A Comprehensive Wellbore Stream/Water Flow Model for Steam Injection and Geothermal Applications

Abstract

Abstract A comprehensive mathematical model was developed to simulate the downward or upward flow of a steam/water mixture in a well. Comparisons of model predictions with actual field data for both steam injection for oil recovery and geothermal production showed the validity of the model.The proposed model is based on mass and momentum balances in the wellbore and on heat balance in the wellbore and the surrounding media. Unlike the previous models, the pressure calculation accounts for slip and the prevailing flow regime, based on noted correlations. Furthermore, heat loss to the surrounding formations is treated rigorously. The overall heat transfer coefficient involved permits the consideration of a variety of well completions.The model was employed for a series of tests to evaluate the effects of the injection pressure, injection rate, time, and well completion on the downhole steam pressure and quality. It was found that the slip concept and the flow regime are essential elements in wellbore steam/water flow calculations. Pressure drop was found to increase with a decrease in the injection pressure, as also with more obvious parameters. An increase in the injection pressure or tubing size and/or a decrease in the injection rate led to a decrease in steam quality at a given depth. Introduction Most steam injection operations for heavy oil recovery involve injection of wet steam down the tubing and occasionally down the casing/tubing annulus. Computations of reservoir heating by the injected steam require a knowledge of steam pressure and quality at the formation face. At the same time, it is important to know the heat loss to the surroundings during flow in the wellbore, as well as the casing temperature, for an appropriate well completion. Although several investigators have presented wellbore models for steam injection, none considered the flow regime concept in a unified approach. Furthermore, all models employed only approximate solutions of the one-dimensional radial heat conduction equation to investigate the heat loss.Vertical two-phase flow of water and steam occurs in geothermal wells. Among the geothermal reservoirs, only a few areas are classified as vapor-dominated systems, producing dry to superheated steam. All others are hot-water systems and generally produce a mixture of water and steam at the surface. Here, again, it is necessary to consider two phase flow in the wellbore, coupled with heat transfer, to predict steam pressure and quality at the surface. This problem was considered in detail by Gould.The main purpose of this work was to develop an integrated and comprehensive wellbore model to simulate vertical, nonisothermal, two-phase flow phenomena. The model is a combination of the previous model of Pacheco and Farouq Ali and the pressure/flow-regime correlations of Gould et al., Chierici et al., and Duns and Ros, as well as a number of refinements such as the rigorous treatment of heat flow, geothermal gradient, etc. Mathematical Model The system to be modeled consists of three parts:the fluid flow conduit (tubing or annulus),tubing/casing annulus, casing wall, and cement,the formation encircling the cement. Within the conduit, steady, homogeneous, one-dimensional, two-phase flow is assumed. This is described mathematically by combining a two-phase mass balance with a momentum balance and is as follows (the vertical coordinate z is taken positive in the downward direction). SPEJ P. 527^