Modeling Flow and Transport in Heterogeneous Media

by
Ramoj K. Paruchuri, MSE

University of Texas at Austin, 2003
Supervisor: Steven L. Bryant

This thesis is based on research on two applications of modeling flow and transport in heterogeneous media. In the first case, the heterogeneity is a growing fracture in a formation surrounding an injection well. The flow and reactive solute transport behavior in the formation is studied as the fracture grows from the well. In the second case, the heterogeneity is in the form of cm-scale vugs distributed within a carbonate rock. New scale-up algorithms are proposed to replace the parallel fine-scale flow calculations for determining an effective permeability of the heterogeneous medium. Also, methods to identify more generic vugs and their connectivity, and to understand the effects of channels are presented.

Many previous models have been developed to understand the flow and solute transport through a static fracture. But growing fractures are commonly seen in deep injection wells, even though injection pressure is below the fracture gradient. In this work a flow and reactive solute transport model has been developed for the flow-field around a single growing fracture. The equations derived in this model are dynamic and are based on the elliptical geometry of the 2D flow-field around a line source. The numerical solutions to these equations are presented in finite-difference forms adopting the pseudo steady-state assumption and are simulated by hypothesizing a pseudo-static approach to the fracture growth. The results indicate that transport at early times depends strongly on location relative to the fracture. The results also exhibit important differences from radial transport that neglects the presence of fracture and from elliptical transport from a static fracture.

For the second case, calculating the effective permeability for highly heterogeneous media such as vuggy carbonates often requires high performance computing. Solving flow equations for pressures and velocities, and finding the equivalent permeability as an inverse problem has been a traditional approach. Though several up-scaling techniques have been developed, few are applicable to a highly heterogeneous medium specially when a heterogeneity spans several grid blocks. New scale-up techniques are proposed in this thesis to estimate the effective permeability of such rocks. These algorithms were validated against the fine-scale flow simulations using Parallel Subsurface Simulator -PARSSIM.

The results present an option in choosing the method of averaging, based on the intensity of heterogeneity in the permeable medium. In the process, it was also seen that the spatial variation in certain classes of averages give a specific response in shape when plotted, which is characteristic of the presence of vugs and of their connectivity. Also, an estimate to understand the presence of channels is presented. This thesis would serve as a reference to understand the fundamentals in flow and reactive transport phenomena in a flow-field around injection well with growing fractures. Also with further evaluating the new scale-up algorithms, one can use them as quick substitutions to the high performance computing involved in estimating the effective permeability.

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