A Case Study of Fluid Transport in Shale Crushed Samples: Experiment and Interpretation

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1 SCA /12 A Cse Study of Fluid Trnsport in Shle Crushed Smples: Experiment nd Interprettion Tinho Wu, Zheng Jing, Dongxio Zhng Energy nd Resources Engineering, College of Engineering Peking University, Beijing, Chin This pper ws prepred for presenttion t the Interntionl Symposium of the Society of Core Anlysts held in Avignon, Frnce, 8-11 September, 2014 ABSTRACT Pulse-decy experiment performed on crushed smples hs been shown to be promising method for mesuring mtrix permebility of extremely low permeble formtions, like shle reservoir, since it is much fster thn the trditionl trnsient tests performed on core plugs. Due to the fct tht the flow of methne in the nnoscle shle mtrix involves complex mechnisms, such s the trnsition flow or slip flow, the physicl model plys key role in resonble interprettion of experimentl dt. The objective of this study is to mesure the intrinsic permebility of crushed shle smples through pulsedecy experiment, interpret the dt with comprehensive model, including Knudsen diffusion s well s dsorption, nd demonstrte the necessity of considering these effects from new perspective bsed on moleculr dynmics (MD) simultion. The MD simultion ddresses the necessity of considering the diffusion nd dsorption effects. A more ccurte model to clculte shle permebility is pplied. By using this model, significnt improvement in the modeling of nnoscle gs flow nd interprettion of intrinsic permebility experimentl dt cn be chieved. This study leds to the following findings: 1) the distribution of gs toms number density cross the nnopore is not uniform, but the gs toms hve the similr selfdiffusion velocity, thus totlly different mss flow rte nd more complicted mechnisms my pper; 2) the diffusion effect nd dsorption effect will chnge the flow regime nd my even dominte the flow regime in ultr-tight porous medi; 3) the comprehensive model cn describe the flow behvior very well for most of the shle smples; 4) there my exist multi-porous medi phenomenon in shle mtrix. INTRODUCTION Permebility is one of the most fundmentl properties for reservoir evlution nd modeling. However, shle permebility hs not yet been fully understood becuse of the complex nnoscle mechnisms nd the time consuming experiments. Accurte nd fst determintion of shle permebility is chllenging, in both experimentl nd theoreticl investigtions. Trditionl stedy-stte gs permebility test method is not pplicble for shle smple becuse it is time consuming nd the flow rte is instble nd too smll to

2 SCA /12 detect. Currently, there re two direct methods in common use for determining permebility of extremely tight rocks in the lbortory, nmely the trnsient pulse-decy method using core plug (Dicker et l. 1988; Jones 1997) nd the crushed smple method (Luffel et l. 1993; Egermnn et l. 2005). Pulse-decy technique on core plug pplies pressure pulse on the upstrem end of confined core nd mesures the pressure chnges in upstrem nd downstrem reservoir, this technique cn mesure permebility s low s 10-9 md, theoreticlly (Cui et l. 2009). Pulse-decy experiment performed on crushed smples hs been shown to be n lterntive for shle formtions becuse it is cheper nd fster thn trditionl trnsient technique, lthough it is restricted to experimentl condition in the bsence of overburden pressure. Shle mtrix is considered s kind of highly compcted sediment with n verge grin rdius of usully smller thn cm nd complex nnopores (Kundert et l. 2009; Sondergeld et l. 2010). Porosity nd permebility in such systems re typiclly ultrlow, nd the pore size is thought to be comprble to the men free pth of methne. In this cse, the gs solid interction hs gret effects on the flow through the porous medi, therefore the widely used first-order Klinkenberg Correction will result in significnt devition, wheres using high-order (e.g. second-order) Klinkenberg correction (Tng et l. 2005; Zhu et l. 2007; Zirni nd Roberto 2012) could led to better result. Among the mjority of the previous work, one of the most widely ccepted pproches is to dopt the conception of intrinsic permebility nd pprent permebility nd pply the pprent permebility correction fctor (Beskok nd Krnidkis 1999; Jvdpour 2009; Civn 2010; Civn et l. 2011, 2012; Skhee-Pour nd Brynt 2012). It hs been shown tht the multi-mechnism, including Knudsen diffusion, slip flow, dsorption, plys criticl roles nd thus cnnot be neglected. In ddition, most of the pprent permebility correltion is bsed on the correction of continuum flow, the ssumption of which is no longer perfectly vlid in the nnoscle flow. Under this circumstnce, moleculr dynmics (MD), which does not require the ssumption of continuum flow ssumption nd models the flow behvior essentilly from the physicl principles, is nother wy to understnd the microscopic phenomenon. Some results of previous work bout MD simultions reveled tht considering the density distribution profile of gs molecules will led to better greement with high-order boundry condition of slip flow nd experimentl results, even suggested tht significnt djustment in shle storge cpcity clcultion is necessry (Zhng et l. 2010; Ambrose et l. 2012). In this pper, the MD simultion of methne in kerogen is crried out nd found to be very helpful for understnding the gs flow mechnisms t microscopic scle in shle formtion. As cse study, we investigte shle mtrix permebility experimentlly nd interpret the experimentl dt with comprehensive model. THEORETICAL BACKGROUND MD simultion of gs trnsport in nnopores is often chieved by the use of equilibrium MD (EMD) or non-equilibrium MD (NEMD). In order to overcome some disdvntges of trditionl EMD nd NEMD methods, dul-control volume grnd cnonicl MD

3 SCA /12 (DCV-GCMD) method is introduced to investigte the gs trnsport behvior in nnoscle porous medi (Crcknell et l. 1995; Skoulids et l. 2002). Firouzi nd Wilcox (2012, 2013) performed DCV-GCMD simultions of gs flow on crbon-bsed nnopores. In this study, the EMD simultion of methne is implemented to determine the density distribution nd describe gs self-diffusion phenomenon. In the simultion, the gs molecules re represented by the Lennrd-Jones prticles, with pir interctions pproximted by the LJ potentil: u LJ r r where is the depth of the potentil well nd is the finite distnce t which the interction is zero. The interction potentil between fluid prticle nd pore wll is given by the potentil of Steele (Steele 1974): u sf sf sf sf 2 5 r r r where is the spce between djcent wll moleculr lyers nd sf denotes solid-fluid interction. The procedure nd pprtus of permebility test of crush smples is the sme with the Helium pycnometer, which is well reviewed by Cui et l. (2009). Gs trnsport in tight porous rock cn be described by diffusion type eqution, which ssumes tht Drcy s lw previls nd the mesured pprent permebility cn be corrected by the Knudsen s correction, with gs pressure or density s the primry unknowns. Therefore, the onedimensionl mss blnce eqution for sphericl shpe prticle cn be described s follows (Cui et l. 2009): q 1 2 k p (1 ) r 2 t r r r t where is porosity, is gs density, t is time, q is dsorbte density per unit smple mss, r is displcement or loction in the prticle, is gs viscosity, p is pressure nd the pprent permebility k is correlted with intrinsic permebility k s follows (Beskok nd Krnidkis 1999): k 3 (1) (2) (3) k f ( Kn) (4) where f ( Kn ) is dimensionless correction fctor determined by 4Kn f ( Kn) 1 Kn1 1 Kn (5)

4 SCA /12 where Kn is Knudsen number, describing the flow regime which is either slip flow ( Kn 0.1) or trnsition flow ( 0.1 Kn 10 ) during shle permebility test, which is given by: Kn (6) R where is the molecules men free pth nd R h is representtive length (men hydrulic rdius of flow tubes in porous medi, for exmple). The is the dimensionless rrefction coefficient whose form nd coefficients cn be given by Civn et l. (2010). 1 A 01, ; A ; B B Kn By rerrnging Eq. (3) we hve the blnce eqution with respect to gs density (Cui et l. 2009): where c g is the gs compressibility, k 1 t c K r r t 2 2 r g (1 ) d c g h (7) (8) 1 d (9) dp nd the gs density is given s rel gs stte of eqution p / zrt, nd K d is the derivtive of dsorbte density with respect to the gs density. The q is given s Lngmuir gs dsorption isotherms: where V L nd K d q (10) p q V L p p L p L re Lngmuir volume nd pressure, respectively. By defining pprent trnsport coefficient K: k K c (1 ) K Eq. (3) becomes the diffusion type eqution: g d (11) (12)

5 SCA /12 K 2 r 2 t r r t For rock prticles, the initil nd boundry conditions re s follows: 0 (13) for 0 r R t t 0 (14) c0 for r R t t 0 (15) 0 t r 0 r k where N is the equivlent prticle number, 2 4 N R Vc t r R cg r t 3 4 b (16) (17) 3M N (18) R M is the smple mss, R is the verge prticle rdius, V c is the totl volume of open spce in reference nd smple cells (excluding the pore within the smple), b is the smple bulk density, 0 is the initil gs density in the smple prticles pore spce before gs expnsion, nd c0 is the verge initil gs density in the void volume in both smple cell nd reference cell when the vlve between the smple cell nd reference cell is turned on by ssuming tht the gs reches equilibrium immeditely. Cui et l. (2009) suggested fitting the permebility through nlyticl solutions for ltetime or erly-time technique. However, the nlyticl solutions re derived under certin ssumptions nd conditions, which re not suitble for model dignosis nd multiprmeter fitting. Therefore, we use the method proposed by Civn et l. (2012), which determines the best fitted vlues by mtching the simultor-bsed numericl solution with experimentl dt. Firstly, this method ssumes tht different tests mrked by i1,2,..., X re conducted for the sme smple. Ech smple provides the discrete vlue of the system s pressure tken t different times mrked by j 1, 2,..., Yi for the ith test. Then, this method pplies lest-squre regression using certin vlues, e.g. pressure or pressure grdient, clculted by numericl solution nd mesured vlues. This objective is ccomplished by minimizing the following root-men-squre reltive devition (Civn et l. 2012): E i1 j1 mesured i, j 2 1 X Y x clculted 1 XY x (19) where x is the specified vlues which cn be chosen ccording to the model, e.g. gs density in this study.

6 SCA /12 We cn determine prmeters Qk : k 1,2,..., S of the model described in the preceding prgrphs to minimize the root-men-squre reltive devition given by solving Eq.(19) : Results nd Discussion E Q 1. Moleculr dynmic simultion k 0, k 1,2,..., S. We implement the EMD simultion of methne trnsport in prllel-crbon-plte slitshpe pore, which represents the kerogen, to investigte the methne trnsport behvior in nnopores. A 3D simultion box is constructed with the length of 30 nm, 4 nm nd 2 nm in the x, y nd z direction (Figure 1), respectively. The distnce between the prllel wlls represents the pore dimeter of shle, corresponding to the pore-size distribution shown in the next section. Periodic boundry condition is pplied on x nd z direction, nd y- direction is confined by the crbon wlls chrcterized by potentil model with =0.335 nm. For the toms LJ prmeters, we use 0.35nm nd / k 28K for crbon toms, CH 0.381nm nd / k CH4 B K for CH 4 (Crcknell et l. 1995). The Lorentz-Berthelot mixing rules re used to determine the size nd energy prmeters between the gs molecules nd wll toms (Allen et l. 1989): C C B (20) 1 ij i j (21) 2 (22) ij i j Then, the prmeters for solid-gs interctions of LJ potentil re nm nd / k 64.4K. The cut-off distnce is sf B 3 CH4, nd the long-rnge corrections re not pplied. The totl number of simulted gs molecules is 682, the temperture is K, nd the pressure of the system is bout 10MP. We set the time step to be 1 fs nd run the simultion for steps. The results re shown in Figures 2~3. Figure 1 shows the simulted domin with snpshots of the molecules for the MD simultion. The blue lines show the loction of the prllel crbon wlls. Figure 2 revels tht the density distribution indeed exists below the scle of 2 nm from the wll, t which the toms number density ner the surfce is much higher thn the center prt. However, Figure 3 shows tht the velocity (self-diffusion) profile is lmost flt, which is consistent with the results in Firouzi nd Wilcox s (2012) study. Moreover, the observtion tht the toms ner the solid wll re of higher number density but hve the sme totl velocity s tht of the center indictes tht the mss flow ner the wll my be lrger thn the center, resulted from the substntil solid-gs interction nd complex mechnisms. sf

SCA2014-071 7/12 Figure 1 Sketch Mp of Simulted Domin (with Snpshots of Molecules) Figure 2 Gs Atom Number Density long Y-Direction Figure 3 Atoms Averged Velocity Although this MD simultion only

7 SCA /12 Figure 1 Sketch Mp of Simulted Domin (with Snpshots of Molecules) Figure 2 Gs Atom Number Density long Y-Direction Figure 3 Atoms Averged Velocity Although this MD simultion only provides n equilibrium MD cse, chrcterizing the phenomenon of self-diffusion t nnoscle, it shows totlly different mechnism from norml viscous flow with the slip effect nd indictes tht dsorption my hve greter effect thn expected, not only on the mss flow rte but lso on the flow regime.

8 SCA /12 Therefore, the diffusion nd dsorption effect must be tken into ccount for the intrinsic permebility estimtion for extremely tight rocks, nd further investigtion is lso required. In this study, we use n existing widely ccepted model to determine the intrinsic permebility from experimentl dt. The nnoscle NEMD simultion under pressure grdient nd the effects of diffusion nd dsorption on flow regime will be investigted in our future study. 2. Bsic petrophysicl test In this study, the rock smples re from the Trissic shle in Ordos bsin, Chin. A series of bsic petrophysicl tests were performed on the sme core smples, which were lso crushed, well prepred nd dried for more thn 24 hours. The petrophysicl tests include bulk density nd pore size distribution mesured by mercury injection cpillry pressure (MICP), smple skeleton density nd porosity with helium pycnometer, nd minerl composition determintion with XRD. The results re shown in Tble 1 nd Figure 4. Tble 1 Bsic Petrophysicl Prmeters Determined from Experimentl Tests Prmeters Results Porosity 12.58% Bulk Density g/cm 3 Minerl Composition Qurtz 42.5% Albite 33.0% Illite 24.5% Figure 4 Pore Size Distribution (Represented by pore surfce re distribution) Since CH 4 nd CO 2 re used to perform crushed smples tests, firstly their dsorption isothermls need to be determined experimentlly s the input prmeters for the permebility clcultion. The pprtus is lso the sme with the Helium pycnometer. We

9 SCA /12 use Helium to test the open spce of the device nd the pore spce of the smple. Then, the CH 4 nd CO 2 dsorption experiments re conducted under different pressures. It is ssumed tht both CH 4 nd CO 2 follow the Lngmuir dsorption type. The finl Lngmuir dsorption isotherml curves for permebility clcultion re shown in Figure Permebility test nd interprettion Figure 5 Lngmuir Isotherml Curves of Shle Smples The permebility tests re conducted under different pressures for certin smple nd interpreted ccording to the method described in previous section. The intrinsic permebility k, verge prticle rdius R nd men hydrulic rdius R h re chosen s fitting prmeters nd determined by tril nd error to mtch the pressure dt. Then, the pprent permebility vlues for CH 4 nd CO 2 under different conditions cn be clculted. The best-estimted prmeter vlues re listed in Tble 2. The fitted verge prticle rdius is smller thn the expected vlue, which uses 10/18 mesh (bout 1-2 mm) for prepring the crushed smple since the shpe of most prticles is slice. The men hydrulic rdius corresponds to the pore size distribution shown in Figure 4. Some sets of results re shown in Figure 6 nd Figure 7, tested with CH 4 nd CO 2, respectively. Figure 6 indictes tht the pressure hd two stges of drwdown, in which both lte-time nd erly-time dt cn be well fitted independently (1.8 nd nd 4.2 nd, respectively). However, good fitting result cnnot be chieved for the full rnge of dt. Figure 4 shows tht there re two peks in the pore-size distribution curve, 9nm nd less thn 3nm, respectively, indicting tht the smple my hve similr property s the dul-porous medi. One wy to interpret this phenomenon is s follow: the gs penetrtes the smple through both reltively lrge nd smll pores, then the pressure in the lrge pores reches the sme pressure with the smple cell (outside of the prticle), but the pressure grdient still exists between the smll pores nd lrge pores. Therefore, pressure decy in the erly-time nd lte-time is dominted by reltively lrge pores nd smll pores, respectively.

10 SCA /12 Tble 2 Best-estimted Prmeter Vlues nd Clculted Apprent Permebility CH 4 CH 4 (Erly-time) (Lte-time) CO 2 Intrinsic Permebility k (nd) Averge Prticle Rdius R (mm) Men Hydrulic Rdius R h (nm) Representtive Apprent Permebility k (nd, under 5MP, K) Figure 6 Fitting Results of Permebility Tests with CH 4 (Left: Fit the lte-time dt only; Right: Fit the erly-time dt only) Figure 7 Fitting Results of Permebility Tests with CO 2 for Different Pressures However, the phenomenon is not observed in the CO 2 test. This is due to the higher pprent permebility of CO 2 thn CH 4 (Tble 2), so tht the erly-time behvior like tht in CH 4 test cnnot be detected or the behviors hve been mixed together. Therefore, further experimentl investigtion should lso focus on providing more vrious nd wellcontrolled pressure nd temperture condition nd even shle s microstructure observtion.

11 SCA /12 CONCLUSION The MD simultion results revel tht the toms number density ner the wll surfce is much higher thn tht in the center prt of nnopores due to dsorption, wheres the toms ner the wll hs the sme order of self-diffusion coefficient with the toms in the center. This results in totlly different velocity profile, especilly ner the boundry t the interfce of solid nd gs. The phenomenon indictes tht diffusion nd dsorption re criticl in nnoscle shle mtrix, nd my even chnge the flow regime. Therefore, their effects must be tken into ccount for the intrinsic permebility estimtion for tight rocks nd n otherwise simplified model my led to significnt devition. Some sets of crushed shle smples hve been tested using the trnsient pulse-decy method. The experimentl dt re interpreted with comprehensive model, considering the effects of Knudsen diffusion nd dsorption, with the implicit or simultor-bsed fitting method insted of the trditionl nlyticl pproximtion method. The interpreted results show tht there exists multi-porous medi phenomenon in shle mtrix. REFERENCES 1. Allen, M. P., nd D. J. Tildesley. "Computer simultion of liquids, 1987." New York: Oxford 385 (1989). 2. Ambrose, R. J., Hrtmn, R. C., Diz-Cmpos, M., Akkutlu, I. Y., & Sondergeld, C. H. "Shle gs-in-plce clcultions prt I: new pore-scle considertions." SPE Journl (2012): Beskok, Ali, nd George Em Krnidkis. "Report: model for flows in chnnels, pipes, nd ducts t micro nd nno scles." Microscle Thermophysicl Engineering 3.1 (1999): Civn, Fruk, Chndr S. Ri, nd Crl H. Sondergeld. "Determining shle permebility to gs by simultneous nlysis of vrious pressure tests." SPE Journl (2012): Civn, Fruk, Chndr S. Ri, nd Crl H. Sondergeld. "Shle-gs permebility nd diffusivity inferred by improved formultion of relevnt retention nd trnsport mechnisms." Trnsport in Porous Medi 86.3 (2011): Civn, Fruk. "Effective correltion of pprent gs permebility in tight porous medi." Trnsport in Porous Medi 82.2 (2010): Crcknell, Roger F., Dvid Nicholson, nd Nichols Quirke. "Direct moleculr dynmics simultion of flow down chemicl potentil grdient in slit-shped micropore." Physicl Review Letters (1995): Cui, X., A. M. M. Bustin, nd Robert M. Bustin. "Mesurements of gs permebility nd diffusivity of tight reservoir rocks: different pproches nd their pplictions." Geofluids 9.3 (2009): Dicker, A. I., nd R. M. Smits. "A prcticl pproch for determining permebility from lbortory pressure-pulse decy mesurements." Interntionl Meeting on Petroleum Engineering. Society of Petroleum Engineers, SPE-17578, 1988.

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Follow this and additional works at: Part of the Materials Science and Engineering Commons

Follow this and additional works at: Part of the Materials Science and Engineering Commons Engineering Conferences Interntionl ECI Digitl Archives 5th Interntionl Conference on Porous Medi nd Their Applictions in Science, Engineering nd Industry Refereed Proceedings Summer 6-4-4 Numericl simultion