Pressure Transient Analysis for Two-Phase Pressure Transient Analysis for Two-Phase (Water/Steam) Geothermal Reservoirs
Abstract
A new diffusivity equation for two-phase (water/steam) flow in geothermal reservoirs is derived. The geothermal reservoir may be initially two-phase or may evolve into a two-phase system during production. Solutions of the diffusivity equation for a continuous line source are presented; the solutions imply that the plot of bottomhole pressure vs. loglot (t=time) should be a straight pressure vs. loglot (t=time) should be a straight line. The slope of the straight line is inversely proportional to the total kinematic mobility. proportional to the total kinematic mobility. Comparison of the theory with a limited number of computer-simulated drawdown histories shows excellent agreement.
Introduction
In petroleum engineering and groundwater hydrology, well tests are conducted routinely to diagnose the well's condition and to estimate formation properties. Well test data may be analyzed to yield quantitative information regarding (1) formation permeability, storativity, and porosity, (2) the presence of barriers and leaky boundaries, (3) the condition of the well (i.e., damaged or stimulated), (4) the presence of major fractures close to the well, and (5) the mean formation pressure. Well testing procedures (and the quality of information obtained) procedures (and the quality of information obtained) depend on the age of the well. During temporary completion, testing involves producing the reservoir using a temporary plumbing system (e.g., drillstem testing), and the estimates obtained for the formation parameters are not very accurate. After completion, parameters are not very accurate. After completion, testing usually is performed in the hydraulic mode. In hydraulic testing, one or more wells are produced at controlled rates, and pressure changes within the producing well itself or nearby observation wells producing well itself or nearby observation wells (interference tests) are monitored.A major concern of well testing is the interpretation of pressure transient data. Much of the existing literature deals with isothermal single-phase (water/oil) and isothermal two-phase (oil with gas in solution, free gas) systems. In general, there is a lack of methodology for analyzing nonisothermal reservoir systems, either single- or two-phase (water/steam). Geothermal reservoirs commonly involve nonisothermal two-phase flow during well testing. This paper presents a theoretical framework for analyzing multiphase pressure transient data in geothermal systems.
Two-Phase Flow in Geothermal Systems
Consider a fully penetrating well located in an infinite reservoir of thickness h. We neglect any variations in either formation or fluid properties in the vertical direction. (This is a common assumption in pressure transient analysis.) The geothermal system may be two-phase before production or may evolve into a two-phase system as a result of fluid production. In the latter case, a boiling front will production. In the latter case, a boiling front will propagate outward from the wellbore. The boiling propagate outward from the wellbore. The boiling front may be treated as a constant-pressure boundary (p=saturation pressure corresponding to the local reservoir temperature).For the sake of simplicity, consider a reservoir that is initially two-phase everywhere. Furthermore, it is convenient to assume that the pressure (and, hence, temperature) is uniform throughout the system. In radial geometry, the pressure response is governed by the following diffusivity equation (see Appendix for a derivation of Eq. 1).
(1)
SPEJ
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