Analytical model of cold water front movement in a geothermal reservoir

Injection of cooled geothermal water back into the producing formation is a procedure that maintains reservoir pressure and increases energy extraction efficiency, but, because reinjected fluids tend to be much colder than the reservoir rock, injection can also cause cooling of the fluid produced from nearby wells. It is therefore essential to determine the cold front velocity in a geothermal reservoir. Constant thermal properties of both rock and fluid are generally assumed in order to solve this problem. In this paper, the rock density and heat capacity of the water–rock system as functions of temperature are assumed. Using the method of characteristics, an analytical solution is obtained. It is shown that the variable heat capacity of rock leads to a temperature-dependent speed of propagation of the thermal front. This results in a steepening of the front when cold water is injected into a hot zone, and eventually the formation of a discontinuous solution, or shock. A method is proposed for finding such discontinuous solutions and an equation for the velocity of the thermal front is presented. The difference between the front velocity obtained by means of the weak solution presented here and the classical model with constant thermal properties varies between about 1 and 14%.     

A survey of geothermal reservoir properties

This paper presents results of a literature survey on thermal, hydrological and chemical characteristics of geothermal reservoirs. The data are presented in a table summarizing important fluid and rock parameters. The primary parameters of interest are the permeability, permeability-thickness, porosity, reservoir temperature and concentration of dissolved solids and non-condensible gases. Some preliminary correlations between these parameters are given.     

State of the art of geothermal reservoir simulation

Computer modeling of geothermal systems has become a mature technology with application to more than 100 fields world-wide. Large complex three-dimensional models having computational meshes with more than 4000 blocks are now used routinely. Researchers continue to carry out fundamental research on modeling techniques and physical processes in geothermal systems. The new advances are adopted quickly by the geothermal industry and have also found application in related areas such as nuclear waste storage, environmental remediation and studies of the vadose (unsaturated) zone. The current state-of-practice, recent advances and emerging trends in geothermal reservoir simulation are reviewed.     

Water content of the Kawah Kamojang geothermal reservoir

A theory is presented for the transient flow of steam in the presence of immobile water, and for transient response of gaseous contaminants in the steam. Simple analyses give the water saturation of the rock, and the porosity-saturation product. For Kawah Kamojang the measured water content is a saturation of 35%.     

A novel flow-resistor network model for characterizing enhanced geothermal system heat reservoir

The fracture characteristics of a heat reservoir are of critical importance to enhanced geothermal systems, which can be investigated by theoretical modeling. This paper presents the development of a novel flow-resistor network model to describe the hydraulic processes in heat reservoirs. The fractures in the reservoir are simplified by using flow resistors and the typically complicated fracture network of the heat reservoir is converted into a flow-resistor network with a reasonably simple pattern. For heat reservoirs with various fracture configurations, the corresponding flow-resistor networks are identical in terms of framework though the networks may have different section numbers and the flow resistors may have different values. In this paper, numerous cases of different section numbers and resistor values are calculated and the results indicate that the total number of flow resistances between the injection and production wells is primarily determined by the number of fractures in the reservoir. It is also observed that a linear dependence of the total flow resistance on the number of fractures and the relation is obtained by the best fit of the calculation results. Besides, it performs a case study dealing with the Soultz enhanced geothermal system (EGS). In addition, the fracture numbers underneath specific well systems are derived. The results provide insight on the tortuosity of the flow path between different wells.     

Galerkin finite-element simulation of a geothermal reservoir

The equations describing fluid flow and energy transport in a porous medium can be used to formulate a mathematical model capable of simulating the transient response of a hot-water geothermal reservoir. The resulting equations can be solved accurately and efficiently using a numerical scheme which combines the finite element approach with the Galerkin method of approximation. Application of this numerical model to the Wairakei geothermal field demonstrates that hot-water geothermal fields can be simulated using numerical techniques currently available and under development.     

Coupled reservoir-wellbore simulation of geothermal reservoir behavior

The reservoir simulator TOUGH and the wellbore simulator WFSA have been coupled to model flow of geothermal brine in the reservoir as well as in the wellbore. An outline of the structure of the two computer codes is given, together with the relevant equations. A new module, COUPLE, has been written to serve as an interface between TOUGH and WFSA. Two sample problems are given to illustrate the use of the coupled codes. One of these problems compares the results of the new simulation method to those obtained by using the deliverability option in TOUGH. The coupled computing procedure is shown to simulate more accurately the behavior of a geothermal reservoir under exploitation.     

Management of the Balcova–Narlidere geothermal reservoir,Turkey

The 2000–2005 management and field monitoring procedures at the Balcova–Narlidere geothermal field, Turkey are described. During that period, fluid production increased from 140 to 300 kg/s and the living space being heated grew from 0.64 to 1.6 million m². The shallow (depth <160 m) injection done between 1996 and 2002 cooled the fluids being produced; the hydraulic connection between shallow production and injection wells was confirmed by tracer tests. Two deep injection wells were drilled to mitigate the problem and to increase injection capacity. Because net fluid extraction was reduced, reservoir pressure drawdown was controlled. Wells drilled after 2000 indicated that the eastern portion of the field had greater potential and yielded higher temperature fluids. After testing and establishing well flow performance, pump capacities were matched to production well capacities. Mineral scaling in wells and surface installations was brought under control reducing the annual cost of inhibitors by about US$100,000. Since all production and injection wells are located near the Agamemnon fault zone and because the capacity of the district heating system is being continuously increased, there is the risk of thermal breakthrough in the production wells.     

Hydrothermal mineral zones in the geothermal reservoir of Cerro Prieto

Detailed petrologic studies completed to date on ditch cuttings and core from 23 wells in the Cerro Prieto field have led to recognition of regularly distributed prograde metamorphic mineral zones. The progressive changes in mineralogy exhibit a systematic relationship with reservoir temperature.The Cerro Prieto reservoir consists of a series of sandstones, siltstones, and shales composing part of the Colorado River delta. The western part of the field contains relatively coarser sediments apparently also derived from the delta and not from the basin margins as formerly thought. The most abundant detrital minerals in the sediments include quartz, feldspar, kaolinite, montmorillonite, illite, chlorite, mixed-layer clays, calcite, dolomite and iron hydroxides. Some of these minerals were also formed diagenetically.The following progressive stages of post-depositional alteration in response to increasing temperature have been observed: (1) diagenetic zone (low temperature), (2) illite-chlorite zone (above ~ 150°C), (3) calc-aluminum silicate zone (above ~ 230°C) and the biotite zone (above ~ 325°C). These zones are transitional to some degree and can be further subdivided based on the appearance or disappearance of various minerals.One immediate application of these studies is the ability, from a study of cuttings obtained during drilling of a well, to predict the temperatures which will be observed when the well is completed.     

Evolution of the Wairakei geothermal reservoir during 50 years of production

The Wairakei geothermal field has been under production for more than 50 years. Exploration wells show that the high-temperature and very permeable, productive resource extends over about 12 km² within a greater area of about 25 km² that shows various effects of thermal activity. Up to 2006, 3 km³ of fluid and 2750 PJ of energy had been extracted at an average rate of 5250 t/h and enthalpy of 1130 kJ/kg. Significant production started in 1955 and up to 1978 there was no injection of cooled geothermal fluids. During the first decade of operation a pressure drawdown of up to 20 bars (2 MPa) developed and spread evenly across the reservoir, even though fluid extraction was focused within an area of 1 km² close to the northeastern field boundary. This pressure reduction resulted in widespread boiling and formation of segregated steam zones at the top of the reservoir together with inflow of cooler fluids into its northeastern part via the original natural outflow channels. From 1975 to 1997 pressures in the deep liquid reservoir stabilized at 23–25 bars (2.3–2.5 MPa) below the original pressure, with little change up to the time injection commenced in 1998. This natural pressure support indicates that prior to injection there was substantial recharge, 80% of which is assessed as high-temperature deep inflow. Since 1998 about 30% of the extracted fluids have been injected and reservoir pressures have increased by 3–4 bars (0.3–0.4 MPa). To date, significant returns of injected fluids have not been detected in the production areas. Over the 50 years of operation, temperatures in the main production areas have declined from 250 to 220 °C while deeper production zones toward the western boundary of the reservoir have remained at about 250 °C. A series of deeper makeup wells to maintain future production have been drilled in the high-temperature recharge area. An increasing fraction of injection, both in-field and out-field is planned over the next few years.     

Acoustic emission analysis of a geothermal reservoir and its application to reservoir control

A detailed analysis has been made of acoustic emissions detected during build-up tests in a geothermal production well in Kakkonda geothermal power plant, Japan, in 1982, 1984 and 1985. The three-dimensional structure of the hydrothermal reservoir in the field and its dynamic behavior have been investigated. The shape and location of the cracked reservoir, the fluid paths and degree of communication between the reservoir and the geothermal wells, have been revealed by this analysis. The dependence of AE (acoustic emission) activity on valve operations has also been studied. The stability of crack-like reservoirs depends on the reduction in flow-rate in the reservoir system, the closing rate of the wellhead valve and on intervals between the tests. Reservoir stability has been successfuly achieved during the 1985 test by valve regulation, according to the results of the AE study.     

Scaling in the reservoir in Kizildere geothermal field, Turkey

At Kizildere geothermal field, the fluid in the reservoir is hot pressurized water at 200°C containing about 2% CO₂ dissolved in the fluid by weight. During production, as the pressure decreases this gas is released into the vapor phase. When the reservoir fluid loses its dissolved CO₂ the equilibrium of the dissolved solids is destroyed and deposition occurs, either in the reservoir or in the well. Scaling in the well can be cleaned mechanically but it is more or less impossible to clean the reservoir. Thus the gas must be kept dissolved in the water until it reaches the well. At Kizildere the wells are cleaned every six months of production. After cleaning it has been observed that some of the wells regain their original production values and others do not. Well KD-14 was deepened and incrustation noted on the cuttings coming from the reservoir. On closing the wells some of them retain their well-head pressure at a constant value, whereas in others a pressure build-up continues at the well-head. Normally the static WHP are around 5 – 6 kg/cm². However, after closure of the master-valve in wells KD14 and KD15 the WHP continued to increase until all the water column in the well was changed by the gas. This phenomenon occurs because of the presence of free gas in the reservoir.     

Analysis of reservoir pressure and decline curves in Serrazzano zone, Larderello geothermal field

An estimate of reserves in the Serrazzano reservoir was obtained from mass balance studies and production decline curve analyses.The Serrazzano reservoir consists of a geometrically well-defined structural high of permeable formations separated from the other productive regions of the Larderello field.Deep drilling began in the 1930s and was limited to a small area exhibiting natural manifestations. After the second World War the area of drilling was extended to about 20 km². Currently the drilling area is about the same. Even though the reservoir has been producing steam since the 1930s, a systematic collection of production data did not begin until after 1953.Data on average reservoir pressures were not available for the material balance calculations made in the study reported here. Calculated bottom hole pressures of shut-in wells were taken therefore to represent local static reservoir pressures. These pressures were used to calculate an “average reservoir pressure” which was graphed as a function of cumulative production. The reservoir pressure history corresponding to the first half of current cumulative production is not known. Data for the second half indicate a linear relationship between “reservoir pressure” and cumulative production.The conventional straight-line p/z vs cumulative production material balance relationship is known to be correct, of course, for closed single-phase gas reservoirs. The validity of this linearity for stream-producing systems with boiling water has not been proved. Regardless of this, the following observations were made: a line connecting the available data points extrapolated back to zero production indicates an initial reservoir pressure approximating at least 40 atm. Extrapolating the same data to zero reservoir pressure indicates the total initial steam in place to be about 170 × 10⁶ tons.An empirical type-curve matching technique was applied to the production decline curves of wells in the reservoir. The curve for each well was extrapolated to infinite production time to obtain an estimate of total past and future production. Summing these values for all producing wells in the reservoir, an estimated total production (past and future) of 200 × 10⁶ tons was obtained.The agreement between the estimated total production applying material balance principles and decline curve analyses is remarkably good. Although these results may be useful, further field and theoretical work are necessary to prove their validity.     

Modeling studies for production potential of Chingshui geothermal reservoir

The Chingshui geothermal power plant was decommissioned in 1993 due to a continued decline in production. Although some geothermal exploration and field investigation had been exercised, the production potential of the reservoir is still not well understood. In this paper, numerical modeling approaches for characterization of the geothermal reservoir, investigation of reservoir production performance, and evaluation of exploitation scheme design are presented. At first, a site-scale refined grid numerical model was developed for simulating the natural state of Chingshui geothermal reservoir. Through the model, the production potential of the geothermal reservoir was estimated and the availability of water resources was assessed. We further built production model to simulate the production history during 1981–1993. From the production model, we can conclude that the abnormal drop of the reservoir production capacity is mainly caused by carbonate scaling. Potential production schemes with different reinjection designs were evaluated through the model. Simulation results indicated that a sustainable hot water production capacity of Chingshui geothermal reservoir is about 200 t/h without reinjection, and 300 t/h or even higher with reinjection which is enough for a 3 MWe power plant. The simulation results indicate that reinjection provides an effective approach for maintaining reservoir pressure during hot water/steam production.     

Characteristics and management of the Sumikawa geothermal reservoir, northeastern Japan

The subsurface temperature gradually increases southward in the Sumikawa geothermal field and decreases sharply toward the north. The geothermal reservoir contains a two-phase zone between the cap rock and hot water zone. The target for production was designated in the deep zone, in the high temperature southern area. The production and reinjection areas have been separated to recover thermal energy efficiently during the recycling of reinjection fluid; the wells have been spaced as far apart as possible to reduce well interference. To improve productivity and injectivity, cold-water well stimulation was applied, and this experiment reduced the number of wells required for 50 MW_e power generation.     

Initial state of the matsukawa geothermal reservoir: reconstruction of a reservoir pressure profile and its implications

Feed-point pressures of some of the earliest production wells in Matsukawa were reconstructed from water levels and temperature profiles measured during warm-up of the wells immediately after drilling. Although most of the wells currently produce dry superheated steam, the reconstructed pressures indicate that the pressure gradient of the production zone was super-hydrostatic and was similar to that of Kakkonda, which is a liquid-dominated system. It implies that the current production zone of the Matsukawa reservoir was induced to produce dry superheated steam by fluid withdrawal.     

Controls on the Karaha–Telaga Bodas geothermal reservoir,Indonesia

Karaha–Telaga Bodas is a partially vapor-dominated, fracture-controlled geothermal system located adjacent to Galunggung Volcano in western Java, Indonesia. The geothermal system consists of: (1) a caprock, ranging from several hundred to 1600 m in thickness, and characterized by a steep, conductive temperature gradient and low permeability; (2) an underlying vapor-dominated zone that extends below sea level; and (3) a deep liquid-dominated zone with measured temperatures up to 353 °C. Heat is provided by a tabular granodiorite stock encountered at about 3 km depth. A structural analysis of the geothermal system shows that the effective base of the reservoir is controlled either by the boundary between brittle and ductile deformational regimes or by the closure and collapse of fractures within volcanic rocks located above the brittle/ductile transition. The base of the caprock is determined by the distribution of initially low-permeability lithologies above the reservoir; the extent of pervasive clay alteration that has significantly reduced primary rock permeabilities; the distribution of secondary minerals deposited by descending waters; and, locally, by a downward change from a strike-slip to an extensional stress regime. Fluid-producing zones are controlled by both matrix and fracture permeabilities. High matrix permeabilities are associated with lacustrine, pyroclastic, and epiclastic deposits. Productive fractures are those showing the greatest tendency to slip and dilate under the present-day stress conditions. Although the reservoir appears to be in pressure communication across its length, fluid, and gas chemistries vary laterally, suggesting the presence of isolated convection cells.     

Modeling the phase partitioning behavior of gas tracers under geothermal reservoir conditions

A model of the liquid-vapor phase partitioning behavior of low concentrations of gas tracers in water at geothermal temperatures and pressures is presented. This model uses Henry's coefficient to describe the variation of the gas tracer solubility with temperature and pressure. A new method is described for the determination and representation of Henry's coefficients. The method uses experimentally determined values of Henry's coefficient and a theoretically predicted value of behavior at the critical point of water to provide data that can be fitted by a semi-empirical correlation. No assumptions regarding ideal behavior are necessary. The semi-empirical correlation is a modified version of that presented by Harvey, A. (1996. Semiempirical correlation for Henry's constants over large temperature ranges. American Institute of Chemical Engineers Journal 42(5), 1491-1494) and better accounts for high temperature and non-ideal behavior. Sets of model coefficients are given for a range of possible gas tracers. The resulting phase partitioning model is simple and may be easily implemented in a numerical geothermal simulator. The use and behavior of the model is illustrated by its application to a number of idealised test problems.     

Probing the pore space of geothermal reservoir sandstones by Nuclear Magnetic Resonance

Pulsed-Field-Gradient–Nuclear Magnetic Resonance (PFG–NMR) is an interesting method to determine microscopic but volumetrically averaged properties of pore space. In the present paper a number of sandstone samples, taken from drill cores of geothermal wells in North Germany, have been investigated. The time-dependent self-diffusion of water molecules in their confined geometry is used to probe the pore space. The short-time behaviour of the self-diffusion coefficient (anomalous diffusion) in the porous matrix allows the determination of the surface-to-pore volume ratio S/V_p. At long diffusion times, molecules scout the tortuosity of the interconnected pore space of the sandstones. The NMR results were compared with data from petrographic image analysis (PIA), adsorption experiments and electric conductivity measurements. The PFG–NMR measurements give surface-to-pore volume ratios S/V_p that are comparable to those estimated with the petrographic image analysis. The tortuosities match in most cases data from conductivity measurements, so the PFG–NMR is regarded as an appropriate tool to determine this quantity. The results are not influenced by the adherence of ‘scout-molecules’ to the pore walls. The surface-to-pore volume ratios and tortuosities were used to calculate permeabilities of the systems of interest, which were in good agreement with measured core-plug permeabilities. Results of additional NMR relaxation experiments are used to obtain adsorption isotherms for cations at active surface sites.     

A 3-D water/rock chemical interaction model for prediction of HDR/HWR geothermal reservoir performance

A three-dimensional (3-D) water/rock chemical interaction model has been developed to examine the effect of water/rock chemical interaction (WRCI) on the long-term performance of hot dry rock and hot wet rock (HDR/HWR) reservoirs. The model, which integrates many field observations and thus generates a fracture network very similar to the natural fracture distribution in the reservoir, can predict the influence of WRCI on the overall fractured reservoir. Factors affecting WRCI and the effect of WRCI on long-term performance of Hijiori deep reservoir (Japan) have been modelled. Simulated results show that fluid chemistry, initial rock temperature, magnitude of flow rate and well spacing have a major effect on WRCI, and for such a multi-well Hijiori geothermal system, WRCI seems to make the flow distribution tend towards uniformity. The model described deals solely with chemical interactions as a function of flow rate and temperature, and takes no account of aperture variation as a result of thermoelastic effects. It is only a partial model, though it could form an important module of a coupled model.