CFD Simulation of Pore Pressure Oscillation Method for the Measurement of Permeability in Tight Porous-Media

Transcription

1 CFD Smulaton of Pore Pressure Oscllaton Method for the Measurement of Permeablty n Tght Porous-Meda Seyed Armn Madan 1, Mehd Mokhtar *, Abdennour Seb 3 1 Ol Center Research, Lafayette, LA, USA.,3 Petroleum Engneerng Department, Unversty of Lousana at Lafayette, Lafayette, LA, USA. *Petroleum Engneerng Department, Unversty of Lousana at Lafayette, P.O. Box: 44690, Lafayette, LA Emal: mokhtar.mehd@lousana.edu Abstract: Accurate estmaton of rock permeablty and porosty play a crucal role n the evaluaton of ol and gas reservors. Ths evaluaton s however, challengng n tght formatons such as shale due to the slow transton of flud n such formatons wth extremely-low permeablty. To overcome the long expermental tme of conventonal technques for permeablty measurement (steady-state methods), transent methods such as pore pressure oscllaton method has been proposed for laboratory measurement of permeablty n tght formatons. In ths method, snusodal pore pressure oscllaton s appled at upstream sde of reservor core sample and the response of the sample at the downstream sde s evaluated. In ths paper, the expermental technque for permeablty and porosty measurement s smulated usng CFD module of COMSOL Multphyscs and the results are compared wth analytcal solutons. An excellent agreement between CFD and analytcal data s observed and the results are analyzed and dscussed n detals. Fnally, two dfferent scenaros are defned for 6 heterogeneous samples and the response of ths technque to such cases are analyzed and studed. Keywords: Permeablty, Porosty, Pressure Oscllaton Method, CFD, Tght Formaton. 1. Introducton By advances n technology and knowledge of petroleum engneerng, geology, and geophyscs, unconventonal reservors have become relatvely a consderable porton of ol and gas resources around the world. Tght gas sands, ol and gas shales, and coalbed methane are examples of unconventonal reservors. The word unconventonal comes from the fact that these reservors have extremely low permeablty and they need specal recovery operatons outsde of the conventonal recovery practces to extract the exstng hydrocarbons. Accurate evaluaton of porosty and permeablty plays a crucal role n reservor characterzaton snce these two parameters are used to estmate the reservor dranage area and optmze the well spacng, drllng, completon, and producton procedures [1]. For tght reservor samples, conventonal core analyss technques are not practcal due to very low permeablty and very long flow transton tme n the core samples. Core analyss technques can be categorzed nto two groups of steady state (SS) and unsteady state (USS) technques. In SS methods, permeablty can be calculated from Darcy s equaton by applyng a constant pressure head or a constant flud flow rate at one sde of the core and montorng the establshed flow rate or pressure head at both sdes. In case of usng SS methods for tght samples, apart from requrng a long tme (days or even weeks) to get an establshed flow along the sample, the mposed hgh pressure gradent creates consderable stress felds nsde the core samples. Dependng on the core mechancal propertes, stress felds can change the structure of the core, whch can result n naccurate measurement of permeablty and porosty. To show the mportance of consderng the effects of hgh pore pressure on formaton characterzaton, Mokhtar et. al. nvestgated the stress dependent permeablty, ansotropy, and wettablty of shale samples and presented the effect of stress on the permeablty of such fractured reservors []. Pulse-Decay method as the frst USS or transent method was developed and used by Brace et al at 1968 [3]. Later, Bonott used the complex pore pressure transent method to measure the permeablty of rocks and examned the ablty of ths method to use them for samples wth hgher permeablty [4]. Generally, USS methods are developed mathematcally based on analyzng the transent response of pressure at the downstream sde of core to the pressure perturbaton (e.g. step or snusodal pressure varaton) at the upstream sde of t [5][6] Excerpt from the Proceedngs of the 016 COMSOL Conference n Boston

2 therefore, they can be conducted n a consderably shorter perod of tme compared to SS methods [7][8]. In pressure oscllaton technque, a snusodal varaton n pressure wth a specfc frequency and ampltude (whch s usually less than 10% of pore pressure) gets appled at the upstream sde of the core. The pressure response at the downstream sde wll be a snusodal wave wth the frequency but wth a phase shft and attenuated ampltude. The pressure response at the downstream s ntally a combnaton of transent response (exponental decay) and steady state response (snusodal). The transent part eventually fades away and only the steady state snusodal wave gets observed. Therefore, the pore pressure oscllaton technque can be consdered as a combnaton of both SS and USS technques. Pressure oscllaton method was orgnally developed as an extenson of a method for measurng hydraulc dffusvty by Kranz et. al. [9]. Later, the theoretcal background, data analyss, and desgn consderatons n experments, were dscussed n detals by Fscher [10]. Bernabé et. al. rearranged the analytcal formulaton and redefned the ampltude attenuaton and phase shft of downstream pressure wave as functons of dmensonless permeablty and dmensonless porosty [11]. Song and Renner appled pressure analyss and flow analyss methods to evaluate the applcaton of pore pressure oscllaton method on two Fontanebleau sandstone samples [1]. Bennon and Goss examned the theory and presented correlatons to desgn snusodal pressure experments to get the frequency response data and characterze the porous medum and ts flud propertes [13]. However, n case of very low permeablty samples, the pressure response at the downstream sde can be greatly affected by the varatons n temperature durng the course of experment and also by the exstng noses from the lab nstruments or the surroundng envronment. In the other words, even small magntudes of error n readng the pressure response at the downstream sde can lead to naccuraces n estmaton of porosty and permeablty. In addton, the theores behnd these technques are derved based on the assumptons of homogenety and sotropy of samples whch are not vald n many cases. Mokhtra and Tutuncu showed the mportance of accurate determnaton of permeablty n shale samples due to ansotropy [14], heterogeneous nature of shale formatons, presence of lamnaton, and exstence of nduced or natural fractures n ther structure [15] t s stll challengng to accurately measure ther propertes. Due to complexty of ncludng the dfferent effects such as temperature, heterogenety, and ansotropy n analytcal formulaton of oscllaton pressure methods, t s not possble to study ther effect by analytcal technques. Computatonal Flud Dynamcs (CFD) as a cheap and robust tool can be always utlzed to mmc physcal condtons that are mpossble, dffcult or very tme consumng to be modeled n laboratory experment. Petroleum engneerng as well as other engneerng felds s beneftng from the advantages of CFD and numercal smulatons. Saleh et. al. utlzed CFD to model the formaton of flter cake on wellbore core surface [16] and Mokhtar used CFD to characterze the ansotropy n organc-rch shale [15]. In ths paper, we smulated the expermental pressure oscllaton technque for permeablty and porosty characterzaton usng CFD module of COMSOL Multphyscs. We compared the results wth analytcal solutons to valdate and ntate the applcatons of CFD for further researches on measurement of permeablty and porosty n samples not ft to the assumptons of analytcal formulatons of ths technque. In next sectons, the theoretcal background and dervaton of analytcal solutons for the flow governng equatons, the methodology, the smulaton results, and the effect of dfferent core and operatonal parameters n experments are presented and dscussed n detals.. Methodology.1 Analytcal Formulaton In pressure oscllaton method, a snusodal pressure wave s appled at the upstream sde of the core and once t travels through the porous meda of core sample, ts ampltude attenuates and ts phase shfts. These two parameters are unque for samples wth dfferent porosty and permeablty therefore, by havng the analytcal formula for the ampltude attenuaton and phase shft as a functon of permeablty and porosty, these two varables can be calculated based on the Excerpt from the Proceedngs of the 016 COMSOL Conference n Boston

3 expermental results. The contnuty and Darcy flow equaton n porous meda can be defned as: ( ) ( u) 0 (1) t x k dp u () dx where, p,, u, k, and are porosty, pressure, densty, flow velocty, permeablty, and vscosty respectvely. Assumng deal gas and combnng (1) and () we get: k p ( ) 0 (3) t x x Based on the assumpton of deal gas we have p t p t therefore, by rearrangng (3) and p defnng as the storage capacty, equaton (3) can be rewrtten as: s / p k p 0 (4) t s x In fact, equaton (4) s the dffuson equaton whch defnes the change n pressure wth respect to tme and dstance along the core sample. In a sample wth length L, the upstream boundary condton for pressure wth frequency, s defned by a snusodal pressure functon of tme: p( L, t) PA sn( t ), x L (5) P A where, and are pressure wave ampltude at upstream reservor and the pressure wave ntal phase. At downstream, boundary condton can be defned by combnng deal gas equaton wth Darcy s equaton. From the Darcy equaton and the assumpton of deal gas at a downstream reservor wth the volume of V D we have: dv ka p (6) dt x dv VD dp (7) dt p dt Defnng d V D / p as the storage of downstream reservor (the requred volume of flud at pressure p to cause one unt change n pressure), equatons (6) and (7) can be combned and the governng condton at the downstream boundary can be derved as: dp ka p 0, x 0 (8) dt d x Usng Laplace transformaton and Brownan ntegral for the nverse Laplace transformaton [10], the permanent and transent solutons of equaton (4) can be defned as [10]: p PA sn( t ) (9) k PA s AL k ( cos sn )[cos( ) d n sl n n sn( n)] s AL n1 k (( ) 4 4 )[( ) cos ( )sn ] n s L d n s AL n s AL d n k n t sl n e In permanent part of soluton, and are the pressure wave ampltude attenuaton and pressure wave phase shft at downstream whch are defned by [10]: s (1 ) cosh[ s (1 ) x] d snh[ s (1 ) x] k k ka k (10) s (1 ) cosh[ s (1 ) L] d snh[ s (1 ) L] k k ka k s (1 ) cosh[ s (1 ) x] d snh[ s (1 ) x] k k ka k arg s (1 ) cosh[ s (1 ) L] d snh[ s (1 ) L] k k ka k (11) where, = the permeablty of core sample = the frequency of pressure wave = the dstance from downstream reservor = the tme at experment k x t P A = the ampltude of oscllated pressure wave A = the cross-sectonal area of core sample = the vscosty of pore flud d = the storage of downstream reservor and n s the roots of s AL tan (1) d s or the sample storage capacty s defned as the combnaton of the core sample), C b (the bulk compressblty of C f (the compressblty of core flud), C r (the compressblty of core sample rock), and (the porosty of core sample) [3]: s Cb C f ( 1 )C (13) In order to smplfy equatons (10) and (11), the dmensonless porosty and the dmensonless can be defned as: permeablty ALs d ATk Ld, (14) 1 1 r e ( snh[(1 ) cosh[( 1 ) ) (15) A r Excerpt from the Proceedngs of the 016 COMSOL Conference n Boston

4 where A r s the upstream to downstream pressure ( 0 A 1) wave ampltude rato and s the phase shft of downstream pressure wave wth respect to upstream pressure wave phase.. Expermental Procedure r Fgure 1 shows the schematc dagram of expermental setup. Before startng the test, the sample gets stablzed at pore pressure and then a snusodal pressure wave wth known ampltude (5% to 10% of pore pressure ) and ntal phase s appled to the upstream sde of a core plug, placed nsde a core holder and confned by pressure. In downstream sde, the pressure value s recorded and by comparng t to ts values at upstream sde, the pressure wave ampltude attenuaton and pressure wave phase shft gets calculated. Then, based on known values of core sample cross secton area A, length of sample L, pressure wave perod T, vscosty of pore flud, and storage of downstream reservor, the P c P 0 P 0 d values of porosty and permeablty k calculated from equaton (15). get (b) Fgure 1: Schematc dagram of expermental setup (a), an example of pressure data recorded at upstream and downstream reservors (b) [17]. At the begnnng of pressure data recordng n downstream, the pressure response s always a combnaton of permanent and transent responses. Therefore, n order to obtan the ampltude attenuaton and phase shft only from the permanent pressure response and to have the effects of transent part faded away, t s requred to do the experment and record the data for at least several perods of pressure wave..3 CFD Modelng We used tme dependent solvers of COMSOL to smulate flow through porous meda. The governng transport equatons are conservaton of mass and Darcy equatons: ( ).( u) 0 (16) t k u p (17) (a) where,, u are porosty of porous doman, densty of pore flud, and the velocty of flud. To mmc the expermental setup condtons and by consderng that the volume of upstream reservor has no effect on pressure response at downstream sde, we created the geometry of CFD model from two parts of core plug and downstream reservor. Core plugs are cylndrcal so, the flow nsde the core s symmetrc and unform over the cross secton of core. As a result, a D model can be used to accurately capture the physcs of problem and save the computatonal tme. Fgure shows the COMSOL CFD model wth a medum mesh resoluton (created by mapped mesh feature of COMSOL and based on the defned dstrbutons on each face) as well as the defned boundary Excerpt from the Proceedngs of the 016 COMSOL Conference n Boston

5 condtons. In CFD models, we dd not consder the effects of exstng stresses generated by the pore pressure on permeablty and porosty of model. Therefore, there was no need to defne the confnng pressure for the model and no-flow boundary condton could mmc the condtons at all surroundng boundares except the upstream boundary. At upstream, the pressure wave was defned by the user as p cpo sn( t 0 ) where c, P o,, t, and 0 are pore pressure wave ampltude rato, pore pressure, pressure wave frequency, tme, and ntal phase of pressure wave. downstream reservor n calculatons usng analytcal formulatons. The Multfrontal Massvely Parallel sparse drect Solver (MUMPS) was used as the tme dependent drect solver to solve the governng equatons for a sngle phase gas flow. In flud propertes secton, the densty of flud can be ether defned as deal gas or the densty can be drectly defned by the user as. In matrx propertes secton, based on the assumptons of homogenous and sotropc porous meda n analytcal formulaton, the value of permeablty should be defned as sotropc permeablty. 0 p / p 0 3. Results and Dscusson 3.1 CFD Model verfcaton (a) (b) Fgure : COMSOL model geometry (a), created computatonal mesh over the model doman (b). At the nterface of core plug and downstream reservor, an abrupt change n meda s characterstcs mght result n dvergence of soluton especally when the core porosty and permeablty are very low and the pressure s hgh. In these cases, the dscontnuty n physcs of porous meda causes hgh gradents n velocty profles at ths nterface and results n lmtatons for transent smulaton tme steppng. As the result, n order to avod stablty ssues, smaller tme steps are requred and overall tme of smulaton wll be much longer. In ths case, we defned the downstream reservor as a second porous meda as a hgh porosty ( 0.9) and 6 m hgh permeablty ( k 10 ) porous meda. Defnng the downstream reservor hgh porosty and permeablty, not only can mmc the reservor as an almost non-porous meda but also, mproves the stablty of soluton and results n several tmes faster convergence of soluton. It s just mportant to consder the real volume of In ths secton, we nvestgate the applcaton of CFD n modellng pressure oscllaton method for homogenous and sotropc cases. A good agreement of smulaton results wth analytcal data can guarantee the applcaton of CFD for modellng and studyng the detals of pressure oscllaton method for more complex cases lke heterogeneous and ansotropc core plugs where the exstng analytcal formulatons are not vald. In fact, equatons (10) and (11) are derved based on smplfcaton assumptons of homogenety and sotropy of core plug. A good number of cases wth dfferent permeablty and porosty were defned and modeled under dfferent downstream reservor szes and pressure wave frequency to verfy the accuracy of CFD n capturng the physcs of problem. Table 1 shows the detals of each smulated case. Table 1: Defned COMSOL CFD models. L D Model k ( m ) (mm) T (s) Excerpt from the Proceedngs of the 016 COMSOL Conference n Boston

6 Other parameters such as length of core plug, magntude of pore pressure, ampltude of pressure wave at upstream, and the P 0 A upstream vscosty of pore flud are kept constant for all models and are summarzed n Table. Table : Parameters of COMSOL CFD models. L(mm) P 0( pa ) A ( pa) upstream ( pa. s) In order to be consstent n modelng, each model was smulated by the tme dependent solver for 36 cycles of ts wave perod usng tme steps of 1 second and at post-processng the values of ampltude attenuaton rato (rato of pressure wave ampltude at upstream to ts value at downstream) and phase shft were calculated. The number of cells n sample part was 50 for all models and dependng on sze of downstream reservor, the number of cells at downstream are 5, 5, and 50. Fgure 3 shows the comparson of pressure data at downstream for CFD model and analytcal soluton durng the entre tme of modeled test. L (the upstream to downstream pressure wave ampltude). As t was expected, for the same wave perod sze of downstream reservor, the hgher the permeablty and porosty, the hgher pressure wave rato and phase shft wll be. As t can be seen from Fgures 4 and 5, the neglgble dfference of results justfes the applcaton of CFD n modelng pressure wave oscllaton technque for calculaton of permeablty and porosty. Fgure 4: Comparson of ampltude attenuaton n CFD models and analytcal soluton results. Fgure 3: Comparson of CFD and analytcal soluton for the model wth permeablty of m porosty of 0.06, pressure wave perod of 100 seconds, and downstream reservor length of 5 mm. As t can be seen n Fgure 3, not only the detals of permanent part of soluton such as ampltude attenuaton and phase shft are perfectly captured wth CFD model but also, the attenuaton of transent pressure magntude (n frst 1 perod of wave) s n very good agreement wth analytcal soluton. Based on ths excellent agreement, we only compared the values of ampltude attenuaton and phase shft of CFD models and analytcal solutons for other models. Fgures 4 and 5 summarze the results of all 1 models (lsted n Table 1) for varous values of A r Fgure 5: Comparson of phase shft n CFD models and analytcal soluton results. Table 3 summarzes the values of relatve error (calculated based on equaton (18)) for CFD model n both ampltude and phase shft of downstream pressure wave. CFDvalue analytcal solutonvalue (%) 100 analytcal solutonvalue E (18) Excerpt from the Proceedngs of the 016 COMSOL Conference n Boston

7 The maxmum error value of 3.79% for pressure wave ampltude and.3% for phase shft show the accuracy of CFD and our COMSOL model n capturng the physcs of the problem. Table 3: Relatve error of CFD models. Model Wave ampltude Phase shft number error (%) error (%) Informaton n Tables 3 shows that n most of the CFD models wth same permeablty and porosty, the magntude of both ampltude attenuaton error and phase shft error, decrease once the perod becomes longer. Ths may due to havng smaller gradents of pressure and velocty along the model doman and t shows the mportance of usng smaller tme steps for models wth smaller wave perods or hgher frequences. Fgure 6 shows the ampltude attenuaton and phase shft for the pressure wave n dfferent locatons along the core n model 8 of Table 1. The pressure profles n Fgure 6 are for steady state part of soluton (no transent effect exsts) and they show the nonlnear attenuaton of wave ampltude and phase shft along core sample. 3. Heterogeneous CFD Models In order to study the physcs and behavor of pressure oscllaton method n heterogeneous core samples, three dfferent heterogenety scenaros (dfferent arrangement of layers) were defned and smulated for two dfferent sets of permeablty and porosty. In all models, the total length of core sample s, the pressure wave perod s, and the length of 400s downstream reservor s L 50mm L D 5mm, the ntal pore pressure s p 510 Pa. Fgure 7 shows the geometry and detals of permeablty and porosty for each model. Layers number 1 have 18 the permeablty of k 10 m and porosty of 0.06 whle layers number and number 3 have permeablty and porosty values of k 10 m, and k 10 m, 0. 1 respectvely. The length of layers and layers 3 s 10mm and the length of layers 1 n models 1, 3, 5, and 6 s 40mm and t s 0mm n models and 4. Model Fgure 6: Pressure wave along length of core sample (model No. 8). Fgure 7: Heterogonous models geometry. Excerpt from the Proceedngs of the 016 COMSOL Conference n Boston

8 All 6 models were smulated usng the same modelng technques for homogeneous cases and the results of ampltude attenuaton and phase shft n downstream reservor locaton are summarzed n Table 4. Table 4: results of heterogeneous CFD models. Model Ampltude Phase shft number attenuaton As t can be seen from the results, n models 1 to 6, the ampltude attenuaton ncreases once the hgh permeablty/porosty layers move toward the downstream reservor. However, ths pattern s not observed n phase shft results and samples wth the layer of hgh permeablty/porosty at the mddle show greater phase shft values. The dfference between the responses of samples wth same layers but dfferent order of placement along the core results n dfferent calculated values of permeablty and porosty. In fact models 1 and 3 or 4 and 6 are the same and only the locaton of upstream and downstream reservors are dfferent n them but stll a sgnfcant dfference n ther response values s gettng observed and ths mples the sgnfcance of further study on accuracy and applcaton of pressure oscllaton technque for heterogeneous and/or ansotropc cases. 4. Conclusons Laboratory experments to measure the permeablty and porosty usng pore pressure oscllaton method use analytcal formulatons that are derved based on smplfcaton assumptons such as homogenety and sotropy of core samples. Not only these assumptons are not vald for all cases, but also t s not possble to derve analytcal formulatons for all heterogeneous and ansotropc cases. Therefore, numercal smulaton can be used as a robust tool to study dfferent models and nvestgate the response of core samples to pressure wave n dfferent scenaros. The pressure oscllaton method was successfully smulated usng COMSOL CFD and t showed excellent agreement wth the analytcal results. Overall, n CFD modelng wth constant tme step, models wth longer pressure wave perod showed less computatonal errors compared to those wth shorter perod or hgher frequency. It was observed that by ncreasng the perod of pore pressure wave the ampltude attenuaton and phase shft decrease. In addton, the results showed n models wth the same porosty and permeablty, the larger the sze of downstream reservor, the hgher the phase shft and ampltude attenuaton would be. In order to have less ampltude attenuaton and phase shft n laboratory experments, t s mportant not to have wave frequency hgher than certan values and keep the sze of downstream reservor as small as possble. Fnally, three dfferent scenaros n form of 6 models of heterogenety were defned and smulated. The sgnfcant dfference n response of each model at downstream reservor shows the mportance of further study on behavor of pressure oscllaton method n measurng the permeablty and porosty or heterogeneous and/or ansotropc core samples. 5. References [1] Wang, Y. and Knabe, R. J., Permeablty Characterzaton on Tght Gas Samples Usng Pore Pressure Oscllaton Method, PETROPHYSICS, 5 (6), p (011). [] Mokhtar, M., Alqahtan, M., Tutuncu, A., Yn, X., Stress-Dependent Permeablty Ansotropy and Wettablty of Shale Resources, Unconventonal Resources Technology Conference, Denver, Colorado, Aug 1-14 (013). [3] Brace, W. F., Walsh, J. B. and Frangos, W. J., Permeablty of Grante under Hgh Pressure, Journal of Geophyscs, 73(6), p (1968). [4] Botnott, G. N., Use of Complex Pore Pressure Transents to Measure Permeablty of Rocks. SPE Annual Techncal Conference and Exhbton, San Antono, Texas, Oct 5-8, (1997). [5] Jones, S. C., A rapd accurate unsteady-state Klnken-berg permeameter, SPE Reservor Evaluaton & Engneerng, 1(5), p (197). Excerpt from the Proceedngs of the 016 COMSOL Conference n Boston

9 [6] Hseh, P. A., Tracy, J. V., Neuzl, C. E., Bredehoeft, J. D., and Sllman, S. E., A transent laboratory method for determnng the hydraulc propertes of tght rocks I. Theory; II. Applcaton, Internatonal Journal of Rock Mechancs and Mnng Scence, 18(3), p (1981). [7] Dcker, A. I. and Smts, R. M., A practcal approach for determnng permeablty from laboratory pressure-pulse decay measurements, Internatonal Meetng on Petroleum Engneerng, Tanjn, Chna, Nov. 1-3 (1988). [8] Egermann, P., Lenormand, R., Longeron, D., and Zarcone, C., A fast and drect method of permeablty measurement on drll cuttngs, SPE Reservor Evaluaton & Engneerng, 8(4), (00) [9] Kranz, R. L., Saltzman, J. S., and Blacc, J. D., Hydraulc dffusvty measurements on laboratory samples usng an oscllatng pore pressure method, Internatonal Journal of Rock Mechancs and Mnng Scence, 7(5), p , (1990). [10] Fscher, G. J., Chapter 8 The Determnaton of Permeablty and Storage Capacty: Pore Pressure Oscllaton Method, Internatonal Geophyscs, 51, p (199). [11] Bernabe, Y., Mok, U., and Evans, B., A note on the oscllaton flow method for measurng rock permeablty, Internatonal Journal of Rock Mechancs & Mnng Scence, 43, p (006). [1] Song, I., Rathbun, I., and Saffer, D., Uncertanty analyss for the determnaton of permeablty and specfc storage from the pulsetransent technque, Internatonal Journal of Rock Mechancs & Mnng Scences, 64, p (013). [13] Bennon, D. W., Goss, M. J., A snusodal pressure response method for determnng the propertes of a porous medum and ts n-stu flud, Fall Meetng of the Socety of Petroleum Engneers of AIME, New Orleans, Lousana, Oct 3-6 (1971). [14] Mokhtar M., Tutuncu A.N., and Botnott G.N., Intrnsc Ansotropy n Fracture Permeablty, Interpretaton, 3(3), p (015). [15] Mokhtar M. & Tutuncu A.N., Characterzaton of Ansotropy n the Permeablty of Organc Rch Shales, Journal of Petroleum Scence and Engneerng, 133, p (015). [16] Saleh, S., Madan, S.A., Kran, R., Characterzaton of drllng fluds fltraton through ntegrated laboratory experments and CFD modelng, Journal of Natural Gas Scence and Engneerng, 9, p (016). [17] Jn G. et al. Permeablty Measurements of Organc-Rch Shale Comparson of Varous Unsteady-State Methods, SPE Annual Techncal Conference and Exhbton, Houston, Texas, Sep 8-30 (015). Excerpt from the Proceedngs of the 016 COMSOL Conference n Boston