Two-phase Geothermal Reservoirs Research Articles

Investigation of meteoric water and parent fluid mixing in a two-phase geothermal reservoir system using strontium isotope analysis: A case study from Southern Bandung, West Java, Indonesia

Determinations of the recharge area and recharge mechanism in geothermal systems are essential for reservoir management and a sustainable resource use. To address this problem, studies aplenty have aimed to identify the recharge elevation using stable water isotopes, δ2H and δ18O. Nevertheless, the physical and chemical processes involved in the generation of a reservoir fluid from a deeply infiltrated recharge flow remain poorly understood. This study aims to clarify this process using strontium (Sr) concentrations and isotope composition from water and well rock samples by selecting a geothermal field with a two-phase reservoir system in Southern Bandung, West Java, Indonesia. The water samples are characterized by variable Sr isotopic compositions (87Sr/86Sr) (0.70450–0.70725) and low Sr concentrations (0.01–0.72 ppm). The 87Sr/86Sr of the well rocks is also variable (0.70400–0.70827) with particularly high Sr concentrations (9.1–53 ppm). Three types of domain that are the combinations of the reservoir fluid mixing with groundwater are identified. The first two types are shallow and deep groundwater composed of 90 % meteoric water and 10 % upflow fluids with Sr concentration 0.01 to 0.11 ppm and the 87Sr/86Sr from 0.7055 to 0.70725. The shallow groundwater may possibly carry a 87Sr/86Sr anomaly (higher than 87Sr/86Sr of plagioclase: 0.7065) from the anthropogenic activities through the pathways created by the intersection of the NW-SE and NE-SW inferred regional faults in the west part of the field, hosted by the Wayang Windu Formation. The deep groundwater type is also a mixture of 10 % parent fluid hosted by the deeper aquifer rocks Malabar Formation, with lower strontium isotopes ratio than the first aquifer (87Sr/86Sr 0.7045–0.7055). The third groundwater refers to the perched aquifer with mixture of 30 %–70 % parent fluid that has undergone condensation and mixing processes in Pangalengan Formation (87Sr/86Sr 0.70452–0.7052). This groundwater is thought to be the source of mostly hot springs in the study area.

Modeling studies of heat transfer and phase distribution in two-phase geothermal reservoirs

Phase distribution as well as mass flow and heat transfer behavior in two-phase geothermal systems have been studied by numerical modeling. A two-dimensional porous-slab model was used with a non-uniform heat flux boundary condition at the bottom. Steady-state solutions are obtained for the phase distribution and heat transfer behavior for cases with different mass of fluid (gas saturation) in place, permeabilities, and capillary pressures. The results obtained show very efficient heat transfer in the vapor-dominated zone due to the development of heat pipes and near-uniform saturations. The phase distribution below the vapor-dominated zone depends on permeability. For relatively high-permeability systems, single-phase liquid zones prevail, with convection providing the energy throughput. For lower permeability systems, a two-phase liquid-dominated zone develops, because single-phase liquid convection is not sufficient to dissipate heat released from the source. These results are consistent with observations from the field, where most high-temperature liquid-dominated two-phase systems have relatively low permeabilities (e.g. Krafla, Iceland; Olkaria, Kenya; Baca, New Mexico). The numerical results obtained also show that for high heat flow a high-temperature single-phase vapor zone can develop below a typical (240°C) vapor-dominated zone, as has recently been found at The Geysers, California, and Larderello, Italy.

Cold-water injection into single- and two-phase geothermal reservoirs

Cold-water injection into single- and two-phase geothermal reservoirs

Effects of Steam/Liquid Counterflow on Pressure-Transient Data From Two-Phase Geothermal Reservoirs

Summary Numerical studies were performed to investigate the effects of localized feed zones on the pressure transients in two-phase reservoirs. Gravity effects were shown to affect the pressure transients significantly because of the large difference in the densities of liquid water and vapor. Production from such systems enhances steam/liquid-water counterflow and expands the vapor-dominated zone at the top of the reservoir. Subcooled liquid regions develop in the center of the reservoir as a result of gravity drainage of cooler liquid water. The vapor zone acts as a constant-pressure boundary and helps to stabilize the pressure decline in the system. The pressure transients at observation wells were shown to depend greatly on the location (depth) of the major feed zone; if this is not accounted for, large errors in deduced reservoir properties will result. At shallow observation points, pressures may actually increase as a result of enhanced steam upflow caused by production at a deep feed zone.

Some effects of non-condensible gas in geothermal reservoirs with steam-water counterflow

A mathematical model is developed for one-dimensional fluid and heat flow in two-phase geothermal reservoirs containing non-condensible gas (CO 2). Vertical profiles of temperature, pressures and phase saturations in steady-state conditions are obtained by numerically integrating the coupled ordinary differential equations describing conservation of water, CO 2 and energy. Solutions, including binary diffusion effects in the gas phase, are generated for cases with net mass throughflow as well as for balanced liquid—vapor counterflow. Calculated examples illustrate some fundamental characteristics of two-phase heat transmission systems with non-condensible gas.

Material Balance Depletion Models For Two-Phase Geothermal Reservoirs

Summary Material balance calculations, often referred to as "zero-dimensional" or "lumped element" reservoir evaluations, have been used extensively in petroleum and geothermal engineering. This paper presents a Havlena and Odeh-type material balance depletion model for two-phase reservoirs incorporating adsorption phenomena. A straight line formed between groups of thermodynamic and adsorption properties of water and the cumulative production history provides the initial fluid in place production history provides the initial fluid in place and the size of the vapor-dominated "steam cap." Adsorption phenomena were found to be the controlling mechanism phenomena were found to be the controlling mechanism in the depletion of vapor-dominated geothermal reservoirs. A material balance for vapor-dominated geothermal reservoirs, demonstrating the importance of adsorption phenomena, is presented also. A straight line provides the initial fluid in place. provides the initial fluid in place. Introduction The general approach to the material balance depletion model was first suggested by Schilthuis. The equation provides a volumetric balance between the expansion of provides a volumetric balance between the expansion of reservoir fluids as a result of the cumulative production. Havlena and Odeh, using the Schilthuis approach, developed linear expressions of the material balance equation for a variety of cases including undersaturated, gas-cap-drive and solution-gas-drive reservoirs. I present a similar development for the two-phase geothermal reservoir. Studies of reservoir and production behavior of vapor-dominated geothermal systems have focused on estimates of resource size. Whiting and Ramey presented an application of material and energy balances to geothermal steam production. Ramey applying conventional techniques for natural gas reservoirs, attempted to estimate the reserves of steam in place. Economides and Miller using the experimental results of Hsieh, in which the importance and magnitude of adsorption were demonstrated, introduced a new approach for material balance calculation of vapor-dominated systems. As I will show, desorption is the controlling mechanism in the depletion of vapor-dominated geothermal systems and the major variable in their material balance calculations. The Form of the Material Balance Equation for a Two-Phase Geothermal Reservoir As in the Havlena and Odeh approach, a volume balance in reservoir cubic feet [m3] may be written (in their work they used res bbl [res m3]): underground withdrawal equals expansion of liquid water, plus boiled-off water, plus expansion of steam cap, plus expansion of desorbed water, plus reduction in the PV. The reduction in PV will be neglected in the case of two-phase and vapor-dominated systems, as has been demonstrated for saturated reservoirs. Fig. 1 is a schematic of the two-phase geothermal model used in this analysis. Expansion of Liquid Water and Boiled-Off Water This term contains two components:liquid water expansion andboiled-off steam expansion. suppose that Wi lbm [kg] were present originally; then WiVli would be the initial volume while Wivl would be the volume at a lower pressure. Hence, the difference would provide the liquid expansion W i (vl-vli)................................(1) The boiled-off steam is taken here as the difference between the product of the initial liquid in place and the corresponding evaporation specific volumes at the given pressure interval. This is analogous to the product of the pressure interval. This is analogous to the product of the initial oil in place, the solution GOR, and the gas FVF in the Havlena and Odeh analysis. In both cases the difference depicts the expansion of the evolved gas. Wi (vlg-vlgi)...............................(2) Expansion of Steam Cap The total mass in the steam cap is taken as mWi, where m is expressed as the ratio of the mass of water in the vapor-dominated zone to the mass in the liquid-dominated zone. Then the expansion of the steam is given by mWi(vg-vgj).................................(3) Expansion of Desorbed Steam As presented by Economides and Miller, the volume occupied by desorbed fluid is given by mrM(Xi-X)vg.................................(4) where mr is the mass of rock, M is the molecular weight (18 in the case that no noncondensable gases exist in appreciable quantities), and Xj and X are the masses of adsorbed water in lbm-mol/lbm [gmol/g] of rock in the pressure increment. pressure increment. JPT P. 1305

Injection and Energy Recovery in Fractured Geothermal Reservoirs

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 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.

Model Studies of the Depletion of Two-Phase Geothermal Reservoirs

Abstract The simulator SHAFT79 of Lawrence Berkeley Laboratory has been used to study the depletion of different types of geothermal reservoirs. Investigations of idealized systems include effects of gravity and fluid injection. Pressure decline is analyzed as a function of cumulative production. The main conclusions are as follows. The well-known p/Z method for estimating fluid reserves is not applicable to two-phase geothermal reservoirs. There is a strong tendency toward spatially uniform boiling. This causes a pressure decline, which allows in many cases estimates of the total reservoir volume and of the total heat content of the reservoir rock. Propagation of a boiling front through a deep water table, as a consequence of fluid production, gives rise to a peculiar pattern of pressure decline. This may allow prediction of the distance of the water table from the producing wells and of the vertical thickness of the water zone, thereby giving important clues to estimating fluid reserves. The pressure effects of injection of colder fluid depend strongly on (one- or two-) phase conditions in the reservoir, injection rate, and absolute permeability. Average pressure actually may decline in two-phase reservoirs rather than increase as a result of injection.

Radial Steam Flow in Two-Phase Geothermal Reservoirs – Comparison of Analytical and Finite Difference Solutions

Abstract A linear closed-form analytical solution for the radial flow of steam toward a producing well in a vapor-dominated geothermal reservoir is compared with a finite difference solution to the nonlinear equations of fluid flow and energy change. Assumptions used in the development of the equations are that (1) the liquid phase, initially uniformly distributed within the reservoir, is immobile, (2) the relative permeability to steam is constant, (3) local thermal equilibrium exists within the reservoir, (4) temperature changes are due only to phase change, and (5) effects of vapor-pressure lowering are negligible. With the onset of production, vigorous vaporization of liquid water in the reservoir near the wellbore creates a dry region that increases in volume as production continues. This behavior produces a circular moving boundary that separates superheated steam in the dry zone from saturated steam in the wet zone. The rate of movement of this boundary, the pressure drawdown, and the temperature and saturation distributions are obtained analytically by applying the solution to the linearized equations of flow in radial coordinates. Results obtained numerically using a finite difference solution to the nonlinear equations of fluid flow and energy agree closely with the analytical approach in spite of the nonlinearities involved.

Pressure Transient Analysis for Two-Phase (Water/Steam) Geothermal Reservoirs

AbstractA new diffusivity equation for two-phase (water/steam) flow in geothermal reservoirs is derived. The geothermal reservoir may be initially two-phase or may evolve into a two-phase system during production. Solutions of the diffusivity equation for a continuous line source are presented; the solutions imply that the plot of bottomhole pressure vs. log10t (t = time) should be a straight line. The slope of the straight line is inversely proportional to the total kinematic mobility. Comparison of the theory with a limited number of computer-simulated drawdown histories shows excellent agreement.

Simulation of a Gas-Dominated, Two-Phase Geothermal Reservoir

Abstract The basic equations governing the behavior of a two-phase mixture of carbon dioxide (CO2) and water are discussed. A Newton-Raphson scheme, based on the alternating direction implicit (ADI) method for multidimensional problems, is used to solve the nonlinear finite difference approximation of the governing nonlinear system of partial differential equations. Sample calculations showing the behavior of hypothetical reservoirs with varying CO2 contents are presented.

Two-Phase, Two-Dimensional Simulation of a Geothermal Reservoir

Abstract A numerical mathematical model for simulating production from a two-phase geothermal reservoir production from a two-phase geothermal reservoir was developed and tested. The model was a two-dimensional areal or cross-sectional unsteadystate description of the flow of mass and heat within an anisotropic, heterogeneous, porous medium containing a single-component, two-phase fluid. Flow in the production well was. taken to be one dimensional and steady state, using an approximate representation of a two-phase mixture. A totally implicit solution scheme was used. The simulator was used to investigate the effects of various levels of porosity, permeability, and initial pressure and liquid-phase saturation distributions on production. The numerical simulator was tested for a wide variety of conditions and was found to be stable for large time steps. Based on the numerical results, the behavior of a two-phase geothermal reservoir was classified into three types, depending on the initial liquid saturation. It was found that superheated regions formed more readily in reservoirs of low porosity and permeability. Introduction A geothermal system occurs as a heat anomaly that can be explained as follows. The earth's interior is hotter than its surface. This difference produces a temperature gradient that, in turn, produces a temperature gradient that, in turn, provides a measure of the heat flow rate. The provides a measure of the heat flow rate. The average heat flux for the earth is 1.5 mu cal/sq cm-sec. A geothermal system involves a flux that is 1 1/2 to 5 times higher than the average. Consequently, a geothermal system occurs as an anomaly in terms of heat flow. A high heat flux, along with surface seeps, is indicative of a geothermal system. Since the main mode of heat transfer within a geothermal fluid reservoir is convection, the reservoir itself is called a hydrothermal convention system. Hydrothermal convection systems have been classified into two types based on the physical state of the dominant pressure-controlling physical state of the dominant pressure-controlling phase: hot-water systems and vapor-dominated phase: hot-water systems and vapor-dominated system. In hot-water systems, fluids exist within the reservoir mostly in the liquid state and generally produce from 70 to 90 percent of their total mass as water at the surface. Vapor-dominated systems generally produce dry to superheated steam, and fluids exist within the reservoir mostly in the vapor state, Surface manifestations will usually take the form of fumaroles, mud pots, mud volcanoes, turbid pools, and acid-leached ground. Only three known areas exist as this type of system. These are the Geysers field in California, the Larderello field in Italy, and the Matsukawa field in Japan. The pressures of vapor-dominated systems are below hydrostatic. Also, the initial pressures and temperatures in vapor-dominated systems are very close to the temperature and pressure relating to the maximum enthalpy of saturated steam - 236 degrees C and 31.8 kg/sq cm. An explanation for this behavior has been given by James and by White et al. Reservoir engineering principles have been used to study production aspects of geothermal systems only during the last decade. In that time, relatively few models have been developed that simulate the production from a geothermal reservoir containing production from a geothermal reservoir containing both a liquid and a vapor phase. In fact, only three models have assumed the presence of a two-phase Hudd within a geothermal presence of a two-phase Hudd within a geothermal reservoir. One of these models, developed by Donaldson, was a steady-state, one-dimensional description of two-phase flow within porous media, but did not simulate production. The other two models, those of Whiting and Ramey and of Brigham and Morrow, were lumped-parameter formulations. Thus, objective of this paper is to develop a model that simulates production from a two-phase geothermal reservoir in greater detail than has been done previously. SPEJ P. 171