Modeling Non-aqueous Phase Liquid Displacement Process

Transcription

1 2007 Petoleum Science Vol.4 No.3 Modeling Non-aqueous Phase Liquid Displacement Pocess Yang Zhenqing, Shao Changjin, Zhou Guanggang and Qiu Chao (Physics Depatment, China Univesity of Petoleum, Beijing , China) Abstact: A poe-netwok model physically based on poe level multiphase flow was used to study the wate-non-aqueous phase liquid (NAPL) displacement pocess, especially the effects of wettability, wate-napl intefacial tension, the faction of NAPL-wet poes, and initial wate satuation on the displacement. The computed data show that with the wettability of the mineal sufaces changing fom stongly wate-wet to NAPL-wet, capillay pessue and the NAPL elative pemeability gadually decease, while wate-napl intefacial tension has little effect on wate elative pemeability, but initial wate satuation has a stong effect on wate and NAPL elative pemeabilities. The analytical esults may help to undestand the mico-stuctue displacement pocess of non-aqueous phase liquid and to povide the theoetical basis fo contolling NAPL migation. Key wods: Non-aqueous phase liquid, poe-netwok model, capillay pessue, elative pemeability 1. Intoduction Non-aqueous phase liquids (NAPLs) ae wate-immiscible hydocabons in the subsuface that exhibit behavio and popeties diffeent fom dissolved contaminants. While dissolved contaminants ae invisible to the naked eye and migate with the flow of goundwate, NAPL foms a visible, sepaate oily phase in the subsuface and its migation is govened by gavity, buoyancy, and capillay foces (Bedient, et al., 1994). When being eleased at the suface, fee-phase o mobile NAPL is foced into the poes of the soil/aquife matix by the hydostatic pessue on the continuous body of NAPL. Because NAPL is unde pessue, it can ente even vey small poes and factues in the subsuface as long as the oiginal NAPL enty point, such as a waste pond o leaking undegound stoage tank, is active. When the supply of new NAPL is exhausted, howeve, the pessue on the fee-phase NAPL is emoved and small blobs of NAPL snap-off o bypass the once continuous NAPL body and become tapped in individual poes o small goups of poes by capillay foce. Any pediction of tempoal and spatial distibution of these fluids is sensitive to the macoscopic desciptos of the pemeable solid (absolute pemeability) and the multiple fluids (elative pemeability and capillay pessue). These macoscopic desciptos ae the volume-aveaged continuum functions oiginated fom the displacement mechanisms at poe scale (Bea, 1972). Theefoe, the macoscopic tanspot of immiscible fluids can be pedicted, if thee ae an adequate desciption of the essential geomety and topology of the poe space, and a sufficient epesentation of the multiphase flow physics. Nowadays, poe netwok models have become indispensable in the investigation of multiphase flow in poous media encounteed in petoleum and envionmental applications. Numeical netwok models with vaious poe-space epesentations have been used to investigate many phenomena elated to multiphase flow in poous media, including seveal ecent papes investigating intefacial aeas in multiphase flow. Lowy and Mille (1995) investigated the elationship between fluid satuation and fluid-fluid intefacial aeas by using an iegula netwok stuctue of spheical nodes and cylindical tubes. Reeves and Celia (1996) developed a netwok model consisting of spheical poes and consticted cylindical tubes in a egula cubic netwok, and elated intefacial aeas to both capillay pessue and satuation. These vaious poe netwok models wee eviewed by Blunt (2001). Howeve most of these models ae geneated stochastically and usually do not epesent natual pemeable media. The ecent advancements in ock imaging have esulted in a quantitative jump in the poe netwok model capabilities (Øen, et al., 1998; 2002; 2003; Patzek, 2001), and thus the Patzek model was used in this pape. 2. Poe netwok model 2.1 Geomety desciption The poe netwok model used in this pape is a ealistic epesentation of a sample of Beea sandstone econstucted fom the 3D mico-focused X-ay CT image, povided by D. Suicmez in Impeial College, London. Detailed desciption of econstuction and its validation wee discussed by Øen, et al. (1998; 2002; 2003) and Patzek (2001). The netwok, with a spatial egion of the volume of 3 3 mm 3, consists of 12,167 poes and 29,827 thoats.

2 Vol.4 No.3 Modeling Non-aqueous Phase Liquid Displacement Pocess 41 Each poe o thoat is epesented by a duct with a tiangula, squae o cicula coss-section, chaacteized by an inscibed adius which contols the theshold capillay enty pessue, effective cone angles which contol the amount of fluid held in wetting layes, and an effective volume which contols the mobile (non-clay bound) satuation. In this model, 10 pecent of these elements ae squaes, 5 pecent ae cicula, and the est ae iegula tiangles. The connection numbes vaies fom 1 to 12, with an aveage of 4.8. The poosity of the netwok is 36% and its absolute pemeability is 2.5 Dacy. 2.2 Poe and thoat sizes The poe size distibution in this model follows the tuncated Weibull distibution. And the inscibed poe adius can be descibed as follows: ch ( max min η ) 1 ch η = { ln[(1 x)e + x]} + (1) whee x is a andom numbe between 0 and 1; max, min and ch ae the maximum, minimum and chaacteistic inscibed adii, espectively, μm; and η is a dimensionless paamete. Hee we set max =100 μm, min =0.1 μm and η =1.5. The distibution of thoat lengths also obeys the tuncated Weibull distibution, and the minimum thoat length is set at 20.0 μm and the maximum thoat length is 50.0 μm. 2.3 Poe and thoat shapes The shapes of poes and thoats in the netwok ae detemined by shape facto, G. The shape facto is a dimensionless vaiable elating the coss-sectional aea, A, of the element to its peimete, P. A G = (2) 2 P Squae and cicula elements have fixed shape factos of and , espectively. The shape facto of tiangula elements obeys the tuncated Weibull distibution, anging fom 0 (slit-shaped) to (equilateal). 2.4 Capillay enty pessue Capillay enty pessue is the capillay pessue at which the non-wetting phase fist displaces the wetting phase. In ode fo the NAPL to ente a poe, the diffeential pessue between the NAPL and the wate must exceed the theshold capillay enty pessue of the poe. The capillay pessue is given by the min Young-Laplace equation: p = p p = σ ( ) (3) NAPL W NW 1 2 whee NW is the NAPL-wate intefacial tension; and 1 and 2 ae the pincipal adii of cuvatue of the inteface. Fo a cicula poe, Eq. (3) can be simplified as: p 2σ cosθ NW cnw = NWR (4) whee NWR is the eceding oil-wate contact angle; and is the inscibed adius (Dullien, 1992). Eq. (4) shows that the smalle the poe spaces, the highe the capillay pessue. The minimum capillay enty pessue is the capillay pessue at which the non-wetting phase (NAPL) fist displaces the wetting phase (wate) contained in the lagest poe thoat within a wate-wet poe netwok. Only a vey small faction of netwok elements has a cicula coss-section. Fo polygonal shaped elements the expession fo the capillay enty pessue is complex as the wetting fluid emains in the cones as ac menisci. In this case, the capillay enty pessue can be calculated with the method poposed by Maye and Stowe (1965)(Mason and Moow, 1991) and Pincen (1970), and this expession was genealized by Øen, et al. (1998; 2002; 2003): σ cos θr(1 + 2 G) pc = Fd( θ R, G, β ) (5) whee F d is a dimensionless coection facto fo wetting fluids etained in the cones; and is the cone half angle of a tiangula coss-section. 3. Poe level displacement mechanisms and pocess Thee ae two basic models of multiphase flow in poe netwoks: dynamic and quasi-static. In dynamic models, capillay, gavity, and viscous foces in the fluids ae accounted fo simultaneously. In quasi-static models, capillay foce dominates; gavity modifies the ode of magnitude of capillay pessue. In this study the quasi-static appoach was used and the effect of viscous and buoyancy foces was ignoed. In the pocess of simulating two-phase flow in poe netwoks, the displacing fluid is injected though an extenal esevoi which is connected by poe thoats to each poe body on the inlet side of the netwok. The displaced fluid escapes though the outlet face on the

3 42 Petoleum Science 2007 opposite side. Peiodical bounday conditions ae imposed along the sides paallel to the main diection of flow. The displacing mechanism is citical fo modeling micoscopic wate-napl displacement, theefoe a suitable physical displacement should be adopted. In pimay dainage, NAPL displaces wate, the only invasion mechanism is piston-type displacement since initially the netwok is filled with wate; wheeas in seconday imbibition wate displaces NAPL, pat of the netwok has been invaded by NAPL, and the displacement mechanisms include piston-type, snap-off and coopeative poe-body filling. This classification of poe level events was fist pesented by Lenomand, et al. (1983), and the calculation of the coesponding capillay enty pessues was pesented by Øen, et al. (1998; 2002; 2003) and Patzek (2001). The step fo pimay dainage ae summaized as follows: 1) Calculate all piston-type capillay enty pessues of links and aange them in a stictly ascending ode. 2) At each capillay pessue level, find all links that have capillay enty pessue less than the cuent level of capillay pessue, have not yet been invaded, and have at least one of the two attached nodes filled with NAPL. 3) Invade these links and the attached nodes if applicable. A node is eady fo invasion if it is occupied by wate and its piston-type capillay enty pessue is less than the cuent level of capillay pessue. 4) New links may now become available to invasion because the attached nodes have been invaded. 5) Repeat steps 2-3 until no futhe nodes o links can be invaded. 6) Having invaded all possible links and nodes, calculate the oveall (aveage) wate-phase satuation in the netwok. 7) Poceed to the next capillay enty pessue level and epeat steps 2-6 until the specified maximum capillay enty pessue is eached. Similaly, the steps fo seconday imbibition ae: 1) Seconday imbibition stats afte a maximum capillay pessue level in pimay dainage has been eached. 2) Stating fom the maximum capillay pessue level, invade links o nodes with wate in the ode of deceasing piston-type, and snap-off capillay enty pessues. All these pessues ae soted in a single list in a stictly descending ode. 3). NAPL is displaced by the invading wate in the altenating piston-type and snap-off manne, until the espective capillay enty pessue exceeds the cuent capillay pessue level. 4) Befoe poceeding to the next capillay pessue level, update the satuations. 5). Repeat step 3-5 at the next, lowe capillay pessue level. 4. Results and discussion 4.1 Effect of wettability The flow behavio in poe netwoks with diffeent wettabilities, wate-wet (advancing contact angles 20 to 55 ), intemediate-wet (55 to 120 ), and NAPL-wet (120 to 150 ), was compaed. Fig. 1 shows that diffeent wetting conditions esult in diffeent capillay pessues and elative pemeabilities, theeby diffeent two-phase flow behavio. Wettability has a significant effect on the capillay pessues and elative pemeabilities. With the wettability of the poe netwok changing fom wate-wet to NAPL-wet, capillay pessues and NAPL elative pemeability decease gadually. Fig. 1 Effect of wettability of poe netwok on capillay pessues and elative pemeabilitis In the case of NAPL-wet poe netwok, wate elative pemeability is the highest and NAPL elative pemeability is the lowest. This is because NAPL

4 Vol.4 No.3 Modeling Non-aqueous Phase Liquid Displacement Pocess 43 moves in the thin intemediate layes, wheeas wate moves fowad along the cones and the centes of the ducts. In the case of intemediate-wet netwok, wate elative pemeability is the lowest because wate emains pinned nea the duct cones without invading the duct centes. NAPL elative pemeability is at fist simila to that in the wate-wet netwok, but then it becomes lowe because of significant NAPL tapping. Fo the wate-wet netwok, wate elative pemeability is between those in the intemediate-wet and NAPL-wet netwoks, while NAPL elative pemeability is the highest because NAPL flows pedominantly in the duct centes. It should be noted that nea the tapped satuation, NAPL elative pemeability cuve has a positive slope fo the wate-wet netwok and appoximately zeo slope fo othe two netwoks. The vaiability of two-phase flow in poous media can be explained by the competition of diffeent poe-level displacement mechanisms in esponse to the change of advancing contact angle a. In stongly wate-wet systems, a = 0, link snap off is favoed. As the capillay pessue deceases, snap-off fills the naowest links with wate thoughout the netwok, and node filling is suppessed until most of the links ae aleady filled. When most links ae wate-filled, NAPL in the nodes is likely to be tapped. Theefoe, the domination of snap-off mechanism is esponsible fo the lagest tapped NAPL satuation obseved in the stongly wate-wet systems. As we incease contact angle hysteesis, snap-off is favoed less and piston-type displacement stats to dominate. The invasion stats by snap-off in the smallest links thoughout the netwok, i.e., by odinay pecolation, followed by piston-like coopeative node filling if the node/link aspect atio is not too lage, i.e., by compact cluste gowth (Lenomand, et al., 1983). The competition between diffeent types of node filling mechanisms plays a majo ole in filling the nodes with wate. The gowth of compact wate clustes leads to mino NAPL tapping, caused by bypassing o coalescence of the gowing clustes of wate-filled nodes and links. This obsevation indicates that in wate-wet systems, the invasion of the wate/napl cental menisci pesent at the inlet face is favoed less than snap-off in the netwok. 4.2 Effect of the faction of NAPL-wet poes The intemediate-wet netwok contains both wate-wet and NAPL-wet ducts, the atio of NAPL-wet ducts to wate-wet ducts is impotant fo seconday imbibition. Hee the faction of the NAPL-wet ducts, f, is defined as the atio of the numbe of NAPL-wet ducts to the total numbe of ducts in the netwok. Fig. 2 shows capillay pessue and elative pemeability as functions of the faction of NAPL-wet ducts. It should be noted that slight changes in the faction of NAPL-wet ducts esult in dastic changes of flow chaacteistics in the poe netwok. Fig. 2 Effect of faction of NAPL-wet poes on capillay pessues and elative pemeabilities 4.3 Effect of NAPL/wate intefacial tension Fo specified netwok wettability (i.e. contact angle), seconday imbibition poceeds on the wate-wet, intemediate wet, and NAPL-wet netwoks at seven diffeent values of intefacial tension. The capillay pessue cuves ae plotted in Fig. 3 fo the wate-wet, intemediate wet, and NAPL-wet netwoks, espectively. The elative pemeability cuve fo the wate-wet netwok is shown in Fig. 3d.

5 44 Petoleum Science 2007 Fig. 3 Effect of intefacial tension on capillay pessues and elative pemeabilities The NAPL-wet seconday imbibition capillay pessue cuves show moe vaiability than the coesponding ones fo the wate-wet and intemediate-wet conditions. While NAPL/wate intefacial tension has a slight effect on elative pemeability. 4.4 Effect of initial wate satuation Fig. 4 shows initial wate satuation, S wi, has significant effect on capillay pessue and elative pemeability. It should be noted that the poe capillay pessue is moe significantly affected by NAPL-wet than wate-wet o intemediate-wet netwok. Fo wate-wet and intemediate-wet netwoks, the tapped NAPL satuation does not expeience lage changes as S wi inceases (±5%). Howeve, in the NAPL-wet netwok, the tapped NAPL satuation inceases noticeably with inceasing S wi. Unde each of the thee wetting conditions, inceasing S wi deceases the wate elative pemeability, this esult is cetified by expeimental data done by Li and his cowokes (2002). Fo lowe initial wate satuation, most of the poes and thoats ae NAPL wetted, the wate-napl displacing pocess is natually of dainage. Unde this condition, wate occupies and moves along the lage poes, and theefoe high wate elative pemeability is obseved. With an incease in initial wate satuation, most lage poes become wate filled, and the small poes play moe and moe impotant ole duing displacement. Because of the small diamete, the totuousness of poes inceases and the wate elative pemeability deceases damatically. So highe initial wate satuation geneates lowe wate elative pemeability.

6 Vol.4 No.3 Modeling Non-aqueous Phase Liquid Displacement Pocess 45 Fig. 4 Effect of initial wate satuation on capillay pessues and elative pemeabilities

7 46 Petoleum Science Conclusion Wettability has a significant effect on NAPL-wate displacement mechanism. Fo the wate-wet poe netwok the displacement modes include snap-off, piston-like, and coopeative poe-body filling. Fo the intemediate-wet netwok, the flow is a mixtue of spontaneous and foced seconday imbibition pocesses. Fo the NAPL-wet netwok, seconday imbibition is mainly foced piston-type displacement. The faction of NAPL-wet poes stongly influences the two-phase flow behavio in the poe media. Acknowledgements This pape was suppoted by the National Natual Science Foundation of China (Gant No: ). Refeences Bea J. (1972) Dynamics of Fluids in Poous Media. Ameican Elsevise Publishing Co., Inc. Bedient P. B., Hanadi S. R., and Chales J. N. (1994). Goundwate Contamination: Tanspot, and Remediation, Pentice-hall. Englewood Cliffs, New Jesey. Blunt M. J. (2001) Flow in poous media: Poe-netwok models and multiphase flow. Cu. Opin. Colloid Inteface Sci., 6, Dullien F. A. L. (1992) Poous Media: Fluid Tanspot and Poe Stuctue (2nd Edition). New Yok: Academic Pess, Li K. W., Chow K. and Hone R. N. (2002) Effect of initial wate satuation on spontaneous wate imbibition. SPE Westen Regional/AAPG Pacific Section Joint Meeting held Anchoage, Alaska, May SPE pape Lenomand R., Zacone C. and Sa A. (1983) Mechanisms of displacements of one fluid by anothe in a netwok of capillay ducts. J. Fluid. Mech., 16, Lowy M. I. and Mille C. T. (1995) Poe-scale modeling of non wetting-phase esidual in poous media. Wate Resou. Res Res., 31(3), Mason G. and Moow N. R. (1991) Capillay behavio of a pefectly wetting liquid in iegula tiangula tubes. J. Colloid Inteface Sci., 141(1), Maye R. P. and Stowe R. A. (1965) Mecuy poosimety-beakthough pessue fo penetation between packed sphees. J. Colloid Inteface Sci. 30, Øen P. E., Bakke S. and Antzen O. I. (1998) Extending pedictive capabilities to netwok models. Soc. Pet. Eng. J. 3 (4), Øen P. E. and Bakke S. (2002) Pocess based econstuction of sandstones and pediction of tanspot popeties. Tanspot Poous Media, 46, Øen P. E. and Bakke S. (2003) Reconstuction of Beea sandstone and poe-scale modelling of wettability effects. Jounal of Petoleum Science and Engineeing, 39, Patzek T. W. (2001) Veification of a complete poe netwok simulato of dainage and imbibition. Soc. Pet. Eng. J. 6, Pincen H. M. (1970) Capillay phenomena in assemblies of paallel cylindes: III Liquid columns between hoizontal paallel cylindes. J. Colloid Inteface Sci. 34, Reeves P. C. and Celia M. A. (1996) A functional elationship between capillay pessue, satuation and intefacial aea as evealed by a poe scale model. Wate Resou. Res., 32(8), About the fist autho Yang Zhenqing was bon in 1977 and eceived his MS degee fom China Univesity of Petoleum (Beijing) in Now he woks in the Physics Depatment, China Univesity of Petoleum (Beijing) with his majo eseach inteests in petoleum engineeing and finite element analysis of ock mechanics. wieless@cup.edu.cn (Received Novembe 2, 2006) (Edited by Sun Yanhua)