Generalized Scaling Approach for Spontaneous Imbibition: An Analytical Model
- Kewen Li (Stanford University) | Roland N. Horne (Stanford University)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- June 2006
- Document Type
- Journal Paper
- 251 - 258
- 2006. Society of Petroleum Engineers
- 1.10 Drilling Equipment, 5.8.6 Naturally Fractured Reservoir, 5.4.7 Chemical Flooding Methods (e.g., Polymer, Solvent, Nitrogen, Immiscible CO2, Surfactant, Vapex), 5.3.1 Flow in Porous Media, 5.5 Reservoir Simulation, 5.3.2 Multiphase Flow, 4.3.4 Scale, 5.5.3 Scaling Methods, 1.6.9 Coring, Fishing, 5.2.1 Phase Behavior and PVT Measurements, 5.9.2 Geothermal Resources, 6.5.2 Water use, produced water discharge and disposal
- 4 in the last 30 days
- 1,294 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 10.00|
|SPE Non-Member Price:||USD 30.00|
Scaling the experimental data of spontaneous imbibition without serious limitations has been difficult. To this end, a general approach was developed to scale the experimental data of spontaneous imbibition for most systems (gas/liquid/rock and oil/water/rock systems) in both cocurrent and countercurrent cases. We defined a dimensionless time with almost all the parameters considered. These include porosity, permeability, size, shape, boundary conditions, wetting- and nonwetting-phase relative permeabilities, interfacial tension (IFT), wettability, and gravity. The definition of the dimensionless time was not empirical; instead, it was based on theoretical analysis of the fluid-flow mechanisms that govern spontaneous imbibition. The general scaling method was confirmed against the experimental data from spontaneous water imbibition conducted at different IFTs in oil-saturated rocks with different sizes and permeabilities. A general analytical solution to the relationship between recovery and imbibition time for linear spontaneous imbibition was derived. The analytical solution predicts a linear correlation between the imbibition rate and the reciprocal of the recovery by spontaneous imbibition in most fluid/fluid/rock systems.
An important fluid-flow phenomenon during water injection or aquifer invasion into reservoirs is spontaneous water imbibition. Scaling the experimental data of spontaneous water imbibition in different fluid/fluid/rock systems is of essential importance in designing the water-injection projects and predicting the reservoir production performances. Ignoring the effects of relative permeability, capillary pressure, and gravity in the dimensionless time might be the reason that the existing scaling methods do not always function successfully. It is known that these parameters influence the spontaneous imbibition in porous media significantly. For that reason, these parameters should be honored properly in the scaling.
Many papers have been published to characterize and scale spontaneous water imbibition in both oil/water/rock systems (Li et al. 2002; Tong et al. 2001; Zhou et al. 2001; Babadagli 2001; Kashchiev and Firoozabadi 2002; Civan and Rasmussen 2001; Akin et al. 2000; Cil et al. 1998; Perkins and Collins 1960; Mattax and Kyte 1962; Du Prey 1978; Hamon and Vidal 1986; Reis and Cil 1993; Cuiec et al. 1994; Ma et al. 1995; Chen et al. 1995; Zhang et al. 1996; Al-Lawati and Saleh 1996; Babadagli 1997; Li and Horne 2002) and gas/liquid/rock systems (Li and Horne 2001, 2004a; Li et al. 2006; Handy 1960). However, few have included the effects of capillary pressure, relative permeability (both wetting and nonwetting phases), wettability, and gravity simultaneously. This is important because all the parameters may play an important role in many cases and may not be ignored. For example, a number of enhanced-/improved-oil-recovery processes relate to low IFT. In these cases, capillary pressure as a driving force may be small, and gravity may not be neglected. In some cases, gravity may also be a driving force, as pointed out by Schechter et al. (1991).
|File Size||1 MB||Number of Pages||8|
Akin, S., Schembre, J.M., Bhat, S.K., and Kovscek, A.R. 2000. Spontaneous ImbibitionCharacteristics of Diatomite. J. of Pet. Sci. & Eng. 25: 149-165.
Al-Lawati, S. and Saleh, S. 1996. Oil Recovery in Fractured OilReservoirs by Low IFT Imbibition Process. Paper SPE 36688 presented at theSPE Annual Technical Conference and Exhibition, Denver, 6-9 October.
Babadagli, T. 1997. Scaling ofCapillary Imbibition Under Static Thermal and Dynamic Fracture FlowConditions. Paper SPE 39027 presented at the SPE Latin American andCaribbean Petroleum Engineering Conference, Rio de Janeiro, 30 August-3September.
Babadagli, T. 2001. Scaling ofCocurrent and Countercurrent Capillary Imbibition for Surfactant and PolymerInjection in Naturally Fractured Reservoirs. SPEJ 6 (4): 465-478.SPE-74702-PA.
Chen, J., Miller, M.A., and Sepehrnoori, K. 1995. Theoretical Investigation ofCountercurrent Imbibition in Fractured Reservoir Matrix Blocks. Paper SPE29141 presented at the SPE Reservoir Simulation Symposium, San Antonio, Texas,12-15 February.
Cil, M., Reis, J.C., Miller, M.A., and Misra, D. 1998. An Examination of CountercurrentCapillary Imbibition Recovery From Single Matrix Blocks and RecoveryPredictions by Analytical Matrix/Fracture Transfer Functions. Paper SPE49005 prepared for presentation at the SPE Annual Technical Conference andExhibition, New Orleans, 27-30 September.
Civan, F. and Rasmussen, M.L. 2001. Asymptotic Analytical Solutions forImbibition Waterfloods in Fractured Reservoirs. SPEJ 6 (2): 171-181.SPE-71312-PA.
Cuiec, L.E., Bourbiaux, B.J., and Kalaydjian, F.J. 1994. Oil Recovery by Imbibition inLow-Permeability Chalk. SPEFE 9 (3): 200-208. SPE-20259-PA.
Du Prey, E.L. 1978. Gravity andCapillarity Effects on Imbibition in Porous Media. SPEJ 18 (3): 195-206.SPE-6192-PA.
Hamon, G. and Vidal, J. 1986. Scaling-Up the Capillary ImbibitionProcess From Laboratory Experiments on Homogeneous and HeterogeneousSamples. Paper SPE 15852 presented at the SPE European PetroleumConference, London, 20-22 October.
Handy, L.L. 1960. Determination of Effective Capillary Pressures for Porous Media From ImbibitionData. Trans., AIME, 219: 75-80.
Henderson, G.D., Danesh, A., Tehrani, D.H., Al-Shaidi, S., and Peden, J.M.1998. Measurement and Correlationof Gas Condensate Relative Permeability by the Steady-State Method. SPEREE1 (2): 134-140. SPE-30770-PA.
Kashchiev, D. and Firoozabadi, A. 2002. Analytical Solutions for 1-DCountercurrent Imbibition in Water-Wet Media. Paper SPE 75166 presented atthe SPE/DOE Improved Oil Recovery Symposium, Tulsa, 13-17 April.
Li, K. and Firoozabadi, A. 2000. Phenomenological Modeling of CriticalCondensate Saturation and Relative Permeabilities in Gas/CondensateSystems. SPEJ 5 (2): 138-147. SPE-56014-PA.
Li, K. and Horne, R.N. 2001. Characterization of Spontaneous WaterImbibition Into Gas-Saturated Rocks. SPEJ 6 (4): 375-384. SPE-74703-PA.
Li, K. and Horne, R.N. 2002. A Scaling Method of Spontaneous Imbibition inSystems With Different Wettability. Paper presented at the Intl. Symposium ofthe Soc. of Core Analysts, Monterey, California, 22-25 September.
Li, K. and Horne, R.N. 2004a. An Analytical Scaling Method forSpontaneous Imbibition in Gas/Water/Rock Systems. SPEJ 9 (3): 322-329.SPE-88996-PA.
Li, K. and Horne, R.N. 2004b. Experimental Study of Gas Slippage inTwo-Phase Flow. SPEREE 7 (6): 409-415. SPE-89038-PA.
Li, Y., Morrow, N.R., and Ruth, D. 2002. Similarity Solution for LinearCounter-Current Spontaneous Imbibition. Paper presented at the 7th Intl.Symposium on Reservoir Wettability, Freycinet, Tasmania, Australia, 12-15March.
Li, K., Chow, K., and Horne, R.N. 2006. Influence of Initial WaterSaturation on Recovery by Spontaneous Imbibition in Gas-Water-Rock Systems andthe Calculation of Relative Permeability. SPEREE (in press). SPE-99329-PA.
Ma, S., Morrow, N.R., and Zhang, X. 1995. Generalized Scaling of SpontaneousImbibition Data for Strongly Water-Wet Systems. Paper 95-138 presented at the6th Petroleum Conference of the South Saskatchewan Section, the Petroleum Soc.of CIM, Regina, Saskatchewan, Canada, 16-18 October.
Mattax, C.C. and Kyte, J.R. 1962. Imbibition Oil Recovery From Fractured,Water-Drive Reservoir. SPEJ 2 (2): 177-184; Trans., AIME, 225.SPE-187-PA.
Perkins, F.M. Jr. and Collins, R.E. 1960. Scaling Laws for Laboratory Flow Models of Oil Reservoirs. JPT 12 (8):69-71. SPE-1487-G.
Reis, J.C. and Cil, M. 1993. A Model for Oil Expulsionby Countercurrent Water Imbibition in Rocks: One-Dimensional Geometry. J.of Pet. Sci. & Eng. 10: 97.
Schechter, D.S., Zhou, D., and Orr, F.M. Jr. 1991. Capillary Imbibition and GravitySegregation in Low IFT Systems. Paper SPE 22594 presented at the SPE AnnualTechnical Conference and Exhibition, Dallas, 6-9 October.
Tong, Z., Xie, X., and Morrow, N.R. 2001. Scaling of Viscosity Ratio for OilRecovery by Imbibition from Mixed-Wet Rocks. Paper SCA 2001-21 presented at theIntl. Symposium of the Soc. of Core Analysts, Edinburgh, U.K., 17-19September.
Zhang, X., Morrow, N.R., and Ma, S. 1996. Experimental Verification of aModified Scaling Group for Spontaneous Imbibition. SPERE 11 (4): 280-285.SPE-30762-PA.
Zhou, D., Jia, L., Kamath, J., and Kovscek, A.R. 2001. An Investigation of Counter-CurrentImbibition Processes in Diatomite. Paper SPE 68837 presented at the SPEWestern Regional Meeting, Bakersfield, California, 26-30 March.