Three-Dimensional Stochastic Flow and Displacement in a Five-Spot Pattern

Abstract

ABSTRACT Flow and miscible displacement through a three-dimensional, single five-spot well field is numerically simulated for heterogeneous reservoirs where the permeability is treated as a spatial stochastic process. Permeability fields are generated geostatistically using a Fast Fourier Transform method and are described in terms of the log of permeability by a mean, variance and covariance. The flow fields are simulated by finite differences, and displacement is simulated using a new front tracking technique. Results of the simulations for the stochastic reservoir show that flow fields, displacement fronts, and breakthrough curves are highly non-uniform. Heterogeneity has a significant effect on reservoir behavior even for small spatial correlation and variance of the log permeability. As permeability correlation length decreases and variance increases recovery curves at pumping wells typically breakthrough earlier and take longer times to reach ultimate recovery. The fronts demonstrate significant three-dimensional fingering, even in the absence of any instabilities. Vertically distributed breakthrough curves and well flow rates provide a good indicator of vertical correlation length and vertical flow behavior. Vertically integrated breakthrough curves and flow rates, the type of information typically available, disguise this behavior. This disguise is related both to parameter sensitivity and the non-linearity of the equations in terms of the parameters.