Modeling Multiphase Flow in Heterogeneous Media Using Streamtubes

Marco R. Thiele
PhD Dissertation, Stanford University, Dept. of Petroleum Engineering, Stanford, CA (Jan. 1995).

Streamtubes are used to determine fast and accurate solutions to multiphase, multicomponent displacements through heterogeneous, cross-sectional systems. Solutions are constructed by treating each streamtube as a one-dimensional system along which mass conservations equations are solved, either analytically or numerically. The nonlinearity of the underlying flow field is resolved by periodically updating the streamtubes and remapping the one-dimensional solution(s) as an integration from TD=0 to TD=TD + Delta TD. Examples for (1) tracer flow, (2) two-phase immiscible flow, (3) first contact miscible flow, and (4) two-phase, compositional flow demonstrate that recoveries and large-scale displacements characteristics dictated by reservoir heterogeneity can be predicted accurately using two to five orders of magnitude less computation time than traditional simulation approaches. Mapping analytical solutions along streamtubes allows diffusion-free, two-dimensional solutions to be found. By comparing streamtube solutions to traditional finite difference solutions, numerical diffusion is shown to reduce substantially and in some cases even to eliminate completely the mobility contrast in compositional displacements. The coupling of phase behavior and numerical diffusion is found to be so dominant as to force only very slow convergence of the solution by progressive grid refinement. The speed of the streamtube method is used to quantify the uncertainty in recovery arising from the statistical description of reservoir heterogeneity interacting with the inherent nonlinearity of the problem formulation. The uncertainty is shown to be significant and characterized by a large spread in overall recovery.

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(The postscript version of this dissertation is too large, even when compressed, to post it here. If you are interested in a copy contact me directly at marcot@pangea.stanford.edu.)