Pressure Buildup Analysis of Geothermal Steam Wells With a Parallelepiped Model
- Michael J. Economides (Stanford U.) | David Ogbe (Stanford U.) | Frank A. Miller (Stanford U.) | Heber Cinco-Ley (U. of Mexico) | Eric L. Fehlberg (Shell Oil Co.)
- Document ID
- Society of Petroleum Engineers
- Journal of Petroleum Technology
- Publication Date
- April 1982
- Document Type
- Journal Paper
- 925 - 929
- 1982. Society of Petroleum Engineers
- 5.6.4 Drillstem/Well Testing, 5.9.2 Geothermal Resources, 1.10.1 Drill string components and drilling tools (tubulars, jars, subs, stabilisers, reamers, etc)
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Geothermal well testing, a discipline that evolved from conventional oil and gas well testing, often requires special considerations. The geometry of the reservoir and those characteristics frequently found in geothermal systems engendered the idea of a parallelepiped model with interpenetrating fractures. Such geometry can be described mathematically using Green's and source functions. Equations of reservoir pressure behavior then can be developed for both drawdown and buildup tests. Graphs describing dimensionless pressure as a function of time and various reservoir parameters are provided in this paper. The general method used is type-curve matching.
There are three major types of geothermal resources: (1) vapor-dominated (dry-steam) such as in The Geysers (CA) or in Tuscany of central Italy, (2) two-phase such as in New Zealand, and (3) hot-water, found in several locations. The most useful, in terms of power production, are the vapor-dominated reservoirs. They are also the most rare. A number of geothermal reservoirs exhibit transient pressure behavior that indicates large, highly conductive fractures. The size of these reservoirs is controlled by faults and overlying impermeable rocks. A constant-pressure boundary, presumably boiling water, often is observed.
A parallelepiped model conceptually could approximate such a configuration. A model with closed, no-flow boundaries on five sides and a constant-pressure boundary on the bottom was described by Cinco-Ley et al. The fracture system was simulated as a rectangular-shaped source. The concept is limited to vapor-dominated reservoirs. Both geologic evidence and production histories have precluded the use of radial models in both The Geysers and Larderello, Italy. Hence, the parallelepiped model, with the included fracture and subformation boiling front, is intended to analyze pressure transient behavior in dry-steam geothermal wells.
The model assumes constant-flow-rate production in an anisotropic, homogeneous reservoir. If the flow rate vases, an influence function such as that described by Economides et al. can be used in the subsequent type-curve matching. The reservoir described by the model contains a slightly compressible fluid of constant viscosity and compressibility c. an assumption totally inadequate in the case of geothermal steam. Yet the shortcomings can be overcome if the pseudopressure function m(p) is used. The real-gas pseudopressure was discussed by Al-Hussainy and Ramey. All of these assumptions normally are used in geothermal well testing, irrespective of the model. Although the solution can be modified to incorporate fracture(s) anywhere in the reservoir, a vertical, partially penetrating fracture has been used. The fracture is in the center of a parallelepiped reservoir of square horizontal cross section.
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