Porosity and permeability for the Bereasandstone exhibiting large interfacial

tensions and non-stabilising pressure-profilefor the absolute oil permeability

Lab 3 and lab 4 by Group 38

Losoi, HenriHenri( a )Losoi.com

Sigvathsen, ChristofferSigvaths( a )Stud.NTNU.No

March 22, 2015

1 IntroductionThe Berea sandstone core is investigated. Its color is light yellowish white. Visualinspection to other Berea cores does not reveal any noticeable difference between therock used for this report and other Berea rocks. Berea sandstone is marketed as ”asedimentary rock whose grains are predominantly sand-sized and are composed of quartzheld together by silica. The relatively high porosity and permeability of Berea Sandstone™makes it a good reservoir rock” [1]. Permeability is investigated with ”3 wt% NaCl brine”and oil D60, it is not specified by which term such as moles or volume the proportion inthe brine is measured.

The air (helium) absolute permeability is meant to be measured as a single phaseflow where core is cleaned with Soxhlet method, dried and vacuum created with thewater flow in the permeability machine. The air permeability is called the Klinkenbergpermeability. The absolute permeability with respect to water is meant to be measuredas a single phase flow where core is saturated with water. The absolute permeabilitywith respect to oil is meant to be measured as a single phase flow where the goal is tosaturate the core with oil.

The paper investigates both the porosity and permeability. Porosity and permeabilitytend to correlate with each other: the deeper you go the worse they tend to become.Permeability measures the ability of a porous material to allow fluids to pass throughit. This paper is only interested in flow with a single fluid so absolute permeabilitiesare considered. The gas permeability machine is used for permeability measurementand it uses nitrogen as a contact fluid. Klinkenberg effect is that the permeability ofporous media to gases is approximately a linear function of the reciprocal pressure.

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Figure 1: System setup consists of a pressure meter, a tube containing the core and aglass to direct the fluid coming from the core. This system is for the abso-lute permeability with respect to water and oil separately where the fluid waspushed through the core.

We demonstrate this by calculating the Klinkenberg constant. Porosity measures thevoid in a material. It is defined as the ratio of the pore volume to the bulk volumeof the porous media. Porosity is measured in two different methods. The first methodis Helium porosimeter. The second method is porosity by saturation method. Thefollowing hypotheses were given in the instructions about permeability and porosity

• Hypothesis 1. The expected porosity is 10-25% and

• Hypothesis 2. The expected permeability is 100-1000mD.

Permeability in porous media can be investigated with Klinkenberg effect. Klinkenbergmeasurements can be made in ”atmospheric flow mode, or backpressure flow mode; undereither constant differential pressure, or constant mass flow rate” (page 373 [3]). The gaspermeability regressed to 1 atmosphere between atmospheric and backpressure flow datais between 3.4% and 4.5% (page 375[3]). So

• Hypothesis 3. The Klinkenberg constant is between 3.4-4.5%.

2 Materials, Methods and Calculations2.1 Working environmentThe experiements are carried 18th February, 23th February and 25th February in NTNUTrondheim, Norway. The experiments are conducted in room temperature about 20C.Outside weather is winter with snow and some sun.

2.2 Setup for the experimentsThe core volume is defined by Equation 1. The pore volume is defined by Equation (2)

Vk = V1 − V2 (1)

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Vp = Vb − Vk (2)

where Vb = πr2h is the volume of the block.

2.3 MaterialsThe core is a Berea sandstone and it has the shape of cylinder. The core is put intoa sleeve for permeability measurement where the confining pressure is 20.0 bar withrespect to helium so helium injection required. The flow rate Q is 10ml per minute. Thesleeve also uses fluids water or Exxsol D60 oil for the absolute permeability measurement.The absolute values can be compared to the permeability with respect to helium thatcorresponds to the Klinkenberg value.

2.4 MethodsThe Helium Porosimeter method and the Liquid Saturation method for porosity areoutlined on the pages 24-25 [4] in the document provided by the personnel in the NTNUuniversity.

Cleaning of the core with the Soxhlet method The Soxhlet removes undesirablesubstances in the intergranual porosity of the material such as impurities from earlierexperiments. The solvent used for distillaton is apparently water, this is not totallycertain because the experiment was conducted by a separate party. The distillationlasted 24 hours. The time of distillation was again confirmed by third party to besufficient, this is not necessarily true. The solvent has no surface contact with theintragranual fluids so they are still left in the rock. After the distillation, the core wasdried in an oven.

Porosity with the Helium Porosimeter method The Helium porosity method is basedon Boyle’s law

PiVi = PfVf (3)

where Pi is the initial pressure, Vi is the inial volume, Pf is the final pressure andVf is the final pressure. Unknown amount of helium gas is isothermally expanded atconstant pressure to an unknown void volume. After the expansion the resulted pressureis mearused and this pressure is independent of the unknown void volume. By the idealgas assumption the void volume can be measured with the Boyle’s law (3). Helium isused for multiple reasons. Firstly it can be modelled as an ideal gas for most pressuresand and temperatures of interest. Secondly helium consists of tiny molecules that canpenetrate pores of the rock. Thirdly helium has low mass and hence high diffusivitywhich means that the helium can be used to determine the porosity of low permeablerock. So the porosity by (4) is determined so that Vk = V1 − V2 and Vp = Vb − Vk.

φe = VpVb

(4)

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Figure 2: Soxhlet method for cleaning the core where the core was placed on top of apermeable material, apparently coal, and then the solvent was heated over 24hours.

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Figure 3: The core is placed inside the metal chamber after which the helium is injectedinto the system and then the pressure reading is recorded. The porosity canbe calculated from this reading by knowing the masses and volumes.

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Porosity with the saturation method The porosity by the Liquid Saturation methodis calculated from the readings containing masses and volumes so the effective porosityby (4) where the mass of brine Wbrine = Wsat −Wdry and the pore volume Vp = Wbrine

ρbrine.

Comparison with the porosity methods.The Helium Porosimeter method depends only on measured volumes while the Liquid

Saturation Method relies on density and masses. In a resorvoir, it can be impossibleto measure volumes because of volumetric expansion while brine saturation can be as-sumed to constant over the whole reservoir. The two methods may result into somewhatdifferent porosity values for example with supersaturated liquids.

Procedure for absolute permeability The procedure to get kabs is

• record sleeve P , Q, µbrine, L and A

• plot ∆P over time to investigate the stabilitization of pressure

• calculate kabs with Equation 5 (and remember to convert units to mD

• compare kabs from the 3% NaCl with brine to the kl from the lab 3

in comparison the industry also uses the method where you vary Qinj so the plot Qversus ∆P and the kabs is more accurate with various injection rates.

The permeability is given by Equation (5)

kabs = µfluidLQ

∆PA (5)

where µfluid can be air or brine. µair is the viscosity of air, L is the height of the block,Q is the flow and A is the area of the block. The Klinkenberg correction for the equation(5) is (6)

k = 2µairLQPi(P 2

1 − P 22 )A (6)

where the gas slippage effect is taken into account and Pi is the initial pressure and here1 bar.

2.5 CalculationsThe measurements are summarised in Table 2. Figure 5 provides necessary informationfor permeability calculations from earlier laboratory works.

Absolute permeabilities with respect to water and oil, separately. The pressure-timeprofile stabilised so the single phase flow with water can be quaranteed. The absolutewater permeability is

kabswater = 1.09926322cP40.84mm10ml/min4.34bar1125.8mm2

= 1.53139 ∗ 10−14m2

= 4.16275mD

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Sample Kineticviscosity (Lab 1/2)

Dynamicviscosity (Lab 1/2)

Perssure(Lab 4)

Absolutepermeability

v µ ∆P kabs(cSt) (cP) (bar) (mD)

Salt 1 0.92680375 0.946019277 4.34 4.16Salt 2 0.93720215 0.956633268 4.34 4.16Oil 1 1.7639968 1.09926322 4.34 3.51Oil 2 1.7640384 1.09928915 4.34 3.51

Table 1: Different viscosity values from Lab 1 and Lab 2.

where the viscosities are from Lab 1 and Lab 2 as shown in Table 1. Figure 4 shows thepressure profile over time when the pressure eventually stabilises.

The measurements of the pressure-time did not stabilise with oil. This means thatthe single-phase behaviour cannot be quaranteed for the absolute oil permeability. Theabsolute permeability for oil is estimated to be

kabsoil≈

0.92680375cP40.84mm1cm3

6s∆Poil1125.8mm2

where ∆Poil is undecided because the pressure front did not stabilise.

Permeability with respect to air Permeability can be analysed with Klinkenberg effect.This can be observed in Figure 7 and Figure 6. The Klinkenberg constant is defined by

b = m

kl(7)

where m is the slope and kl is the intercept in the y-axis as shown in Figure 6. Theslope is 0.1655−0.1545

0.8−0.5375 = 0.0419047... so the Klinkenberg constant is

b = 0.0419047...1.5425

= 0.02716678...≈ 2.72%.

Saturation porosity method The brine saturation is 3%. It is given in [4] that thismeans ρbrine = 1.02g/cc and ρbrine = 36g/l, this information is not verified. The massesWsat = 109.974g and Wdry = 102.524g so their difference is 7.45g. So

Vp = Wbrine

ρbrine= 7.45g

1.02g/cc = 7.303921...cc

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Figure 4: Absolute water permeability stabilises in the pressure-time profile of Lab 4 at4.34 bars.

Figure 5: Measurements contained pressures P1, P2, ∆P and Q by which the perme-ability was calculated with (5) and the information about the core profile.

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Figure 6: The intercept and the slope for calculating the Klinkenberg constant.

So the porosity φe is

φe = 7.303921...cc45.97756...cc = 15.8858...

≈ 15.9%

Porosity with the Helium Porosimeter method The porosity φe is

φe = 6.97756853186...cc45.97756...cc = 0.15176...

≈ 15.2%.

3 Results and observationsThe Berea sandstone was investigated. The fluids used for investigation of visconsityare air, brine (salt water) and D60 oil. Permeability was analysed with the Klinkenbergmodel that formulates the flow for porous media [3]. The permeability measurementswere characterised with too high pressures particularly with oil. This hints about largepressure inside the rock which means that the absolute permeability value with respectto oil must be considered with care.

Permeabilities were investigated conceptually and numerically. The Klinkenberg ef-fect for permeability is confirmed in Figure 7 while the numerical permeabilities did not

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Figure 7: Klinkenberg effect can be visualised with the reciprocal of pressure against thepermeability. The reasons for this behaviour contain the ideal gas behaviourand isothermal expansion.

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satisfy Hypothesis 2 and Hypothesis 3. The result for the Klinkenberg constant is 2.72%which does not the satisfy Hypothesis 3. The results for the absolute permeabilities are4.16mD and undecided for salt and oil, respectively, which do not satisfy Hypothesis 2.The absolute permeability with respect to oil cannot not be decided because the pressurefront did not stabilise in the planned time. A key assumption in determining the per-meability is the steady-state Darcy flow. This assumption should not be provocated bythe large interfacial tension observed in Figure 8 because the permeability was measuredas a single phase system. In the two phase system, the measured permeabilities canbe lower than expected because increasing interfacial tension is known to decrease therelative permeability values at least in the case of gas and gas condensate [2]. Raynoldsnumber, investigating viscous forces and inertial forces, should be calculated to analysewhether the flow was laminar or not. Non-Darcy flow should exhibit decreasing effectivepermeability when the flow rate increases [2], this is easy to experiment to investigatethe flow nature. So

• Hypothesis 4. The Berea sandstone by Group 38 exhibits non-Darcy non-steadystate flow when the oil is stuck in the intergranual porosity due to high capillaryforces which should demostrate itself in the permeability profiles with different flowrates.

where it is possible that the Berea sandstones naturally have low permeability and/orthe Soxhlet cleaning was not sufficient. The easiest way to investigate this is to redo theSoxhlet with longer cleaning time and then observe whether the permeabilities are stillas low as earlier. It is worth to notice that when the pressure front stabilises the systemshould act as a single phase flow.

Porosity was investigated with different methonds. The effective porosity by the He-lium Porosimeter method is 15.2% while the porosity with the Saturation Liquid methodis 15.9%. The target range given by the teacher is 10-25%. Then again the the providerstates that their cores have ”ambient porosities from 13% to 23%” [1]. Hypothesis 1about porosity is satisfied.

The Berea sandstones are manufactured by BereaSandStonesCores.com and they offera range of products where permeabilities range ”from 19mD thru 2500mD” [1]. Thecores with 100-200 mD are usual while other cores are classified as ”rare” [1]. Hence themeasured absolute permeabilities may be incorrect or the stone is an outliner: a corewith permeabilities in the range of 3-4mD should not exist from this provider.

4 Discussion and possible errorsThe comparison between the porosity and the permeablitity results from both tests willbe discussed. The permeability and the porosity have a tendency to correlate with eachother (one of the last chapters in [5]). The porosity value and permeability value areassociated with more poor quality reservoirs: particularly the permeability values arevery low.

The possible errors contain

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Figure 8: Bubbles observed in Lab 5 and Lab 6 mean large interfacial tensions that keepthe oil on the surface of the rock and/or bad cleaning process with the Soxhletin which case the capillary forces inside would have kept the intergranual oilsmore stuck where the chosen temperature, chosen solvent and cleaning timewere not sufficient. The bubbles on the surface were not observed with rocksof other groups which can be seen on the background. The large interfacialtensions and the high capillary forces can block the flow of fluids inside therock damaging the permeability.

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• The distillation temperature and the distillation time for the Soxhlet method maybe insufficient to remove the intergranual materials such as impurities and fluids.

• The gas permeability machine had some leakages in the connectors because ofunexpectedly high pressures caused by the resistance to flow, more in Figure 8.

• The chamber in the Helium Porosimeter may not be totally tight.

• The room temperature may not be precisely 20C affecting the visconsity value inpermeability measurements.

• The masses in Liquid Porosity Saturation method may not be totally precise ifparticularly if the scales were not calibrated presently.

where the most dominant error and its extent are unknown. Instrumental errors arerelated to the fact that the profiles of the instruments were not designed to work withcores having extremely high capillary pressure. The best way to analyse this error is torepeat the experiment and make sure the connectors are tightly connected and use aslow flow rate as possible not to cause the pressure to go over the measurement range orthe durability of instruments.

5 ConclusionThe rock is probably a bad reservoir rock. This is because of the low porosity valueand low permeability value. It is not optimal for hydrocarbon flow. Typical good Bereareservoir rocks are 100-200mD according to [1] while our results are about 3-4mD forpermeability while porosity values at the lower bounds i.e. near bad reservoir porosities.The bad quality of the reservoir rock is supported by the observation about bubblesforming on the top of the rock surface in Figure 8 hinting about non-Darcy and/or non-steady-state flow that requires more accurate optimization in possible drilling situation.

The results are tested in standard conditions and the necessary adjusting and conver-sions to reservoir conditions are not done so this synthesis must be read with cautionfor hydrocarbon production.

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Cylinder core feature Value Hypothesis DescriptionBulk volume 45.97cc NA NAPore volume 6.978cc NA NA

Dimensions (diameter) 37.87mm NA NADimensions (height) 40.84mm NA NA

Porosity by saturation method (effective) 15.9% 10-25% Satisfied.Porosity by Helium porosimeter 15.2% 10-25% Satisfied.

Final absolute permeability (salt) 4.16mD 100-1000mD Not satisfied.Final absolute permeability (oil) Undecided 100-1000mD Not satisfied.

Klinkenberg constant 2.72% 3.4-4.5% Not satisfied.

Table 2: Core properties contain bulk volume, dimensions, pore volume, final porosityand final absolute permeability. All measurements for permeabilities do notsatisfy their hypothesis namely Hypothesis 2 and Hypothesis 3. This can bedue to too large capillary forces within the rock and large interfacial tensionson the surface that result into non-Darcy flow. The absolute permeability withrespect to oil is undecided because the pressure front did not stabilise in theplanned time.

References[1] BereaSandStonesCores.com. Provider for the sandstones used in the experiment.

url: http://www.bereasandstonecores.com/.[2] G.D. Henderson et al. “The effect of velocity and interfacial tension on relative per-

meability of gas condensate fluids in the wellbore region”. In: Journal of PetroleumScience and Engineering (1997).

[3] Colin A. McPhee and Kevin G. “Klinkenberg permeability measurements: problemsand practical solutions”. In: Edinburgh Petroleum Services Limited, UK. (1991).

[4] Torsæter O. and Abtahi M. Experimental Reservoir Engineering Laboratory WorkBook. Aug. 2000. url: http://www.ipt.ntnu.no/˜oletor/kompendium4015.pdf.

[5] The millennium atlas: petroleum geology of the central and northern North Sea. TheGeological Society of Lonodon, Norwegian Petroleum Society, Geological Survey ofDenmark and Greenland, Millennium Atlas Company Limited, 2003.

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