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Mathematical modeling of the behavior of geothermal systems under exploitation

Description: Analytical and numerical methods have been used in this investigation to model the behavior of geothermal systems under exploitation. The work is divided into three parts: (1) development of a numerical code, (2) theoretical studies of geothermal systems, and (3) field applications. A new single-phase three-dimensional simulator, capable of solving heat and mass flow problems in a saturated, heterogeneous porous or fractured medium has been developed. The simulator uses the integrated finite difference method for formulating the governing equations and an efficient sparse solver for the solution of the linearized equations. In the theoretical studies, various reservoir engineering problems have been examined. These include (a) well-test analysis, (b) exploitation strategies, (c) injection into fractured rocks, and (d) fault-charged geothermal reservoirs.
Date: January 1, 1982
Creator: Bodvarsson, G.S.
Partner: UNT Libraries Government Documents Department

Numerical modeling of geothermal systems with applications to Krafla, Iceland and Olkaria, Kenya

Description: The use of numerical models for the evaluation of the generating potential of high temperature geothermal fields has increased rapidly in recent years. In the present paper a unified numerical approach to the modeling of geothermal systems is discussed and the results of recent modeling of the Krafla geothermal field in Iceland and the Olkaria, Kenya, are described. Emphasis is placed on describing the methodology using examples from the two geothermal fields.
Date: August 1, 1987
Creator: Bodvarsson, G.S.
Partner: UNT Libraries Government Documents Department

Numerical studies of enthalpy and CO/sub 2/ transients in two-phase wells

Description: Numerical studies of enthalpy and CO/sub 2/ transients for wells completed in composite reservoir systems are carried out. Both constant rate and constant pressure production are considered. The results show that relatively small variations in hydrologic parameters and vapor saturation can have large effects on the enthalpy and CO/sub 2/ content of the produced fluids. Field data are presented that illustrate the theoretical results obtained.
Date: August 1, 1984
Creator: Bodvarsson, G.S.
Partner: UNT Libraries Government Documents Department

Reinjection into geothermal reservoirs

Description: Reinjection of geothermal wastewater is practiced as a means of disposal and for reservoir pressure support. Various aspects of reinjection are discussed, both in terms of theoretical studies as well as specific field examples. The discussion focuses on the major effects of reinjection, including pressure maintenance and chemical and thermal effects. (ACR)
Date: August 1, 1987
Creator: Bodvarsson, G.S. & Stefansson, V.
Partner: UNT Libraries Government Documents Department

Some design considerations for the proposed Dixie Valley tracer test

Description: A tracer test for the Dixie Valley, Nevada, geothermal resource is planned for the summer of 1988, in order to study the fluid flow paths that will develop under typical operating conditions. During the test six production wells will provide the power plant with steam sufficient for generation of 60 MWe, requiring fluid production at a rate of approximately 600 kg/sec. Up to 75% by mass of the extracted fluid will be reinjected into the reservoir, using four injection wells. Tracer will be added to the injected fluid for a twenty-minute period, and subsequently the produced fluid will be monitored for the tracer. 5 refs., 9 figs., 5 tabs.
Date: June 1, 1988
Creator: Doughty, C. & Bodvarsson, G.S.
Partner: UNT Libraries Government Documents Department

Analysis of internal wellbore flow

Description: Most two-phase geothermal wells are located in fractured rocks and intersect a few major feedzones. It is well known that internal wellbore flow between feedzones often occurs during warmup or pressure recovery periods. The internal flow can occur even when the reservoir is initially in pressure equilibrium because of the different phase composition that develops within the wellbore. Internal flow can cause large apparent pressure drawdowns and significantly affect pressure and temperature surveys as well as pressure buildup tests. This paper presents an analytic method for using static pressure surveys to calculate internal flowrates between two zones when the reservoir characteristics are known. Conversely, the transmissivity of the feedzone with the lowest transmissivity can be calculated from measurements of internal flowrates and wellbore pressures. 3 refs., 6 figs.
Date: January 1, 1988
Creator: Ripperda, M. & Bodvarsson, G.S.
Partner: UNT Libraries Government Documents Department

Effects of non-condensible gases on fluid recovery in fractured geothermal reservoirs

Description: Numerical simulations are performed in order to investigate the effects of noncondensible gases (CO/sub 2/) on fluid recovery and matrix depletion in fractured geothermal reservoirs. The model used is that of a well producing at a constant bottomhole pressure from a two-phase fractured reservoir. The results obtained have received a complex fracture-matrix interaction due to the thermodynamics of H/sub 2/O-CO/sub 2/ mixtures. Although the matrix initially contributes fluids (liquid and gas) to the fractures, later on, the flow directions reverse and the fractures backflow fluids into the matrix. The amount of backflow depends primarily upon the flowing gas saturation in the fractures; the lower the flowing gas saturation in the fractures the more backflow. It is shown that the recoverable fluid reserves depend strongly on the amount of CO/sub 2/ present in the reservoir system.
Date: February 1, 1986
Creator: Bodvarsson, G.S. & Gaulke, S.
Partner: UNT Libraries Government Documents Department

Thermal effects of reinjection in geothermal reservoirs with major vertical fractures

Description: Possibilities for characterizing the thermal properties of fast paths by means of different types of tests (tracers, pressure transients, non-isothermal injection) are discussed. Thermal breakthrough in vertical fractures is examined in some detail, using an idealized model for which an analytical solution is available. The model shows that rapid tracer returns are not necessarily indicative of rapid thermal interference. Thermal breakthrough predictions can be made from tracer data only, if both fluid residence time and tracer dispersion are taken into account. However, due to the geometric simplifications necessary in analyzing the tracer data, thermal interference estimates on this basis appear questionable. Pressure transient tests can provide additional parameters for thermal interference predictions, but they cannot resolve the problem of non-uniqueness. A more reliable determination of thermal characteristics of fast paths appears possible from non-isothermal injection tests, combined with numerical simulation. A mixed numerical/semi-analytical approach is employed to model the three-dimensional fluid and heat flow in injection-production systems in vertical fractures, with heat transfer to and from the adjacent rock matrix. Illustrative calculations of thermal recovery after different injection periods suggest that shutting-in an injection well can prevent unacceptable temperature declines at production wells.
Date: October 1, 1983
Creator: Pruess, K. & Bodvarsson, G.S.
Partner: UNT Libraries Government Documents Department

Modeling studies of geothermal systems with a free water surface

Description: A numerical simulator was developed for the modeling of air-steam-water systems. The simulator was applied to various problems involving injection into or production from a geothermal reservoir in hydraulic communication with a shallow free-surface aquifer. First, a one-dimensional column problem is considered and the water level movement during exploitation is studied using different capillary pressure functions. Second, a two-dimensional radial model is used to study and compare reservoir depletion for cases with and without a free-surface aquifer. Finally, the contamination of a shallow free-surface aquifer due to cold water injection is investigated. The primary aim of these studies is to obtain an understanding of the response of a reservoir in hydraulic communication with a unconfined aquifer during exploitation or injection and to determine under which circumstances conventional modeling techniques (fully saturated systems) can be applied to such systems.
Date: December 1, 1983
Creator: Bodvarsson, G.S. & Pruess, K.
Partner: UNT Libraries Government Documents Department

A multi-feedzone wellbore simulator

Description: A multi-feedzone wellbore simulator has been developed. This computer code is quite general as it enables one to compute downhole conditions in wells with an arbitrary number of feedzones during discharge or injection. The simulator is applied to flowing pressure and temperature surveys from various wells in Mexico, Iceland and Kenya. It is demonstrated that such a model can be used to estimate flow rates and enthalpies of individual feedzones.
Date: June 1, 1987
Creator: Bjornsson, G. & Bodvarsson, G. S.
Partner: UNT Libraries Government Documents Department

Combined analytical/numerical approaches to solving fluid flow problems in the unsaturated zone at Yucca Mountain

Description: Various analytical and numerical approaches are presented for the study of unsaturated flow processes in the vicinity of the Yucca Mountain, Nevada, the proposed site of an underground radioactive waste repository. Approximate analytical methods are used to study absorption of water from a saturated fracture into the adjacent rock. These solutions are incorporated into a numerical simulator as fracture/matrix interaction terms to treat problems such as flow along a fracture with transverse leakage into the matrix. An automatic fracture/matrix mesh generator is described; it allows for more efficient mesh generation for fractured/porous media, and consequently leads to large savings in computational time and cost. 21 refs., 6 figs.
Date: January 1, 1990
Creator: Zimmerman, R.W. & Bodvarsson, G.S.
Partner: UNT Libraries Government Documents Department

Numerical studies of gravity effects in two-phase reservoirs

Description: Numerical studies are performed to investigate the effects of localized feed zones on the pressure transients in two-phase reservoirs. It is shown that gravity effects can significantly affect the pressure transients, because of the large difference in the density of liquid water and vapor. Pressure transients for shallow and deep feed zones and the resulting fluid flow patterns are discussed.
Date: June 1, 1986
Creator: Bodvarsson, G.S. & Cox, B.L.
Partner: UNT Libraries Government Documents Department

Convective heat transport in geothermal systems

Description: Most geothermal systems under exploitation for direct use or electrical power production are of the hydrothermal type, where heat is transferred essentially by convection in the reservoir, conduction being secondary. In geothermal systems, buoyancy effects are generally important, but often the fluid and heat flow patterns are largely controlled by geologic features (e.g., faults, fractures, continuity of layers) and location of recharge and discharge zones. During exploitation, these flow patterns can drastically change in response to pressure and temperature declines, and changes in recharge/discharge patterns. Convective circulation models of several geothermal systems, before and after start of fluid production, are described, with emphasis on different characteristics of the systems and the effects of exploitation on their evolution. Convective heat transport in geothermal fields is discussed, taking into consideration (1) major geologic features; (2) temperature-dependent rock and fluid properties; (3) fracture- versus porous-medium characteristics; (4) single- versus two-phase reservoir systems; and (5) the presence of noncondensible gases.
Date: August 1, 1986
Creator: Lippmann, M.J. & Bodvarsson, G.S.
Partner: UNT Libraries Government Documents Department

Pressure transient method for front tracking

Description: A pressure transient technique for tracking the advance of cold water fronts during water flooding and goethermal injection operations has been developed. The technique is based on the concept that the steady state pressure buildup in the reservoir region inside the front can be calculated by a fluid skin factor. By analyzing successive pressure falloff tests, the advance of the front in the reservoir can be monitored. The validity of the methods is demonstrated by application to three numerically simulated data sets, a nonisothermal step-rate injection test, a series of pressure falloffs in a multilayered reservoir, and a series of pressure falloff tests in a water flooded oil reservoir.
Date: August 1, 1983
Creator: Benson, S.M. & Bodvarsson, G.S.
Partner: UNT Libraries Government Documents Department

Preliminary studies of two-phase effects on pressure transient data

Description: In this paper we perform scoping calculations on the effects of two-phase zones on well pressure transients. Three different cases are considered. The first is that of a fully two-phase system (e.g. Krafla, Iceland). Some of the complexities of this type of system are discussed. The second problem is that of a single-phase liquid reservoir with a localized two-phase zone. Possible field examples include Cerro Prieto, Mexico and Baca, New Mexico, USA. We investigate the pressure transients in a well located near an isolated two-phase zone in a single-phase liquid reservoir, and compare them to type curves based upon the constant pressure approximation. The third problem considered is that of a two-phase layer overlying a single-phase liquid layer. One example of such a reservoir is the Svartsengi geothermal field in Iceland. The numerical code MULKOM is used to simulate the three cases.
Date: March 1, 1986
Creator: Cox, B.L. & Bodvarsson, G.S.
Partner: UNT Libraries Government Documents Department

Generating capacity of the Heber geothermal field, California

Description: Using numerical simulation techniques and the radial model developed for the study of the natural state of the Heber field (Lippmann and Bodvarsson, 1983b), the response of this geothermal system to exploitation is analyzed. In this study the generation rate in the field is allowed to build up over a period of 10 years; after that, 30 years of constant power production is assumed. Full (100%) injection of the spent brines is considered, the fluids being injected 2250 m (near injection) or 4250 m (far injection) from the center of the system. The study shows that a maximum of 6000 kg/s (equivalent to approximately 300 MW/sub e/) of fluids may be produced for the near injection case, but only 3000 kg/s (equivalent to approximately 150 MW/sub e/) for the far injection case. The results indicate that the possible extraction rates (generating capacity) generally are limited by the pressure drop in the reservoir. The average temperature of the produced fluids will decline 10 to 18/sup 0/C over the 40-year period.
Date: December 1, 1983
Creator: Lippmann, M.J. & Bodvarsson, G.S.
Partner: UNT Libraries Government Documents Department

Flow rate decline of steam wells in fractured geothermal reservoirs

Description: Decline curves are commonly used at The Geysers geothermal field to assess the generating capacity of a producing lease. It is generally assumed that wells will initially be drilled using 40-acre (400 m) spacing, with infill drilling used later to provide additional producing wells as needed. It is commonly believed that the final well spacing should not be less than 10 acres (200 m). Decline curves are used with this approach to estimate the number of make-up wells during a project lifetime (up to 30 years), as well as the appropriate plant size (MWe). A rather simple two-dimensional model was used to investigate the factors that control flow rate decline in steam wells. The effects of parameters such as fracture spacing and permeability are considered, as well as the effects of permeability, porosity and initial liquid saturation in the rock matrix. Also, the conventional P/z method that is commonly used in analyzing gas well production is investigated in terms of its applicability to fractured vapor dominated systems.
Date: January 1, 1985
Creator: Bodvarsson, G.S. & Witherspoon, P.A.
Partner: UNT Libraries Government Documents Department

Analysis of pressure, enthalpy and CO/sub 2/ transients in well BR21, Ohaaki, New Zealand

Description: Numerical studies are undertaken, which incorporate both double porosity and noncondensible gas effects, to determine the characteristics of the reservoir near well BR21 of Ohaaki geothermal field, New Zealand. It is shown that the application of numerical techniques to analyze two-phase well data can provide valuable information that may not otherwise be obtained. Numerical techniques allow more of the true reservoir complexities to be included, further constraining the results. The model developed adequately matches observed pressure, enthalpy and flowing CO/sub 2/ mass fraction while providing estimates of important reservoir parameters.
Date: June 1, 1987
Creator: Gaulke, S.W. & Bodvarsson, G.S.
Partner: UNT Libraries Government Documents Department

Injection into a fractured geothermal reservoir

Description: A detailed study is made on the movement of the thermal fronts in the fracture and in the porous medium when 100{sup 0}C water is injected into a 300{sup 0}C geothermal reservoir with equally spaced horizontal fractures. Numerical modeling calculations were made for a number of thermal conductivity values, as well as different values of the ratio of fracture and rock medium permeabilities. One important result is an indication that although initially, the thermal front in the fracture moves very fast relative to the front in the porous medium as commonly expected, its speed rapidly decreases. At some distance from the injection well the thermal fronts in the fracture and the porous medium coincide, and from that point they advance together. The implication of this result on the effects of fractures on reinjection into geothermal reservoirs is discussed.
Date: May 1, 1980
Creator: Bodvarsson, G.S. & Tsang, C.F.
Partner: UNT Libraries Government Documents Department

Modeling study of the natural state of the Heber geothermal field, California

Description: As a first step in simulating the behavior of the Heber field under exploitation, the system is modeled in its natural (pre-exploitation) state. Using Lawrence Berkeley Laboratory's (LBL) computer code PT and a radially symmetric model, a reasonable match between published and calculated temperature and pressure distributions is obtained. The results of the study indicate that the Heber geothermal system is created by the upflow of hot water through a central zone of higher permeability. The model shows that in its natural state the system is recharged at depth by a 15 MW(thermal) convective heat source. The existence of a radially symmetric convection pattern, whose axis coincides with that of the Heber anomaly is suggested. At the lower part of the ascending hot water plume, the deep recharge water mixes with colder water moving laterally towards the axis of the system. On the upper part, the rising plume spreads radially outward before reaching the bottom of the caprock, at 550 m depth. The model results suggest that the caprock is quite permeable, with convection controlling the temperature distribution. The low permeability of the upper zones in the outer region of the system may be due to mineral precipitation.
Date: June 1, 1983
Creator: Lippmann, M.J. & Bodvarsson, G.S.
Partner: UNT Libraries Government Documents Department

Nonisothermal injection tests in fractured reservoirs

Description: The paper extends the analysis of nonisothermal pressure transient data to fractured reservoirs. Two cases are considered: reservoirs with predominantly horzontal fractures and reservoirs with predominantly vertical fractures. Effects of conductive heat transfer between the fractures and the rock matrix are modeled, and the resulting pressure transients evaluated. Thermal conduction tends to retard the movement of the thermal front in the fractures, which significantly affects the pressure transient data. The purpose of the numerical simulation studies is to provide methods for analyzing nonisothermal injection/falloff data for fractured reservoirs.
Date: January 1, 1985
Creator: Cox, B.L. & Bodvarsson, G.S.
Partner: UNT Libraries Government Documents Department

Analysis of production data from the Krafla geothermal field, Iceland

Description: The analysis of flow rate and enthalpy data from several wells completed in the same two-phase zone of Krafla geothermal reservoir has yielded consistent relative permeability parameters. It is found that k/sub rl/ + k/sub rv/ = 1 over the entire range of two-phase flow conditions from immobile liquid to immobile vapor. The available data provide relative permeability parameters as a function of flowing enthalpy only. The relationship between flowing enthalpy and in-place vapor saturation remains unknown, so that the relative permeability information obtained is of limited value for quantitative modeling of geothermal reservoir performance. Numerical simulation of flow rate and enthalpy transients has yielded excellent matches to production data from well 12. However, there is little information about the reservoir which can be deduced in an unambiguous way, because the field data could be matched with a variety of rather different parameter choices. The only unambiguous piece of information obtained is that the water injected into the well during drilling and completion remains in the vicinity of the wellbore during several weeks of warmup.
Date: December 1, 1983
Creator: Pruess, K.; Bodvarsson, G. S. & Stefansson, V.
Partner: UNT Libraries Government Documents Department

Decline curve analysis of production data from The Geysers geothermal field

Description: Production data for over two hundred wells at The Geysers geothermal field were compiled and analyzed. Decline curves for groups of wells with 5, 10, and 40 acre spacing are presented and compared to curves published previously by Budd (1972) and Dykstra (1981). Decline curves for several individual wells and leases are discussed to illustrate the effects of well spacing and location, as well as the heterogeneous nature of the reservoir.
Date: January 1, 1987
Creator: Ripperda, M. & Bodvarsson, G.S.
Partner: UNT Libraries Government Documents Department

Nonisothermal effects during injection and falloff tests

Description: The results show that to correctly analyze pressure transients governed by a moving thermal front, the values used for the fluid properties must correspond to the temperature of the injected fluid. On the other hand, for pressure falloff tests and for injection tests conducted in a well cooled by previous injection or drilling, the physical properties of the in situ reservoir fluids must be used. It is also shown that the application of conventional isothermal methods for calculating skin values from injection and falloff data will give erroneous results. A new method is presented for calculating skin values from injection and falloff data that accurately corrects for nonisothermal effects. A number of detailed examples are given that illustrate the suggested method of analysis. The technique is applied to the analysis of injection test data from a well located in the East Mesa geothermal field in southern California.
Date: September 1, 1982
Creator: Benson, S.M. & Bodvarsson, G.S.
Partner: UNT Libraries Government Documents Department