Geothermal Reservoir Modelling

Abstract

Abstract This paper describes and partially evaluates an implicit, three-dimensional geothermal reservoir simulation model. The evaluation emphasizes stability or time-step tolerance of the implicit finite-difference formulation. In several illustrative multiphase flow problems, the model stably accommodated time steps corresponding to grid block saturation changes of 80–100% and grid block throughput ratios the order of 10(8). This compares to our experience of limits of 3 to 10% saturation change and roughly 20,000 throughput ratio with semi-implicit oil and geothermal reservoir models. The illustrative applications shed some light on practical aspects of geothermal reservoir behavior. Applications include single- and two-phase single-well behavior, fractured-matrix reservoir performance and well test interpretation, and extraction of energy from fractured hot dry rock. Model stability allows inclusion of formation fractures and wellbores as grid blocks. An analytical derivation is presented for a well deliverability reduction factor which can be used in simulations using large grid blocks. The factor accounts for reduced deliverability due to hot water flashing and steam expansion accompanying pressure decline near the well. This paper describes a numerical model for simulating geothermal well or reservoir performance. The model is considerably more performance. The model is considerably more general than any described in the literature to date. It treats transient, three-dimensional, single- or two-phase fluid flow in normal heterogeneous or fractured-matrix formations. Both conductive and convective heat flow are accounted for and fluid states in the reservoir can range from undersaturated liquid to two-phase steam-water mixtures to superheated steam. Aquifer water influx and heat source/sink terms necessary in simulating free convection cells are included in the model formulation. The primary purpose of the work described here was evaluation of the capability of an implicit model formulation. our experience with semi-implicit simulation of petroleum and geothermal reservoirs has shown time step restrictions related to conditional stability. In multiphase flow problems, the maximum tolerable time step size generally corresponds to a maximum of 3 to 10 percent saturation change in any grid block in one time step. In some steamflood and geothermal simulations, we have found this to result in very small time steps and correspondingly high computing costs. This work was performed with the hope that the implicit model formulation would give unconditional stability with no time step restriction other than that imposed by time truncation error. Calculated results are presented for a variety of geothermal well and reservoir illustrative problems. Emphasis in connection with these results is placed on the stability or time step tolerance of the model. However, the applications are also intended to shed some light on practical aspects of geothermal reservoir practical aspects of geothermal reservoir behavior.