A Set of New Correlations for the Compressibility of Two-Phase Water and for the Steam Z Factor in a Wide Thermodynamic Range

摘要

The methods used in the interpretation of transient pressure tests (TPT) range from very simple analytical models up to highly complex numerical techniques. The models of the traditional TPT analysis use several simplifications, for example, that the fluid is lightly compressible and the flow has a simple geometry. Other assumptions include homogeneous rock properties, uniform pressure in the reservoir and constant extraction rates. Computer-aided current methods are capable of handling more complex scenarios with concrete geological characteristics and fluid realistic behavior. In the most advanced models, it is not necessary to assume a small compressibility and the fluid may be non-isothermal and two-phase. The TPT analyses in both cases allow studying the local behavior of the reservoir under dynamic conditions of phase change. In these models, the accurate calculation of fluid compressibility in the total rock-liquid-steam system is needed. In case that the reservoir produces only steam or the system conditions goes farther the critical point presenting a supercritical phase, the calculus of the steam compressibility is the key point in the correct interpretation of the pressure test. When the drain volume of a well contains pure steam, the traditional pressure equations based on the Theis model, cannot be used directly. This is due to the high compressibility of the steam and to the fact that all the thermodynamic properties of steam depend on pressure and temperature (p, T). This means that the differential equations of the simplest model become nonlinear. The Z compressibility factor is defined as the ratio of the volume occupied by a real gas to the volume occupied by an ideal gas at the same (p, T) conditions. The Z factor is not constant and depends on (p, T) for different gases. Under geothermal conditions the radial flow differential equation can be formulated by defining a normalized pseudopressure of the real gas, which depends on both, its dynamic viscosity and Z. In this paper, we present new correlations for the computation of the geothermal fluid compressibility for each one of its two phases. A new correlation to compute approximately the Z factor is also included. In the case of the steam, its compressibility behaves in a strange way when its temperature is between the critical point and 450°C. These correlations cover a wide thermodynamic range, [1, 400] bar and [10, 450] °C, which includes some observed singularities, the traditional geothermal enthalpy as well as reservoirs with very high enthalpy at supercritical temperature conditions.