App1,ication of a Lumped Parameter Model to the Cerro Prieto Geothermat, Field

In this paper, a lumped parameter mathematical model for hot water geothermal reservoirs is developed and applied to the Cerro Prieto geothermal field in Mexico. The production and pressure histories of Cerro Prieto were assembled from field data. A computer program was then used to perform sensitivity studies on reservoir size, porosity, aquifer recharge, and temperature of recharge fluid. Two types of depletion schemes were investigated; in the first, the reservoir remains essentially one-phase liquid, and in the second, the reservoir becomes two-phase at a point early in its history. the history of the field has been obtained. This paper shows the usefulness of a lumped parameter model in clarifying the basic behavior of a hot water geothermal system and in giving focus to more complex twoand threedimensional modeling efforts. The results obtained specifically for the Cerro Prieto field will also be of value to the scientists and engineers studying this reservoir. Introduction Typically, a geothermal power plant must have a lifetime of thirty years to be economic. Because of the large increments of investment necessary at each successive stage of development, it is especially important to be able to forecast the future performance of a field from existing knowledge. Geothermal reservoir models attempt to serve this predictive function. In the beginning of the life of a field, when relatively little is known, the simplest models, which require the least amount of information, are appropriate. Later, as more information is accumulated about the geologic, geochemical, hydrodynamic, and thermodynamic characteristics of the field, these models may be refined and a better understanding of the resource achieved. One of the simplest types of mathematical models is the so-called "lumped parameter" model. The purpose of this kind of simulator is to match average reservoir behavior. The reservoir is treated as a homogeneous body, whose characteristics change as quantities of mass and energy enter and exit. parameter throughout the model reservoir is the average value of that parameter in the real system. A satisfactory match of The value of a particular .L n Now with Marathon Oil. In this paper, a lumped parameter approach to geothermal modeling is investigated. The amount of data required is minimal compared to finite-difference models. The Cerro Prieto geothermal field in Mexico was the subject of the modeling study; the lumped parameter model is most appropriate here since the field is still "young,11 having entered its eighth year of commercial production. Some examples of lumped parameter models can be found in the literature. Whiting and Ramey (8) first used this concept in 1969 to model the Wairakei reservoir in New Zealand. Brigham and Morrow (2) in 1974 developed three models appriate for closed, vapor-dominated reservoirs. In 1979 Brigham and Neri (3) modeled the Gabbro zone o f the Larderello field. Castanier, Sanyal, and Brigham ( 4 ) included heat transfer in the recharge region to simulate the behavior of the East Mesa reservoir. To date, there have been no lumped parameter studies of the Cerro Prieto field similar to those reviewed above. However, a few preliminary simulation efforts have been made. In 1978, Lippmann, Bodvarsson, et al. ( 6 ) , formulated a simplified three-dimensional, finitedifference model of the reservoir. In 1979, Lippmann and Goyal presented the results of two three-dimensional, finite-difference, hydrogeoloeic models of Cerro Prieto (7). Liguori(5) in 1979 used a simplified finite-difference reservoir model coupled to a wellbore model. The Cerro Prieto Field The Cerro Prieto field is located about 30 km south of Mexicali, Mexico. This study is concerned with modeling the area of the field shown in Fig. 1, which supplies Units 1 and 2 and which has been in production since 1973. forated interval of 100-200 m at an average depth of 1200-1300 m. However, because of the complex interbedding, it is not obvious what the thickness of the reservoir is in this area Porosity ranges from .15 to .35 in sand or sandstone, but is lower in shales. Various estimates of the permeabilities range from 40 to 100 md. The temperature of most wells in the Unit 1 and 2 area is about 300°C. Noncondensable gases, predominantly Cog and HzS, are present in sufficient quantity to affect both the compressibility and the phase behavior. The wells have a per-