Numerical Simulation of Geopressured Geothermal Aquifer Phenomena

Date

1986-09

Authors

Ohkuma, Hiroshi

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Abstract

Hot brines in geopressured sandstones contain significant quantities of dissolved natural gas. If these sandstones are capable of producing brines at high rates, the natural gas and thermal energy may be economically recovered. However, brine withdrawal will result in a large pressure reduction over an extensive reservoir volume, and it may cause pronounced land subsidence. To minimize subsidence and increase recovery, brines may be reinjected into producing reservoirs. A local volume averaging technique was employed to derive the differential equations that describe the geopressured aquifer phenomena. These equations were then approximated by an integrated finite-difference method, which generates discrete equations having a more .,,: rigorous conservation property than conventional difference analogs, Energy transport associated with cold brine reinjection is a convection-dominant process. Numerical solutions for such problems are known to display oscillations and/or numerical diffusion. To eliminate oscillations and reduce numerical diffusion, the optimum upwind approach was adopted in this study. Due to large time truncation errors, however, the explicit and implicit applications of this approach were found ineffective for the cell Peclet number greater than 100. When combined with the Crank-Nicolson differencing, solutions became sufficiently accurate. This scheme, however, is subjected to quite restrictive non-oscillation conditions and will not be applicable to a practical reservoir problem in which the local Peclet number greatly varies. Should shales encasing the sandstone aquifers be semipermeable, they will discharge their pore water vertically to the aquifers. Their influence on aquifer pressures can be substantial. Shales also discharge heat vertically to the aquifer zone swept by injected brines. The semi-analytic Vinsome-Westerveld method was accurate and computationally economical in handling this vertical fluid and heat flow in cap and base shales. However, its modified version for an interbedding shale layer yielded errors up to 10 percent and hence, needs refinement. The explicit finite difference shale treatment produced satisfactory results with relatively coarse shale grids and a reasonable time step size, and did not require excessive computer time. The developed computer model incorporates the optimum upwinding and the semi-analytic shale treatment.

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