Analysis of Internal Steam Drive in Geothermal Reservoirs

Abstract

Petroleum reservoir analysis methods are applied to simple closed geothermal reservoirs that produce by internal steam drive. The fundamental assumption is that fluid flow in a geothermal reservoir can be treated as flow through a porous medium, and Darcy's law and relative permeabilities are applicable. Calculated performances are given for various types of reservoirs. Results indicate that hot-water reservoirs can have complicated behaviors. Introduction Testing of geothermal energy prospects has accelerated in recent years. Increased understanding is needed of the fundamental heat and fluid flow involved in geothermal reservoir production. Techniques used by petroleum production researchers are particularly well suited to the study of these fundamentals and to geothermal reservoir engineering research in general. Some geothermal reservoirs are similar to oil and gas reservoirs. These reservoirs are porous media through which the fluids flow according to Darcy's law. Furthermore, some geothermal reservoirs have the equivalent of cap rocks. The analogy of geothermal reservoirs with oil and gas reservoirs is the basis for the fundamental assumption of this paper; fluid flow in a geothermal reservoir can be treated as flow through a porous medium, and Darcy's law and relative permeabilities are applicable. There are many analogies between petroleum and geothermal reservoir engineering. For example, a number of the drives that supply reservoir energy are similar. The edge water drive in a petroleum reservoir is analogous to influx from cooler aquifers in geothermal reservoirs. Solution gas drive in petroleum reservoirs is analogous to two-phase, internal steam drive in geothermal reservoirs. Compaction drive can occur in both types of reservoir. Waterflooding an oil reservoir is analogous to water cycling in a hot-water geothermal reservoir. Methods of analysis similar to those used in petroleum reservoir engineering can be used for geothermal reservoirs, as illustrated by the development of the material and heat balances in Ref. I. The present paper presents an analysis of internal steam drive using methods similar to those used for solution gas drive in Ref. 2. The analysis is based on the following assumptions. The temperature, pressure, and fluid saturation gradients are small; the steam and hot water are produced according to their respective mobilities as determined by relative permeabilities and viscosities; and the effects of capillary pressure and gravity can be neglected. Some gravitational effects, however, are treated qualitatively in the discussion. Throughout the analysis and discussion, the produced steam and hot water are calculated neglecting the pressure and temperature drops near the wells and in the well bores . The effects of these additional changes must be introduced to obtain steam and hot-water production rates at the wellhead. Discussion Temperature-Pressure Behavior As pointed out in Ref. 1, initial temperature and pressure in a geothermal reservoir determine its reservoir type. The solid line in Fig. I presents the boiling curve for pure water. (Curves for actual geothermal brines will be modified by the dissolved salts.3) Points to the right of the curve and below the critical temperature represent hot-water reservoirs. Points to the left of the curve and above the critical temperature represent single-phase or steam reservoirs. Temperature-Pressure Behavior As pointed out in Ref. 1, initial temperature and pressure in a geothermal reservoir determine its reservoir type. The solid line in Fig. I presents the boiling curve for pure water. (Curves for actual geothermal brines will be modified by the dissolved salts.3) Points to the right of the curve and below the critical temperature represent hot-water reservoirs. Points to the left of the curve and above the critical temperature represent single-phase or steam reservoirs.