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Abstract Numerical studies of the effects of injection on the behavior of production wells completed in fractured two-phase geothermal reservoirs are presented. In these studies the multiple-interacting-continua (MINC) method is employed for the modeling of idealized fractured reservoirs. Simulations are carried out for a five-spot well pattern with various well spacings, fracture spacings, and pattern with various well spacings, fracture spacings, and injection fractions. The production rates from the wells are calculated using a deliverability model. The results of the studies show that injection into two-phase fractured reservoirs increases flow rates and decreases enthalpies of producing wells. These two effects offset each other so that injection tends to have small effects on the usable energy output of production wells in the short term. However, if a sufficiently large fraction of the produced fluids is injected, the fracture system may become liquid-filled and an increased steam rate is obtained. Our studies show that injection greatly increases the long-term energy output from wells because it helps extract heat from the reservoir rocks. If a high fraction of the produced fluids is injected, the ultimate energy recovery will increase many-fold. Introduction At present, reinjection of geothermal brines is employed or being considered at most high-temperature geothermal fields under development. At many geothermal fields, primarily those in the U.S. or Japan, reinjection is a primarily those in the U.S. or Japan, reinjection is a necessity because environmental considerations do not permit surface disposal of the brines (unacceptable permit surface disposal of the brines (unacceptable concentrations of toxic minerals). At other fields (e.g., The Geysers, CA) reinjection is used for reservoir management to help maintain reservoir pressures and to enhance energy recovery from the reservoir rocks. The effectiveness of injection in maintaining reservoir pressures has been illustrated at the Ahuachapan geothermal field in El Salvador. During the last decade various investigators have studied the effects of injection on pressures and overall energy recovery from geothermal fields. Theoretical studies have been carried out by Kasameyer and Schroeder, Lippmann et al., O'Sullivan wad Pruess, Schroeder et al., and Pruess, among others. Site-specific studies were reported by Morris and Campbell on East Mesa, CA; Schroeder et al. and Giovannoni et al. on Larderello, Italy; Bodvarsson et al. on Baca, NM; Tsang et al. on Cerro Prieto, Mexico; and Jonsson and Pruess et al. on Krafla, Iceland. These studies have given valuable insight into physical processes and reservoir response during injection. However, there is limited understanding of injection effects in fractured reservoirs, especially high-temperature, two-phase systems. Fundamental studies and quantitative results for the design of injection programs in such systems are greedy needed. The objectives of the present work are to investigate the effects of injection on the behavior of fractured two-phase reservoirs. Several questions will be addressed.How will injection affect flow rates and enthalpies of the production wans? Can injection increase the short-term usable energy output of well? What are the long-term effects of injection? How is the efficiency of injection dependent on factors such as well spacing and fracture spacing? Reliable answers to these questions should be valuable for field operators in the design of injection systems for two-phase fractured reservoirs. Approach In the present work we consider wells arranged in a five-spot pattern (Fig. 1). Because of symmetry we only need to model one-eighth of a basic element as shown in Fig. 1; however, our results always are presented for the full five spot. The "primary" (porous medium) mesh shown in Fig. 1 consists of 38 elements; some of the smaller ones close to the wells are not shown. The mesh has a single layer, so that gravity effects are neglected. The fractured reservoir calculations are carried out by the MINC method, which is a generalization of the double-porosity concept introduced by Barenblatt et al. and Warren and Root. The basic reservoir model consists of rectangular matrix blocks bounded by three sets of orthogonal infinite fractures of equal aperture b and spacing D (Fig. 2a. M the mathematical formulation the fractures with high transport and low storage capacity are combined into one continuum and the low-permeability, high storativity matrix blocks into another. The MINC method treats transient flow of fluid (steam and/or water) and heat between the two continua by means of numerical methods. Resolution of the pressure and temperature gradients at the matrix/fracture interface is achieved by partitioning of the matrix blocks into a series of interacting partitioning of the matrix blocks into a series of interacting continua. SPEJ P. 303
- North America > United States > California (0.47)
- North America > El Salvador > Ahuachapรกn > Ahuachapรกn (0.24)
- Europe > Italy > Tuscany > Pisa Province > Larderello (0.24)
- Geology > Geological Subdiscipline > Volcanology (0.48)
- Geology > Mineral (0.34)
- Energy > Renewable > Geothermal > Geothermal Resource (1.00)
- Energy > Oil & Gas > Upstream (1.00)
Abstract A multiple interacting continua (MINC) method is presented, which is applicable for numerical simulation presented, which is applicable for numerical simulation of heat and multiphase fluid flow in multidimensional, fractured porous media. This method is a generalization of the double-porosity concept. The partitioning of the flow domain into computational volume elements is based on the criterion of approximate thermodynamic equilibrium at all times within each element. The thermodynamic conditions in the rock matrix are assumed to be controlled primarily by the distance from the fractures, which leads to the use of nested gridblocks. The MINC concept is implemented through the integral finite difference (IFD) method. No analytical approximations are made for coupling between the fracture and matrix continua. Instead, the transient flow of fluid and heat between matrix and fractures is treated by a numerical method. The geometric parameters needed in simulation are preprocessed from a specification of fracture spacings and apertures and geometry of the matrix blocks. The numerical implementation of the MINC method is verified by comparison with the analytical solution of Warren and Root. Illustrative applications are given for several geothermal reservoir engineering problems. Introduction In this paper, we present a numerical method for simulating transient nonisothermal, two-phase flow of water in fractured porous medium. The method is base on a generalization of a concept originally proposed by Barenblatt et al. and introduced into the petroleum literature by Warren and Root, Odeh, and others in the form of what has been termed the "double-porosity" model. The essence of this approach is that in a fractured porous medium, fractures are characterized by much porous medium, fractures are characterized by much larger diffusivities (and hence, much smaller response times) than the rock matrix. Therefore, the early system response is influenced by the matrix. In seeking to analytically solve such a system, all fractures were grouped into one continuum and all the matrix blocks into another, resulting in two interacting continua coupled through a mass transfer function determined by the size and shape of the blocks, as well as the local difference in potentials between the two continua. Later, Kazemi and Duguid and Lee incorporated the double-porosity concept into a numerical model. For a more detailed description of the concept and its application, see Refs. 6 through 8. Very little work has been done in investigating nonisothermal, two-phase fluid flow in fractured porous media. Moench and coworkers used the discrete fracture approach to study the behavior of fissured, vapor-dominated geothermal reservoirs. The purpose of our work is first to generalize the double-porosity concept into one of many interacting continua. We then incorporate the MINC model into a simulator for nonisothermal transport of a homogeneous two-phase fluid (water and steam) in multidimensional systems. Our approach is considerably broader in scope and more general than any previous models discussed in the literature. The MINC previous models discussed in the literature. The MINC method permits treatment of multiphase fluids with large and variable compressibility and allows for phase transitions with latent heat effects, as well as for coupling between fluid and heat flow. The transient interaction between matrix and fractures is treated in a realistic way. Although the model can permit alternative formulations for the equation of motion, we shall assume that, macroscopically, each continuum obeys Darcy's law; in particular, we shall use the "cubic law" for the flow of particular, we shall use the "cubic law" for the flow of fluids in fracture. While the methodology presented in this paper is generally applicable to multiphase compositional thermal systems, our illustrative calculations were restricted to geothermal reservoir problems. The numerical method chosen to implement the MINC concept is the IFD method. In this method, all thermophysical and thermodynamic properties are represented by averages over explicitly defined finite subdomains, while fluxes of mass or energy across surface segments are evaluated through finite difference approximations. An important aspect of this method is that the geometric quantities required to evaluate the conductance between two communicating volume elements are provided directly as input data rather than having them generated from data on nodal arrangements and nodal coordinates. Thus, a remarkable flexibility is attained by which one can allow a volume element in any one continuum to communicate with another element in its own or any other continuum. Inasmuch as the interaction between volume elements of different continua is handled as a geometric feature, the IFD methodology does not distinguish between the MINC method and the conventional porous-medium type approaches to modeling. porous-medium type approaches to modeling. SPEJ p. 14
- Energy > Oil & Gas > Upstream (1.00)
- Energy > Renewable > Geothermal > Geothermal Resource (0.88)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Multiphase flow (1.00)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- Reservoir Description and Dynamics > Non-Traditional Resources > Geothermal resources (1.00)
- Data Science & Engineering Analytics > Information Management and Systems (1.00)
Abstract A method of designing and analyzing pressure transient well tests of two-phase (steam/water) reservoirs is given. Wellbore storage is taken into account, and the duration of it is estimated. It is shown that the wellbore flow can dominate the downhole pressure signal completely such that large changes in the downhole pressure that might be expected because of changes in kinematic mobility are not seen. Changes in the flowing enthalpy from the reservoir can interact with the wellbore flow so that a temporary plateau in the downhole transient curve is measured. Application of graphical and nongraphical methods to determine reservoir parameters from drawdown tests is demonstrated. Introduction Pressure transient data analysis is the most common method of obtaining estimates of the in-situ reservoir properties and the wellbore condition. Conventional graphical analysis techniques require that. for a constant flowrate well test in an infinite aquifer, a plot of the downhole pressure vs. log time yields a straight line after wellbore storage effects are over. The slope of that line is inversely proportional to the transmissivity (kh/u) of the reservoir. The extrapolated intercept of this line with the pressure axis at a specified time (1 hour or 1 second depending on the units used) gives the factor 0 Cth(re2), which is used to calculate the skin value of a well. In this study, the effects of a two-phase steam/water mixture in the reservoir and/or the wellbore on pressure transient data have been investigated. There have been a number of attempts to extend conventional testing and analysis techniques to two-phase geothermal reservoirs including drawdown analysis by Garg and Pritchett, Garg, Grant, and Moench and Atkinson. Pressure buildup analysis has been investigated by Sorey et al. To solve the diffusion equation that governs the pressure change in a two-phase reservoir analytically, it is necessary to make a number of simplifying assumptions. One assumption is that the fluid compressibility in the reservoir is initially uniform and remains uniform throughout the test. With this approach, it can be shown that a straight line on a pressure vs. log time plot will be obtained, the slope being inversely proportional to the total kinematic mobility When conducting a field test it is rarely possible to maintain the uniform saturation distribution in the reservoir required for that type of analysis to be applicable. In addition, the very high compressibility of the two-phase fluid creates wellbore storage of very long duration. Since most of the available instrumentation for hot geothermal wells (greater than 200C) can withstand geothermal environments for only limited periods, long-duration wellbore storage further complicates data analysis. Thus numerical simulation techniques must be used to study well tests to determine the best method of testing two-phase reservoirs. This work investigates and defines more thoroughly the well/reservoir system when the reservoir or wellbore is filled with a two-phase fluid. Four examples are considered:a single-phase hot water reservoir connected to a partially two-phase wellbore, a hot water reservoir that becomes two-phase during the test, a two-phase liquid-dominated reservoir, and a two-phase vapor-dominated reservoir. State-of-the-art analysis techniques are applied to pressure transient data after wellbore storage effects have ended. In the first example, a nongraphical method of analysis is discussed, which is applicable at early times when wellbore storage effects still dominate the pressure response. Note that our analysis has been done for a two-phase homogeneous, nonfractured reservoir. Previous studies of well test methods for two-phase reservoirs have been restricted to this case. SPEJ P. 309^
- Energy > Renewable > Geothermal > Geothermal Resource (1.00)
- Energy > Oil & Gas > Upstream (1.00)