Theoretical Investigation of the Transition From Spontaneous to Forced Imbibition
- Lichi Deng (Texas A&M University) | Michael J. King (Texas A&M University)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- February 2019
- Document Type
- Journal Paper
- 215 - 229
- 2019.Society of Petroleum Engineers
- Stability Envelope, Transient Solution, Capillary Pressure, Spontaneous Imbibition, Forced Imbibition
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- 186 since 2007
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Spontaneous and forced imbibition are recognized as important recovery mechanisms in naturally fractured reservoirs because the capillary force controls the movement of the fluid between the matrix and the fracture. For unconventional reservoirs, imbibition is also important because the capillary pressure is more dominant in these tighter formations, and a theoretical understanding of the flow mechanism for the imbibition process will benefit the understanding of important multiphase-flow phenomena such as waterblocking. In this paper, a new semianalytic method is presented to examine the interaction between spontaneous and forced imbibition and to quantitatively represent the transient imbibition process. The methodology solves the partial-differential equation (PDE) of unsteady-state immiscible, incompressible flow with arbitrary saturation-dependent functions using the normalized water flux concept, which is identical to the fractional-flow terminology used in the traditional Buckley-Leverett analysis. The result gives a universal inherent relationship between time, normalized water flux, saturation profile, and the ratio between cocurrent and total flux. The current analysis also develops a novel stability envelope outside of which the flow becomes unstable caused by strong capillary forces, and the characteristic dimensionless parameter shown in the envelope is derived from the intrinsic properties of the rock and fluid system, and it can describe the relative magnitude of capillary and viscous forces at the continuum scale. This dimensionless parameter is consistently applicable in both capillary-dominated and viscous-dominated flow conditions.
|File Size||1 MB||Number of Pages||15|
Bennion, B. D. and Thomas, F. B. 2005. Formation Damage Issues Impacting the Productivity of Low Permeability, Low Initial Water Saturation Gas Producing Formations. J. Energy Resour. Technol. 127 (3): 240–247. https://doi.org/10.1115/1.1937420.
Bjørnarå, T. I. and Mathias, S. A. 2013. A Pseudospectral Approach to the McWhorter and Sunada Equation for Two-Phase Flow in Porous Media With Capillary Pressure. Computational Geosciences 17 (6): 889–897. https://doi.org/10.1007/s10596-013-9360-4.
Buckley, S. E. and Leverett, M. C. 1942. Mechanism of Fluid Displacement in Sands. Trans. of the AIME 146 (1): 107–116. SPE-942107-G. https://doi.org/10.2118/942107-G.
Chen, Z. X. 1988. Some Invariant Solutions to Two-Phase Fluid Displacement Problems Including Capillary Effect (Includes Associated Papers 18744 and 19037). SPE Res Eval & Eng 3 (2): 691–700. SPE-14874-PA. https://doi.org/10.2118/14874-PA.
Deng, L. and King, M. J. 2015. Capillary Corrections to Buckley-Leverett Flow. Presented at the SPE Annual Technical Conference and Exhibition, Houston, 28–30 September. SPE-175150-MS. https://doi.org/10.2118/175150-MS.
Deng, L. and King, M. J. 2016. Estimation of Relative Permeability From Laboratory Displacement Experiments Application of the Analytic Solution With Capillary Corrections. Presented at the Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, 7–10 November. SPE-183139-MS. https://doi.org/10.2118/183139-MS.
Deng, L. and King, M. J. 2018. Theoretical Investigation of Two-Ends-Open Free Spontaneous Imbibition. Presented at the ECMOR XVI1: 6th European Conference on the Mathematics of Oil Recovery, Barcelona, Spain, 3–6 September.
Desai, K. R., Pradhan, V. H., Daga, A. R. et al. 2015. Approximate Analytical Solution of Non-Linear Equation in One-Dimensional Imbibition Phenomenon in Homogeneous Porous Media by the Homotopy Perturbation Method. Procedia Engineering 127 (Supplement C): 994–1001. https://doi.org/10.1016/j.proeng.2015.11.448.
Fokas, A. and Yortsos, Y. 1982. On the Exactly Solvable Equation St = [(βS + γ)–2Sx]x + α(βS + γ)–2Sx Occurring in Two-Phase Flow in Porous Media. SIAM Journal of Applied Mathematics 42 (2): 318–332. https://doi.org/10.1137/0142025.
Fucík, R., Mikyška, J., Beneš, M. et al. 2007. An Improved Semi-Analytical Solution for Verification of Numerical Models of Two-Phase Flow in Porous Media. Vadose Zone Journal 6 (1): 93–104. https://doi.org/10.2136/vzj2006.0024.
Helba, A. A., Sahimi, M., Scriven, L. E. et al. 1992. Percolation Theory of Two-Phase Relative Permeability. SPE Res Eval & Eng 7 (1): 123–132. SPE-11015-PA. https://doi.org/10.2118/11015-PA.
Johnson, E. F., Bossler, D. P., and Naumann Bossler, V. O. 1959. Calculation of Relative Permeability From Displacement Experiments. Petroleum Trans. AIME 216: 370–372. SPE-1023-G. https://doi.org/10.2118/1023-G.
Karimaie, H., Pourmohammadi, S., Samiei, M. et al. 2004. 1D-Simulation of Countercurrent Imbibition Process in a Water Wet Matrix Block. Presented at the International Symposium of the Society of Core Analysis, Abu Dhabi, 5–9 October. SCA2004-52.
Longoria, R. A., Liang, T., Huynh, U. T. et al. 2017. Water Blocks in Tight Formations: The Role of Matrix/Fracture Interaction in Hydrocarbon-Permeability Reduction and Its Implications in the Use of Enhanced Oil Recovery Techniques. SPE J. 22 (5): 1393–1401. SPE-185962-PA. https://doi.org/10.2118/185962-PA.
Mathworks. 2018. Optimization Toolbox User’s Guide (R2018a). https://www.mathworks.com/help/pdf_doc/optim/optim_tb.pdf (downloaded 22 April 2018).
McWhorter, D. B. and Sunada, D. K. 1990. Exact Integral Solutions for Two-Phase Flow. Water Resources Research 26 (3): 399–413. https://doi.org/10.1029/WR026i003p00399.
McWhorter, D. B. and Sunada, D. K. 1992. Reply to “Comment on ‘Exact Integral Solutions for Two-Phase Flow’ by David B. McWhorter and Daniel K. Sunada”. Water Resources Research 28 (5): 1479–1479. https://doi.org/10.1029/92WR00474.
Nooruddin, H. A. and Blunt, M. J. 2016. Analytical and Numerical Investigations of Spontaneous Imbibition in Porous Media. Water Resources Research 52 (9): 7284–7310. https://doi.org/10.1002/2015WR018451.
Ruth, D. W., Mason, G., Ferno, M. A. et al. 2015. Numerical Simulation of Combined Co-Current/Counter-Current Spontaneous Imbibition. Presented at the International Symposium of the Society of Core Analysis, St. John’s, Newfoundland and Labrador, Canada, 16–21 August. SCA2015-002.
Schmid, K. S., Geiger, S., and Sorbie, K. 2011. Semianalytical Solutions for Cocurrent and Countercurrent Imbibition and Dispersion of Solutes in Immiscible Two-Phase Flow. Water Resources Research 47 (2). https://doi.org/10.1029/2010WR009686.
Schmid, K. S. and Geiger, S. 2012. Universal Scaling of Spontaneous Imbibition for Water-Wet Systems. Water Resources Research 48 (3). https://doi.org/10.1029/2011WR011566.
Schmid, K. S., Alyafei, N., Geiger, S. et al. 2016. Analytical Solutions for Spontaneous Imbibition: Fractional-Flow Theory and Experimental Analysis. SPE J. 21 (6): 2308–2316. SPE-184393-PA. https://doi.org/10.2118/184393-PA.
Wang, F. P. and Reed, R. M. 2009. Pore Networks and Fluid Flow in Gas Shales. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 4–7 October. SPE-124253-MS. https://doi.org/10.2118/124253-MS.
Wu, Y.-S. and Pan, L. 2003. Special Relative Permeability Functions With Analytical Solutions for Transient Flow Into Unsaturated Rock Matrix. Water Resources Research 39 (4). https://doi.org/10.1029/2002WR001495.
Yortsos, Y. C. and Fokas, A. S. 1983. An Analytical Solution for Linear Waterflood Including the Effects of Capillary Pressure. SPE J. 23 (1): 115–124. SPE-9407-PA. https://doi.org/10.2118/9407-PA.