Abstract
In this paper we consider porous media flow without capillary effects. We present a streamline method which includes gravity effects by operator splitting. The flow equations are treated by an IMPES method, where the pressure equation is solved by a (standard) finite element method. The saturation equation is solved by utilizing a front tracking method along streamlines of the pressure field. The effects of gravity are accounted for in a separate correction step. This is the first time streamlines are combined with gravity for three-dimensional (3D) simulations, and the method proves favourable compared to standard splitting methods based on fractional steps. By our splitting we can take advantage of very accurate and efficient 1D methods. The ideas have been implemented and tested in a full field simulator. In that context, both accuracy and CPU efficiency have tested favourably.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- S i :
-
saturation of phase i
- (Si) t :
-
partial derivative of S i, w.r.t. t, ∂Si/∂t
- x :
-
space coordinates
- γ :
-
gravity vector
- P i :
-
pressure within phase i
- ϱ i :
-
density of phase i
- μ iί :
-
dynamic viscosity of the phase i
- K :
-
absolute permeability of the rock
- k ί :
-
relative permeability of phase i
- λ ί :
-
mobility of phase i = Kk i/μi
- f ί :
-
fractional flow = λ i/(λn + λw)
- v ί :
-
Darcy velocity (specific discharge)
- v tot :
-
total Darcy velocity = v n + vw
- q ί :
-
mass rate of injection or production per unit of volume
- φ :
-
porosity of the rock
References
Aziz, K. and Settari, A.: 1979, Petroleum Reservoir Simulation, Elsevier, Amsterdam.
Bratvedt, F., Bratvedt, K., Buchholz, C., Holden, H., Holden, L. and Risebro, N. H.: 1992, A new front tracking method for reservoir simulation, SPE J. Res. Sim. 107–116.
Bratvedt, F., Bratvedt, K., Buchholz, C., Gimse, T., Holden, H., Holden, L. and Risebro, N.H.: 1993, FRONTLINE and FRONTSIM. Two full scale, two phase black oil reservoir simulators based on front tracking, Surv. Math. Ind. 3, 185–215.
Cordes, C. and Kinzelbach, W.: 1992, Continuous velocity fields and pathlines in finite element groundwater flow models, Proc. IX Int. Conf. Comp. Meth. Water Res. Denver, Colorado Vol. 1, pp. 247–254.
Crandall, M. and Majda, A.: 1980, The method of fractional steps for conservation laws, Numer. Math. 34, 285–314.
Dafermos, C. M.: 1972, Polygonal approximations of solutions of the initial value problem for a conservation law, J. Math. Anal. Appl. 38, 33–41.
Blunt, M., Lin, K., Thiele, M. and Batycky, R.: A generalized streamline method to predict reservoir flow, Presented at 1995 Affiliates Meeting of the Stanford Center for Reservoir Forecasting (SCRF).
Holden, H., Holden, L. and Høegh-Krohn, R.: 1988, A numerical method for first order nonlinear conservation laws in one dimension, Comput. Math. Appl. 15, 595–602.
Holden, H. and Risebro, N. H.: 1993, A fractional steps method for scalar conservation laws without the CFL-condition, Math. Comput. 60, 221–232.
Peaceman, D. W.: 1977, Fundamentals of Numerical Reservoir Simulation, Elsevier, Amsterdam.
Tijink, P. J. A., Gimse, T. and Kaasschieter, E. F.: 1994, Streamline Computation for Front Tracking, in: Alexander Peters et al. (eds), Computational Methods in Water Resources X, Kluwer Acad. Publ., pp. 1481–1488.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bratvedt, F., Gimse, T. & Tegnander, C. Streamline computations for porous media flow including gravity. Transp Porous Med 25, 63–78 (1996). https://doi.org/10.1007/BF00141262
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00141262