0.5), with k1/k2 varying from 1x100 to 1x103.

Dimensionless Cumulative Production for an Individual Layer: (GpDj)

0)()0.5(1

0.5 =

+= wD

Ddj

DdjpDj p

t

tG ..............................................(11)

[ ][ ]

0)()exp(-)(1)(1

)exp(-1)(1 2

ptppp

tp-p-G wD

DdjwDwDwD

DdjwDwDpDj

+

= .....(12)

Dimensionless Cumulative Production for the Total System: (GpD)

0)()0.5(1

0.5

1

=+

=

=wDDdj

Ddj

pDp

t

tG

n

j ................................... (13)

[ ][ ]

0)()exp(-)(1)(1

)exp(1)(1 2

ptppp

tp--p-G wD

n

1j DdjwDwDwD

DdjwDwDpD

+

==

(14)

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Dimensionless Cumulative Production Versus Dimensionless Time: (pwD = 0.1)

Fig. 5 - Dimensionless cumulative gas production versus dimensionless decline time for a

commingled well produced at various constant wellbore pressures (pwD = (pwf/zwf)/

(pi/zi) = 0.1), with k1/k2 varying from 1x100 to 1x103.

For Eqs. 1-3, and Eqs. 7-14, the index and layer counters are given by:

j = layer index

n = number of layers

Definitions of Dimensionless Variables:

In addition to the dimensionless rate and pressure solutions, the following dimen-

sionless definitions are used:

=

2

1

-ln1-2

1

1

0.00634

22

wa

e

wa

ewatiijj

j

Ddj

r

r

r

rrc

tkt

..........................(15)

=

2

1-ln1-

2

1

1

rc

0.00634

22

wa

e

wa

ewatii

Dd

r

r

r

r

tkt

..............................(16)

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=

=

=n

jhj

n

jh jkj

k

1

1...................................................................................(17)

=

=

=n

jhj

n

jh jj

1

1

...................................................................................(18)

)(

)(

ii

wfwfwD

/zp

/zpp = .................................................................................(19)

)(

)(

iiD

/zp

p/zp = .......................................................................................(20)

Pseudosteady-State Flow Equation:

)/(-)/( 22 wfwfjgj zpzpCq = ..........................................................(21)

where:

reft

wa

e

jjj

pp

z

r

rT

hkC

=

c

4

3-ln1.4232

.......................................(22)

Rate and Cumulative Production Relations:

Total gas production rate: (qg,t)

1=

=n

j

gjg,t qq .......................................................................................(23)

Cumulative gas production for each layer: (Gp,n)

)(1 tqGG gjp,n-p,n += .................................................................(24)

Cumulative gas production for the total (multilayer) system (Gp,t)

1

=

=n

j

pjt,p GG ................................................................................(25)

(p/z)2(pwf/zwf)2 Versus Gas Production Rate : (pwD = 0.1)

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Fig. 6 - (p/z)2 - (pwf/zwf)2 versus gas production rate for a commingled well produced at

various constant wellbore pressures (pwD = (pwf/zwf)/(pi/zi) = 0.1), with k1/k2 varying

from 1x100 to 1x103.

2. Construction of generalized plots/type curves for layered reservoirs using Eqs. 114.

The following plots are included for reference: (variations and extensions of these

plots will be provided in the dissertation)

Fig. 1: p/zversus Total Cumulative Gas Production (pwD = 0.1 case)

Fig. 2: Total Cumulative Gas Production versus Production Time (pwD = 0.1 case)

Fig. 3: Dimensionless p/z difference function versus Dimensionless Total

Cumulative Gas Production function (pwD=0.1 to 0.5)

Fig. 4: Type Curve Layered (No Crossflow) Gas Reservoir (pwD=0.1 to 0.5) Fig. 5: Dimensionless Cumulative Production Dimensionless Time (pwD = 0.1)

Fig. 6: (p/z)2(pwf/zwf)2 Versus Gas Production Rate (pwD = 0.1)

3. Application of the analytical liquid flow solutions and the quasi-analytical gas flow

solutions as mechanisms for characterizing the performance of layered gas reser-voirs

in particular, cases of commingled production (no crossflow in the reservoir).

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The properties to be estimated include:

Decline Type Curve Analysis:

The total original gas-in-place (G). The permeability ratio (2-layer case). The total flow capacity (kh product).

Specialized Analysis: (p/zversus Gp multilayer analysis plots)

The total original gas-in-place (G). The permeability ratio (2-layer case). The moveable (or recoverable) reserves in each layer.

Estimated Ultimate Recovery (EUR)Analysis: (qg versus Gp plots)

The moveable (or recoverable) reserves in each layer (EURj).

4. To investigate the sensitivity of individual layer properties on the depletion perfor-

mance of layered reservoirs. The reservoir properties to be investigated include:

The permeability ratio (2-layer case),

Skin factors for individual layers, Reservoir layer volumes, and The effect of drawdown (i.e., the magnitude of the wellbore flowing pressure).

This investigation will include the use of synthetic data (derived using numerical

simulation), as well as a variety of field data.

5. Analysis, interpretation, and correlation of gas well performance data taken from the

Hugoton Field, Kansas, USA. The following data are required.

Production rates and wellhead pressures (on a monthly basis).

Shut-in bottomhole pressures. Fluid properties. Reservoir layer properties (porosity, thickness, etc.).

A complete database of "parent" and "infill" wells.

We will use these data to create a systematic analysis and interpretation of the

reservoir, and in particular, we will attempt to characterize the "dominant" and

"subordinate" layer systems. Specifically, we will perform the following subtasks:

a. p/zversus Gp analysis for each well where a sufficient data are available.

Standardp/zversus Gp analysis (straight-line approach).

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Multilayerp/z versus Gp analysis, use of the quasi-analytical solution to

analysis the totalp/zversus Gp performance. Regression and (possibly) type

curve methods will be used.

b. New rate decline type curve analysis approach for the analysis of rate-time data

from layered (no crossflow) gas reservoir systems. This will require new typecurves specifically constructed for multilayered reservoir systems.

c. Direct extrapolation technique for the estimated ultimate recovery (EUR).

d. Correlation of results using areal mapping of the results.

6. Apply these results of this study for the purpose of reservoir managementsuch as

infill drilling, well stimulation, optimizing production practices, future reservoir

performance etc.

Organization of the Research

The outline of the proposed research dissertation is as follows:

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1. Chapter I Introduction

1.1 Background of Analysis Layered Gas Reservoir1.2 Research objectives

1.3 Summary of results layered gas reservoirs

1.3.1 p/zanalysis1.3.2 Decline type curve analysis

1.3.3 EUR analysis

1.4 Organization of the dissertation

2. Chapter II Literature Review

2.1 Analysis of gas reservoir performance using material balance

2.2 Decline type curve analysis (single-layer reservoir)2.3 Depletion performance of a layered gas reservoir

3. Chapter III Development of Semi-Analytical Solutions for the Analysis of Reser-

voir Performance Data from a Layered Gas Reservoir3.1 Summary

3.2 Description of the reservoir model

3.3 Development of solutions for a multilayer gas reservoir

3.3.1 Gas productivity/stabilized flow equation (rigorous model)

3.3.2 (p/z)2 gas flow equation (proposed model)

3.3.3 p/zanalysis for layered gas reservoir3.3.4 Dimensionless variables/parameters for a new rate decline type curve for

layered gas reservoir systems

3.4 Discussion

4. Chapter IV Development of Decline Type Curve Analysis Techniques for LayeredGas Reservoir Systems

4.1 Decline Type Curve Analysis

4.1.1 Plotting functions for decline type curve analysis (general approach)

4.1.2 Decline type curve model for a layered gas reservoir

4.1.3 Orientation/methodology for decline type analysis techniques applied to

layered gas reservoir systems

4.2 Illustrative applications of the new rate decline type curve for layered gas reser-

voir systems

4.3 Discussion

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5. Chapter V Validation and Application of the New Production Performance Type

Curve for a Layered Gas Reservoir

5.1 Summary5.2 Numerical Simulation Case

5.2.1 p/zPerformance Analysis

5.2.2 Decline type curve analysis5.2.3 EUR analysis

5.3 Application Field Case (Hugoton Gas Field, Kansas, USA)

5.3.1 p/zPerformance Analysis5.3.2 Decline type curve analysis

5.3.3 EUR analysis

5.3 Discussion

6. Chapter VI Summary and Conclusions

6.1 Summary

6.2 Conclusions

6.3 Recommendations for Future Work

7. Nomenclature

8. References

9. Appendices:

Appendix A Derivation of the Gas Well Productivity Index and Derivation of

the Gas Material Balance Equation for Layered Reservoirs.

Appendix B Derivation of an Approximate Relation for Gas Flow Behavior at

a Constant Bottomhole Pressure (Pseudosteady-State Flow

Conditions).

Appendix C Derivation of the Dimensionless Solutions for Production Rate

and Average Reservoir Pressure Behavior in a Multilayer GasReservoir.

Appendix D Summary of Field Case Analyses Hugoton Gas Field, Kan-

sas, USA

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References

1. Fetkovich, M.J., Bradley, M.D., Works, A.M., Thrasher, T.S.: "Depletion Performance of

Layered Reservoir Without Crossflow," SPEFE, September 1990. 310-18.

2. Arps, J.J.: "Analysis of Decline Curves," Trans., AIME (1945) 160, 228-247.

3. Fetkovich, M.J.: "Decline Curve Analysis Using Type Curves," paper SPE 4629 presented at

the 1973 SPE Annual Conference and Technical Exhibition, Sept. 30 Oct. 3, 1973, 1-28.

4. Carter, R.D,.:"Type Curves for Finite Radial and Linear Gas-Flow Systems: Constant-Termi-

nal-Pressure Case," SPEJ(Oct. 1985) 719-728.

5. Fraim, M.L. and Wattenbarger, R.A.: "Gas Reservoir Decline-Curve Analysis Using Type

Curves With Real Gas Pseudopressure and Normalized Time," SPEFE, (Dec. 1987) 671-682.

6. Aminian, K., Ameri, S., and Hyman, M.: "Production Decline Type Curves for Gas Wells

Producing Under Pseudosteady State Conditions," paper SPE 15933 presented at the 1986

SPE Eastern Regional Meeting, Columbus, OH, 12-14 November 1986.

7. Blasingame, T.A., McCray, T.L, and Lee, W.J.: Decline Curve Analysis for Variable

Pressure Drop/variable Flowrate Systems, paper SPE 21513 presented at the SPE Gas

Technology Symposium held in Houston, Texas, January 23-24, 1991.

8. Palacio, J.C. and Blasingame, T.A.: "Decline-Curve Analysis Using Type CurvesAnalysis

of Gas Well Production Data," paper SPE 25909 presented at the 1993 Joint Rocky MountainRegional and Low Permeability Reservoir Symposium, Denver, CO, April 26-28.

9. Knowles, S.R.: Development and Verification of New Semi-Analytical Methods for the

Analysis and Prediction of Gas Well Performance, M.S. Thesis, Texas A&M University,

College Station, TX (1999).

10. Ansah, J., Knowles, R.S. and Blasingame, T.A.: "A Semi-Analytic (p/z) Rate-Time Relation

for the Analysis and Prediction of Gas Well Performance," SPERE (December 2000) 525-

533.

11. Doublet. L.E, Pande. P.K, McCollum, T.J., and Blasingame, T.A.: "Decline Curve Analysis

Using Type CurvesAnalysis of Oil Well Production Data Using Material Balance Time:

Application to Field Cases," paper SPE 28688 presented at the 1994 SPE Petroleum

Conference and Exhibition in Mexico held in Veracruz, Mexico, 10-13 October 1994.

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12. Templaar-Lietz, W.: "Effect of Oil Production rate On performance of Wells Producing from

More Than One Horizon," SPEJ, (March. 1961) 26-31.

13. Lefkovits, H. C., Hazebroek, P., Allen, E. E., and Matthews, C.S.: "A Study of the Behavior

of Bounded Reservoirs Composed of Stratified Layers," SPEJ(March. 1961) 43-58.

14. Raghavan, R.: "Behavior of Wells Completed in Multiple Producing Zones," SPEFE, June

1989, 219-30.

15. Johnston, J.L., Lee, W.J.: "Application of a New Analytical Solution for Multilayered,

Commingled Reservoirs to Provide More Accurate Performance Prediction and Well Test

Analyses," paper SPE 21830 presented at the SPE Rocky Mountain Regional/Low Permea-

bility Reservoirs Symposium and Exhibition held in Denver, Colorado, April 15-17, 1991.

16. Gao, C., and Lee, W.J.: "Modelling Commingled Reservoirs With Pressure Dependent Pro-

perties and Unequal Initial Pressure in Different Layers," paper SPE 26665 presented at the

SPE Annual Technical Conference and Exhibition held in Houston, TX 3-6 October 1993.

17. McCoy, T.F, Reese, D.E., and Johnson, P.G.: "Depletion Performance of Poorly Stimulated

Layered Reservoirs Without Crossflow," paper SPE 59757 presented at the 2000 SPE/CERI

Gas Technology Symposium held in Calgary, Alberta, Canada, 3-5 April 2000.

18. Kuppe, F, Chugh, S., and Connell, P.: "Material Balance for Multilayered, Commingled,

Tight Gas Reservoirs," paper SPE 59760 presented at the 2000 SPE/CERI Gas Technology

Symposium held in Calgary, Alberta, Canada, 3-5 April 2000.

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