نشریه ژئومکانیک و ژئوانرژی

نشریه ژئومکانیک و ژئوانرژی

A closed-form screening criterion for stress-dependent permeability effects on waterflood performance

نوع مقاله : مقاله پژوهشی

نویسندگان
بهنام ابراهیمی 1
احسان طاهری 2
1 بلوار کشاورز، بعد از خیابان فلسطین، کوچه رویان، پلاک 4
2 دانشگاه تربیت مدرس
10.22107/ggj.2026.594380.1268
چکیده
Coupled flow–geomechanics simulation is expensive, and it needs to be known whether it changes the forecast. For single-phase flow to a single well the answer has been known since the 1980s: an exponential dependence of permeability on effective stress reduces the problem to one dimensionless group. Whether this extends to two-phase displacement in heterogeneous rock has not been examined. This is tested on a field-scale quarter five-spot, in which a stress-dependent permeability is imposed through a uniaxial-strain poroelastic closure and swept over one homogeneous and four heterogeneous log-normal fields, in 104 simulations. At issue is not the constitutive law, assumed alike by simulation and scaling, but whether the geometric cancellation behind the single-well result is preserved under heterogeneity and a second mobile phase. It is shown to be preserved. The ratio of coupled to uncoupled injector-to-producer pressure difference is collapsed onto a closed-form curve with a median error below one per cent, even though the uncoupled difference itself is shifted by a factor of four across the heterogeneity levels tested; the collapse is insensitive to grid resolution, the pressure solver, and whether permeability is tied to effective stress directly or through porosity. The displacement measures are barely affected: although permeability is varied by an order of magnitude and injection pressure is reduced by up to three quarters, breakthrough time and recovery factor shift by less than one per cent. Under a prescribed rate, the pressure field is rescaled by the coupling without the flow being redirected, and the same dimensionless group is shown to govern a well held at fixed pressure, where the coupling appears as a gain in injectivity rather than as a drop in pressure. Inverting the scaling yields a screening rule that costs nothing to apply and determines whether a coupled simulation is required.
کلیدواژه‌ها
stress-dependent permeability
hydromechanical coupling
waterflooding
injectivity
reservoir screening
موضوعات
[1] Terzaghi, K. (1943). Theoretical soil mechanics.
New York, NY: John Wiley & Sons. DOI:
10.1002/9780470172766.
[2] Biot, M. A. (1941). General theory of three
dimensional consolidation. Journal of Applied
Physics, 12(2), 155–164. DOI:
10.1063/1.1712886.
[3] Jaeger, J. C., Cook, N. G. W., & Zimmerman, R. W.
(2007). Fundamentals of rock mechanics (4th ed.).
Oxford, UK: Blackwell Publishing.
[4] Rutqvist, J., & Stephansson, O. (2003). The role of
hydromechanical coupling in fractured rock
engineering. Hydrogeology Journal, 11(1), 7–40.
DOI: 10.1007/s10040-002-0241-5.
[5] Davies, J. P., & Davies, D. K. (2001). Stressdependent
permeability: Characterization and
modeling. SPE Journal, 6(2), 224–235. DOI:
10.2118/71750-PA.
[6] Schutjens, P. M. T. M., Hanssen, T. H., Hettema, M.
H. H., Merour, J., de Bree, P., Coremans, J. W. A.,
& Helliesen, G. (2004). Compaction-induced
porosity/permeability reduction in sandstone
reservoirs: Data and model for elasticitydominated
deformation. SPE Reservoir
Evaluation & Engineering, 7(3), 202–216. DOI:
10.2118/88441-PA.
[7] Settari, A., & Mourits, F. M. (1998). A coupled
reservoir and geomechanical simulation system.
SPE Journal, 3(3), 219–226. DOI:
10.2118/50939-PA.
[8] Dean, R. H., Gai, X., Stone, C. M., & Minkoff, S. E.
(2006). A comparison of techniques for coupling
porous flow and geomechanics. SPE Journal,
11(1), 132–140. DOI: 10.2118/79709-PA.
[9] Kim, J., Tchelepi, H. A., & Juanes, R. (2011).
Stability and convergence of sequential methods
for coupled flow and geomechanics: Drained and
undrained splits. Computer Methods in Applied
Mechanics and Engineering, 200(23–24), 2094–
2116. DOI: 10.1016/j.cma.2011.02.011.
[10] Longuemare, P., Mainguy, M., Lemonnier, P.,
Onaisi, A., Gérard, Ch., & Koutsabeloulis, N.
(2002). Geomechanics in reservoir simulation:
Overview of coupling methods and field case
study. Oil & Gas Science and Technology, 57(5),
471–483. DOI: 10.2516/ogst:2002031.
[11] Minkoff, S. E., Stone, C. M., Bryant, S.,
Peszynska, M., & Wheeler, M. F. (2003). Coupled
fluid flow and geomechanical deformation
modeling. Journal of Petroleum Science and
Engineering, 38(1–2), 37–56. DOI:
10.1016/S0920-4105(03)00021-4.
[12] Sadrnejad, S. A., Ghasemzadeh, H., & Taheri, E.
(2014). Multiscale multiphysic mixed
geomechanical model in deformable porous
media. International Journal for Multiscale
Computational Engineering, 12(6), 529–547.
DOI: 10.1615/IntJMultCompEng.2014011296.
[13] Taheri, E., Sadrnejad, S. A., & Ghasemzadeh, H.
(2015). Multiscale geomechanical model for a
deformable oil reservoir with surrounding rock
effects. International Journal for Multiscale
Computational Engineering, 13(6), 533–559.
DOI: 10.1615/IntJMultCompEng.2015014333.
[14] Ghasemzadeh, H. (2019). Multiscale multiphysic
mixed geomechanical model for deformable
porous media considering the effects of
surrounding area. Journal of Petroleum
Geomechanics, 3(1), 79–99. DOI:
10.22107/JPG.2019.88412.
[15] Pedrosa, O. A. (1986, April). Pressure transient
response in stress-sensitive formations. Paper
SPE-15115 presented at the SPE California
Regional Meeting, Oakland, CA. DOI:
10.2118/15115-MS.
[16] Kikani, J., & Pedrosa, O. A. (1991). Perturbation
analysis of stress-sensitive reservoirs. SPE
Formation Evaluation, 6(3), 379–386. DOI:
10.2118/20053-PA.
[17] Chin, L. Y., Raghavan, R., & Thomas, L. K.
(2000). Fully coupled analysis of well responses in
stress-sensitive reservoirs. SPE Reservoir
Evaluation & Engineering, 3(5), 435–443. DOI:
10.2118/66222-PA.
[18] Raghavan, R., & Chin, L. Y. (2004). Productivity
changes in reservoirs with stress-dependent
permeability. SPE Reservoir Evaluation &
Engineering, 7(4), 308–315. DOI: 10.2118/88870-
PA.
[19] Brooks, R. H., & Corey, A. T. (1964). Hydraulic
properties of porous media (Hydrology Paper No.
3). Fort Collins, CO: Colorado State University.
[20] Geertsma, J. (1957). The effect of fluid pressure
decline on volumetric changes of porous rocks.
Petroleum Transactions, AIME, 210, 331–340.
DOI: 10.2118/728-G.
[21] Taheri, E. (2015). Multiscale modeling of oil
transport in deformable porous media
(Unpublished doctoral dissertation). K. N. Toosi
University of Technology, Faculty of Civil
Engineering, Tehran, Iran. (in Persian)
[22] Buckley, S. E., & Leverett, M. C. (1942).
Mechanism of fluid displacement in sands.
Transactions of the AIME, 146(1), 107–116. DOI:
10.2118/942107-G.
[23] Welge, H. J. (1952). A simplified method for
computing oil recovery by gas or water drive.
Journal of Petroleum Technology, 4(4), 91–98.
DOI: 10.2118/124-G.
نشریه ژئومکانیک و ژئوانرژی
دوره 8، شماره 4
زمستان 1404
صفحه 47-57