Petroleum Reservoir Engineering Research Articles

Fluid Flow, Heat Transfer, and Solute Transport at Nuclear Waste Storage Tanks in the Hanford Vadose Zone

At the Hanford Site, highly radioactive and chemically aggressive waste fluids have leaked from underground storage tanks into the vadose zone. This paper addresses hydrogeological issues at the 241‐SX tank farm, especially focusing on Tank SX‐108, which is one of the highest heat load, supernate density and ionic strength tanks at Hanford and a known leaker. The behavior of contaminants in the unsaturated zone near SX‐108 is determined by an interplay of multiphase fluid flow and heat transfer processes with reactive chemical transport in a complex geological setting. Numerical simulation studies were performed to obtain a better understanding of mass and energy transport in the unique hydrogeologic system created by the SX tank farm. Problem parameters are patterned after conditions at Tank SX‐108, and measured data were used whenever possible. Borrowing from techniques developed in geothermal and petroleum reservoir engineering, our simulations feature a comprehensive description of multiphase processes, including boiling and condensation phenomena, and precipitation and dissolution of solids. We find that the thermal perturbation from the tank causes large‐scale redistribution of moisture and alters water seepage patterns. During periods of high heat load, fluid and heat flow near the tank are dominated by vapor–liquid counterflow (heat pipe), which provides a much more efficient mechanism than heat conduction for dissipating tank heat. The heat pipe mechanism is also very effective in concentrating dissolved solids near the heat source, where salts may precipitate even if they were only present in small concentrations in ambient fluids. Tank leaks that released aqueous fluids of high ionic strength into the vadose zone were also modeled. The heat load causes formation dry‐out beneath the tank, which is accompanied by precipitation of solutes. These may become remobilized at a later time when tank temperatures decline and previously dried out regions are rewetted. Simulated temperature and moisture distributions compare well with borehole measurements performed in 2000. The temperature maximum observed beneath Tank SX‐108 can be explained from past thermal history of the tank; it is not necessary to invoke heat generation from leaked radioactive contaminants. A novel composite medium model is used to explore effects of moisture tension–dependent anisotropy, which is shown to have important impacts on fluid flow and solute transport in the Hanford sediments.

Fluid Flow, Heat Transfer, and Solute Transport at Nuclear Waste Storage Tanks in the Hanford Vadose Zone

At the Hanford Site, highly radioactive and chemically aggressive waste fluids have leaked from underground storage tanks into the vadose zone. This paper addresses hydrogeological issues at the 241-SX tank farm, especially focusing on Tank SX-108, which is one of the highest heat load, supernate density and ionic strength tanks at Hanford and a known leaker. The behavior of contaminants in the unsaturated zone near SX-108 is determined by an interplay of multiphase fluid flow and heat transfer processes with reactive chemical transport in a complex geological setting. Numerical simulation studies were performed to obtain a better understanding of mass and energy transport in the unique hydrogeologic system created by the SX tank farm. Problem parameters are patterned after conditions at Tank SX-108, and measured data were used whenever possible. Borrowing from techniques developed in geothermal and petroleum reservoir engineering, our simulations feature a comprehensive description of multiphase processes, including boiling and condensation phenomena, and precipitation and dissolution of solids. We find that the thermal perturbation from the tank causes large-scale redistribution of moisture and alters water seepage patterns. During periods of high heat load, fluid and heat flow near the tank are dominated by vapor–liquid counterflow (heat pipe), which provides a much more efficient mechanism than heat conduction for dissipating tank heat. The heat pipe mechanism is also very effective in concentrating dissolved solids near the heat source, where salts may precipitate even if they were only present in small concentrations in ambient fluids. Tank leaks that released aqueous fluids of high ionic strength into the vadose zone were also modeled. The heat load causes formation dry-out beneath the tank, which is accompanied by precipitation of solutes. These may become remobilized at a later time when tank temperatures decline and previously dried out regions are rewetted. Simulated temperature and moisture distributions compare well with borehole measurements performed in 2000. The temperature maximum observed beneath Tank SX-108 can be explained from past thermal history of the tank; it is not necessary to invoke heat generation from leaked radioactive contaminants. A novel composite medium model is used to explore effects of moisture tension–dependent anisotropy, which is shown to have important impacts on fluid flow and solute transport in the Hanford sediments.

Multiphase flow dynamics during CO2 disposal into saline aquifers

Injection of CO2 into saline aquifers is described by mass conservation equations for the three components water, salt (NaCl), and CO2. The equations are discretized using an integral finite difference method, and are solved using methods developed in geothermal and petroleum reservoir engineering. Phase change processes are treated through switching of primary thermodynamic variables. A realistic treatment of PVT (fluid) properties is given which includes salinity and fugacity effects for partitioning of CO2 between gaseous and aqueous phases. Chemical reactions and mechanical stress effects are neglected. Numerical simulations are presented for injection of CO2 into a brine aquifer, and for loss of CO2 from storage through discharge along a fault zone. It is found that simulated pressures are much more sensitive to space discretization effects than are phase saturations. CO2 discharge along a fault is a self-enhancing process whose flow rates can increase over time by more than an order of magnitude, suggesting that reliable containment of CO2 will require multiple barriers.

Fluid Flow, Heat Transfer, and Solute Transport at Nuclear Waste Storage Tanks in the Hanford Vadose Zone

At the Hanford Site, highly radioactive and chemically aggressive waste fluids have leaked from underground storage tanks into the vadose zone. This paper addresses hydrogeological issues at the 241-SX tank farm, especially focusing on Tank SX-108, which is one of the highest heat load, supernate density and ionic strength tanks at Hanford and a known leaker. The behavior of contaminants in the unsaturated zone near SX-108 is determined by an interplay of multiphase fluid flow and heat transfer processes with reactive chemical transport in a complex geological setting. Numerical simulation studies were performed to obtain a better understanding of mass and energy transport in the unique hydrogeologic system created by the SX tank farm. Problem parameters are patterned after conditions at Tank SX-108, and measured data were used whenever possible. Borrowing from techniques developed in geothermal and petroleum reservoir engineering, our simulations feature a comprehensive description of multiphase processes, including boiling and condensation phenomena, and precipitation and dissolution of solids. We find that the thermal perturbation from the tank causes large-scale redistribution of moisture and alters water seepage patterns. During periods of high heat load, fluid and heat flow near the tank are dominated by vapor–liquid counterflow (heat pipe), which provides a much more efficient mechanism than heat conduction for dissipating tank heat. The heat pipe mechanism is also very effective in concentrating dissolved solids near the heat source, where salts may precipitate even if they were only present in small concentrations in ambient fluids. Tank leaks that released aqueous fluids of high ionic strength into the vadose zone were also modeled. The heat load causes formation dry-out beneath the tank, which is accompanied by precipitation of solutes. These may become remobilized at a later time when tank temperatures decline and previously dried out regions are rewetted. Simulated temperature and moisture distributions compare well with borehole measurements performed in 2000. The temperature maximum observed beneath Tank SX-108 can be explained from past thermal history of the tank; it is not necessary to invoke heat generation from leaked radioactive contaminants. A novel composite medium model is used to explore effects of moisture tension–dependent anisotropy, which is shown to have important impacts on fluid flow and solute transport in the Hanford sediments.

The Role Of The University Of Calgary In The Development Of A Centre Of Excellence In Petroleum Technology

Abstract Calgary is the recognized centre of the Canadian oil and gas industry, and as such it is home to a large concentration of engineers and technologists employed in the petroleum sector. The Department of Chemical and Petroleum Engineering at the University of Calgary, has long recognized the importance of the petroleum industry to the economic well-being of Albertans, and has been serving various training and research needs of the industry since its inception. Dr. A.H. Younger was appointed special sessional lecturer in engineering in 1964, and the gas processing courses which he developed are still being offered today. The first full-time appointments to the department were Dr. D.W. Bennion and Dr. K. Aziz. The first Ph.D. and the first M.Eng. graduated by the Department were in the areas of petroleum reservoir and natural gas engineering respectively. While the Department of Chemical and Petroleum Engineering has never been able to grant either undergraduate or graduate Petroleum engineering degrees, it has continued to serve the petroleum industry in many ways. The Department offers a M.Eng. degree with specialization in petroleum reservoir engineering. By far, the vast majority of our M.Eng. graduates have this specialization. Approximately two thirds of the graduate level courses are oil or gas related. Undergraduate courses on Petroleum Reservoir Engineering, Petroleum Production Engineering and Waterflooding are very well subscribed by students from Chemical and Petroleum Engineering, Mechanical Engineering and by students from industry. The Department is very fortunate that it can draw on local expertise as it does not have sufficient fulltime faculty to teach all of the courses which are currently offered. External teaching and consultative support are provided by two Honourary Professors (Dr. N. Mungan and Dr. K. Aziz) and six Adjunct Professors (Dr. J.K. Donnelly, Dr. G.A. Gregory, Dr. A. Kantzas, Dr. B. Maini, Dr. A. Settari, and Dr. A. Younger). The Department also benefits from a large number of industrial personnel who provide specialized lectures in the gas processing and final year design courses. Research interest in reservoir engineering in recent years, have emphasized thermal recovery processes which prompted the Department to develop world-class facilities in the areas of steam assisted gravity drainage processes (SAGD), solvent assisted process (VAPEX) and in situ combustion based processes. The Department has developed excellent thermodynamic property measurement capabilities for application to heavy oils and bitumens and a first-rate facility for determining the kinetics of gas hydrate formation. Property predictions for natural gas streams have long been a strong area of interest in the Department and our expertise in the area of computational thermodynamics using equations of state is world class. The direct support of the petroleum industry has resulted in the placement of two research chairs in the Department (Petroleum Chair and Hydrogen Chair) a third chair (Bituminous Materials) is shared with the Department of Civil Engineering. A close association is maintained with TITM Laboratories, which is located on the campus and provides specialized core and flow imaging services. In addition, the Petroleum Recovery Institute provides both facilities and supervision to graduate students.

Integral transform methodology for convection-diffusion problems in petroleum reservoir engineering

The convection-diffusion equation is present in the formulation of many petroleum reservoir engineering problems. A representative example, the tracer injection problem, is solved analytically here, through the generalized integral transform technique so as to illustrate the usefulness of this approach, for this class of problems. Classical assumptions, such as steady-state single phase flow and unit mobility ratio, are adopted. Comparisons with alternative analytical (when available) or numerical (finite difference) solutions are performed and benchmark results are established.

Modeling permeability in imperfectly layered porous media. I. Derivation of block-scale permeability tensor for thin grid-blocks

Practical expressions are given for the nine components of the block-scale permeability tensor of a thin block. These expressions are derived from the local-scale continuity equation and Darcy's law in an anisotropic layered porous medium. The flow problem is separated in a bottom-flux problem and a top-flux problem, both of which can be solved in essentially the same way. The bottom-flux problem has been worked out in detail, and has been separated in two parts: a vertical potential difference and a horizontal potential difference part. Each is solved with a different approach specially designed for it. Depth-averaged expressions are obtained first, after which block-scale expressions are obtained by assuming a constant depth-averaged flux. In the zeroth order, this results in the well-known Dupuit approximation in geohydrology, and the vertical equilibrium (VE) approximation in petroleum reservoir engineering. The novelty of the theory presented here stems from the application of a perturbation technique to obtain first-order corrections to these well-known results. The local-scale laws are applied in the coordinate system coinciding with the principal axes of the local-scale permeability tensor. Only in this coordinate system the local-scale permeability tensor has zero off-diagonal components. However, since the porous medium is imperfectly layered, the first-order corrections show that the off-diagonal components of the block-scale permeability tensor are not zero. Furthermore, the block-scale permeability tensor is generally nonsymmetric, which implies that a coordinate system in which the off-diagonal terms disappear does not exist.

Effects of single fractures on seismic wave propagation : Myer, L R; Pyrak-Nolte, L J; Cook, N G W Proc International Symposium on Rock Joints, Loen, 4–6 June 1990P467–473. Publ Rotterdam: A A Balkema, 1990

Detection and characterization of fractures, joints and faults remains an important problem in mining and geotechnical engineering, as well as in petroleum reservoir engineering. A theoretical model has been developed which predicts the amplitude and group time delay of the transmitted, reflected, and converted waves resulting from a plane wave incident upon a single fracture. It is assumed that seismic stresses are continuous across the interface. Seismic particle displacements, however, are assumed to be discontinuous. For completely dry conditions, the magnitude of the displacement discontinuity is given by the ratio of the seismic stress to the stiffness, {kappa}, of the fracture. If a fluid is present in the fracture, we postulate that, in addition to the displacement discontinuity, a velocity discontinuity exists which is equal to the ratio of the seismic stress to specific viscosity, {eta}. The wave equation has been solved for two sets of boundary conditions, with each set incorporating both specific stiffness and specific viscosity. These boundary conditions have been designated as Kelvin and Maxwell models. 12 refs., 5 figs.

Pennsylvania's Contribution to Petroleum Geology

John F. Carll of the Second Geological Survey of Pennsylvania laid the foundations of both petroleum geology and reservoir engineering. J. P. Lesley, director of the Second Survey, had introduced structure contours when he was working in the anthracite fields. He pointed out that the great oil fields of Pennsylvania were in the only part of the state where there were no anticlines. I. C. White, another geologist with the Second Survey, emphasized the anticlinal theory adopted as a method of prospecting until the discovery of the Cushing field in Oklahoma in 1912. George Ashley, state geologist of Pennsylvanian in the 1930s and 1940s, said that after the gas companies had drilled all the anticlines there would still be the synclines. David White in 1915 noticed the relation between the metamorphosis (rank) of coal and the occurrence of oil and gas. This method (vitrinite reflectance) is now widely applied in the evaluation of basins. In the late 1930s, the resurvey of the Pennsylvania oil regions showed that the reservoirs were shoreline sands, probably barrier islands. In the 1950s the AAPG recommended a study of the recent sediments of the Mississippi delta by Scripps Institute of Oceanography. The ability to recognizemore » depositional environments has caused a revolution in petroleum geology, and recently has been recognized by petroleum engineers as the key to reservoir characterization.« less

New Correlation for Estimating the Viscosity of Undersaturated Crude Oils

Abstract A new general correlation for estimating the viscosity of undersaturated crude oils has been developed using 253 experimentally obtained oil viscosities on 41 different oil samples collected from two different unpublished sources. The developed correlation is derived from plotting (P-Pb) vs. (µoa - µob) on log-log paper. The plot reveals a series of straight lines of a constant slope equal to 1.11. It is found that the intercepts of the resulting lines can be accurately represented as a function of API gravity and solution gas-oil ratio at bubble point pressure. The present correlation shows excellent results and clearly outperforms the existing correlations, when tested against the present data bank (253 points) and against available data from the literature (137 points). Introduction Viscosity in general can be defined as the internal resistance of fluid to flow. Like other physical properties of liquids, the viscosity is sensitive to changes in pressure and temperature. Increasing temperature always causes a decrease in viscosity. Increasing pressure always increases viscosity above the bubble point. However, below the bubble point, an increase in pressure causes an increase in solution gas which in turn decreases viscosity. Crude oil viscosity is essential for both petroleum reservoir engineering and production design operations. The present work deals with the correlations of viscosity of undersaturated crude oils (above bubble point pressure). The common empirical correlations available for predicting this property are those of Beal and Vasquez. In 1946, Beal presented a graphical method derived as the rate of change of the undersaturated oil viscosity per unit pressure increase above the bubble point pressure and the bubble point crude oil viscosity. The disadvantages of Beal's correlation are:it is based on only 26 data points covering limited ranges of flow conditions, andno analytical expression is given for the correlation. Using only 11 data points, obtained from Figure 11 of Beal's work, Standing found that Beal's correlation can be approximated by the following equation, which fit the 11 points with average error = 1% and standard deviation = 4.64%.

Multiphase flow and transport in porous media

Multiphase flow and transport of compositionally complex fluids in geologic media is of importance in a number of applied problems which have major social and economic effects. In petroleum reservoir engineering, efficient recovery of energy reserves is the principal goal. Unfortunately, some of these hydrocarbons and other organic chemicals often find their way unwanted into the soils and groundwater supplies. Removal in the latter case is predicated on ensuring the public health and safety. In this paper, principles of modeling fluid flow in systems containing up to three fluid phases (namely, water, air, and organic liquid) are described. Solution of the governing equations for multiphase flow requires knowledge of functional relationships between fluid pressures, saturations, and permeabilities which may be formulated on the basis of conceptual models of fluid‐porous media interactions. Mechanisms of transport in multicomponent multiphase systems in which species may partition between phases are also described, and the governing equations are presented for the case in which local phase equilibrium may be assumed. A number of hypothetical numerical problems are presented to illustrate the physical behavior of systems in which multiphase flow and transport arise.

A Summary of the Geothermal and Methane Production Potential of U.S. Gulf Coast Geopressured Zones From Test Well Data (includes associated papers 16455, 16460, 16480, and 16521 )

Summary Extensive testing in 12 wells in Texas and Louisiana has produceda significant body of production and test data from the U.S. gulf coastgeopressured zones. Results indicate that these deep sediments containsome reservoir-quality sandstones capable of extended production ofmoderately hot brine saturated with dissolved natural gas. The best of thetest wells to date, the U.S. DOE Pleasant Bayou Well 2 in Brazoria County, TX, flowed at a sustained rate of about 18,000 B/D [2860 m3/d] for about 7months. The reservoir may cover an area as large as 58 sq miles [150 km2]. None of the other 11 wells equaled the performance of the PleasantBayou test. From an economic standpoint, dissolved methane shows littlepromise of competitive performance in the foreseeable future. As a promise of competitive performance in the foreseeable future. As a geothermal energy source, the temperatures are disappointingly low. Theresource overall appears to be large but diffuse. Introduction Hottman's 1966 patent apparently represents the firstformal recognition of the deep gulf coast sediments, known as geopressured zones, as an energy resource. Thepatent claims that under certain conditions, overpressured patent claims that under certain conditions, overpressured formations (i.e., geopressured formations) are capable ofproducing hot water and dissolved methane gas under producing hot water and dissolved methane gas under natural flow. The patent was assigned to Hottman'semployer, Shell Oil Co., and no specific implementationsteps were ever reported. In the years following, the resource received theattention of the U.S. Geological Survey (USGS). The USGSwork was documented in a series of publications preparedby Jones, and his associates during 1968–74. After the OPEC oil embargo of 1973, geopressure, along with other alternative energy sources, began toreceive relatively large research support from the U.S.DOE and its predecessors. That work culminated in aseries of well flow tests, the results of which have removedmuch of the speculation surrounding the resource. Description of Geopressured Sediments In the gulf coast basin, as in many similar geologicalstructures throughout the world, buried sediments aresaturated with water, generally under hydrostatic pressure. Under certain conditions, however, the fluid may betrapped within the pore spaces, either by faulting ordepositional conditions, and attain pressures approaching lithostatic. Such formations are said to be geopressured. Along the Texas and Louisiana gulf coast, geopressuredconditions are general at depths below about 10,000 ft[3050 m]. Geological formations in these horizonsconsist of sandstone and shale; the latter accounts for about90% the total volume. Where reservoir-quality sandstonesexist in this sequence, production wells are potentially capable of flowing water at high rates. For reasons associated with the depositional history, formation temperatures are also higher than normal andconstitute some geothermal potential, Perhaps mostimportant is the dissolved methane with which the containedwater is apparently saturated. Questions about theusefulness of the resource involve primarily productioneconomics, including the producibility and production lifeof the potential reservoirs, the temperature of the producedwater, and the quantity of producible methane containedin solution. While geopressured conditions are known toexist over an area covering at least 100,000 sq miles[259 000 km2], the magnitude of the technically andeconomically producible fraction of the resource is open toconsiderable doubt. Estimates of production costs havenot been encouraging. Requirements of a GeopressuredProduction Well Production WellOn the basis of early study of the resource, pioneerresearchers at Louisiana State U. (LSU) considered theproduction of geopressured aquifers. In a classic paper production of geopressured aquifers. In a classic paper on the subject, Parmigiano, using established principlesof petroleum reservoir engineering, developed methodsfor predicting the performance of single wells or of wellsin clusters under geopressured conditions. JPT P. 1365

Wave methods for an inverse problem in diffusion

The usual inverse problem in petroleum reservoir engineering seeks rock permeability and porosity distributions from data on fluid property, well pressure and production rate. A simple, but potentially useful, specialisation considers flow of a single fluid phase along radial lines to a single well. An approach to this diffusion problem is presented, following an analogy to an existing one for wave propagation problems. This development is based on a parallel to the progressing wave expansion and may also be considered a transformation to the corresponding inverse problem for a wave equation. Several equivalent formulations are possible. All are severely affected by data errors. In fact, for some small deviations from correct data, the coefficient identification problem for diffusion has no reasonably smooth solution.

Geotechnical and groundwater geophysics

Because of a change in emphasis from power plant siting to projects principally involving process and facility monitoring and certification of existing structures (dams, pipelines, etc.), geotechnical and groundwater geophysics is in quite a healthy state after some lean years following the demise of nuclear energy construction projects. The orders‐of‐magnitude jump in the computational capability of geophysicists working in these fields has overshadowed advances in instrumentation (e.g., digital enhancement seismographs), field methods (e.g., cross‐borehole EM), and interpretive procedures. The advent of powerful, affordable microcomputers has enabled expansion into applications demanding finer resolution and quicker turnaround of results. As a result, shallow seismic reflection, seismic and electromagnetic geotomography, and the complementary use of surface and borehole electrical resistivity and seismic data will soon be common if not dominant methods in geotechnical and groundwater investigations. Future trends point to increased emphasis on environmental and economic issues (e.g., toxic wastes or the stability of underground petroleum storage facilities), cross‐fertilization with petroleum reservoir engineering (process monitoring and detailed reservoir description), and greater involvement of computers in the planning, data acquisition, and interpretive phases of our projects. As computers take over more of the data collection‐processing‐interpretation sequence, one of the greatest challenges facing us will be to define the proper role of humans and to use the new technology wisely.

Architectural-element analysis: A new method of facies analysis applied to fluvial deposits

Existing methods of facies analysis for fluvial deposits rely extensively on vertical profile analysis and comparisons with a limited array of fixed “end member” facies models. However, vertical profiles are not sufficiently diagnostic for this purpose because they cannot adequately represent three-dimensional variations in composition and geometry. A new method of analysis is proposed which subdivides fluvial deposits into local suites consisting of one or more of a set of eight basic three-dimensional architectural elements. These are channels, gravel bars and bedforms, sandy bedforms, foreset macroforms, lateral accretion deposits, sediment gravity flow deposits, laminated sand sheets and overbank fines. Twelve fluvial styles are selected to illustrate possible combinations of these elements. It is suggested that the same methodology could be used for other clastic facies. The better documentation of three-dimensional facies variability that can be obtained should be of considerable use in interpreting sedimentary controls and in carrying out petroleum field development, reservoir engineering or ore grade studies.

Petroleum reservoir engineering for crude oil and natural gas developments.

This paper presents characteristic studies that should be considered in oil and gas field developments. Several significant articles are illustrated and discussed, covering the following items; (1) reservoir rock properties, (2) waterflooding, (3) underground natural gas storage and (4) petroleum reserves and techno-economics. The effects of clays and clay minerals on relative permeability curves are clarified. The new porosity measurement of shaly sand cores is devised. At the planning stage, A and B blocks in Sarukawa oil field were given the priority of waterflooding projects by means of application of reservoir engineering data, in addition to the usual geological and geophysical information. The reservoir engineering study on Sekihara gas field has contributed to research for underground natural gas storage. The proposed procedure on moving boundary problem may be required in relatively smaller reservoir. The developed probability model on estimation of oil reserves and techno-economical appraisal method are discussed.

Geothermal Reservoir Engineering

The goal of the authors in writing Geothermal Reservoir Engineering was to bring together all the currently available information on geothermal reservoir engineering published before late 1981. The available information not only includes geothermal publications but also related publications in the areas of petroleum reservoir engineering and groundwater hydrology. Such a text would be a needed and worthwhile addition to many libraries, if the goal of the authors were achieved. Unfortunately, Geothermal Reservoir Engineering falls short of its potential contribution.

Mechanics of fluids in porous media

Transport of quantities such as mass component of a phase and/or heat occurs in fields as diversified as petroleum reservoir engineering, groundwater hydraulics, soil mechanics, industrial filtration, water purification, wastewater treatment, soil drainage and irrigation, and geothermal energy production. In all these areas, scientists, engineers, and planners make use of mathematical models; these models describe the relevant transport processes that occur within controlled porous medium domains and enable forecasting of the future behavior of these domains in response to planned activities. The mathematical models, in turn, are based on the understanding of phenomena, often within the void space, and on theories that relate these phenomena to measurable quantities.Because of the pressing needs in areas of practical interest such as the development of groundwater energy storage and geothermal energy production, a vast amount of research in all these fields has contributed, especially in the last two decades, to our understanding and ability to describe transport phenomena in porous media. In recent years these research efforts have been significantly accelerated, attracting scientists from many disciplines. The practical needs of solving boundary value problems in heterogeneous domains, irregular boundaries, coupled phenomena and multiple dependent variables led to the development of a variety of powerful numerical techniques. The realization that fields are highly heterogeneous and that the degree of heterogeneity depends on the scale of the problem led to the introduction of stochastic concepts as an additional tool for the description of phenomena.

Comment on ‘Identification and validation of some geothermal models’ by Larissa Ju. Fradkin et al.

Water Resources ResearchVolume 18, Issue 5 p. 1591-1592 CommentsFree Access Comment on ‘Identification and validation of some geothermal models’ by Larissa Ju. Fradkin et al. Charles R. Faust, Charles R. FaustSearch for more papers by this authorJames W. Mercer, James W. MercerSearch for more papers by this author Charles R. Faust, Charles R. FaustSearch for more papers by this authorJames W. Mercer, James W. MercerSearch for more papers by this author First published: October 1982 https://doi.org/10.1029/WR018i005p01591Citations: 1AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL No abstract is available for this article. References Bolton, R. S., The behavior of the Wairakei geothermal field during exploitationU.N. Symposium of Development and Utilization of Geothermal ResourcesUnited NationsPisa, ItalySeptember 22-October 1, 1970. Craft, B. C., M. F. Hawkins, Applied Petroleum Reservoir Engineering, Prentice-Hall, Englewood Cliffs, New Jersey, 1959. Donaldson, I. G., M. A. Grant, Heat extraction from geothermal reservoirs, Geothermal Systems: Principles and Case Histories L. P. J. Muffler, L. Ryback, John Wiley, New York, 1980. Fradkin, L. J., M. L. Sorey, A. McNabb, On identification and validation of some geothermal models, Water Resour. Res., 174, 929– 936, 1981. Grant, M. A., Approximate calculations based on a simple one-phase model of a geothermal field, N.Z.J. Sci., 20, 19– 25, 1977. , INTERCOMP, A model for calculating effects of liquid waste disposal in deep saline aquifers, U.S. Geol. Survey Water Res. Inv., 76–61, 1976. Mercer, J. W., C. R. Faust, Geothermal reservoir simulation, 3, Application of liquid- and vapor-dominated hydrothermal modeling techniques to Wairakei, N.Z., Water Resour. Res., 153, 653– 671, 1979. Pritchett, J. W., L. F. Rice, S. K. Garg, Summary of reservoir engineering data: Wairakei geothermal field, New ZealandRep. LBL-8669 GREMP-2Lawrence Berkeley Lab., Univ. of Calif., Berkeley, 1979. Citing Literature Volume18, Issue5October 1982Pages 1591-1592 ReferencesRelatedInformation

Well-testing in travale-radicondoli field. Part I. Geothermal well test analysis, principles and practice

The theory and applications of pressure transient (well test) analysis have been studied intensively for more than 40 yr by petroleum reservoir engineers and groundwater hydrologists. Only in the past decade, however, have geothermal-fluid wells been tested for the purpose of making pressure transient studies. Results of these studies disclose various well conditions, for example, restrictions to fluid flow into the wellbore. They also disclose reservoir heterogeneities, boundaries and permeability-thickness products of reservoir rocks. Probably most important, they can be used in estimations of energy reserves. This powerful analytical tool is discussed with special reference to the Travale reservoir. This reservoir is complicated geologically and hydrologically. It lies on the margin of a graben near a widespread outcrop of the reservoir rocks, which also form an absorption area for the meteoric waters. The area explored can be divided into three zones: in one of these (the nearest to the absorption area) some noncommercial wells produce two-phase water-steam mixtures; in the second zone the wells produce superheated steam, while a well drilled in the graben itself produces a fluid with an uncondensable gas content of about 80%. The reservoir is described in relation to defining areas for further exploration. The nature of the reservoir has affected the design of programs for collecting pressure-production data and other well performance data. The performance history prior to the advent of pressure transient studies pertains mainly to what is known as the ‘old’ Travale reservoir to the southwest of the ‘new’ Travale-Radicondoli reservoir in which the more recent wells are drilled and in which modern well test analysis methods have been applied. Data on the “old” reservoir are discussed first. Because of its initial performance and relationship to nearby wells the most important well in the “new” reservoir is Travale well 22. It has been subjected to extensive well testing. Nearly all the wells in the “new” reservoir have been involved, however, through well-interference tests. In these tests the wells surrounding Travale well 22 are shut in and their pressure responses to different Travale well 22 production rates are measured. Well interference tests indicate the characteristics of fluid flow in the reservoir between test wells and in a qualitative way the heterogeneous nature of the reservoir itself. Pressure transient theory is developed from ideal system behavior: one vertical, fully-penetrating well producing at a constant rate from a horizontal reservoir of uniform thickness and of infinite extent in any direction from the wellbore. A great deal of research has been done to aid well-test analysts in their interpretation of pressure buildup and pressure drawdown curves constructed from data taken on wells in actual reservoirs. This research generally is accomplished with model studies. Some of the models developed in the present research fit reasonably well with the build-up behavior of Travale well 22. The research done on the Travale reservoir is summarized here with the objective of showing what has been learned, how it can be applied, and what should be done next. Confidence in applications of pressure transient analyses in the Travale reservoir has been gained. New concepts of the reservoir system have emerged as a result of the research. Additional testing and more precise measurements in the field should lead to good engineering estimates of energy reserves.