The development of a general technique of analyzing well tests with variable flow rates is reported. The variable flow is approximated by a series of sequential straight line segments of arbitrary length and slope. (MHR)

The conventional methods of well tests analysis usually assume a constant rate of discharge of the producing well. The procedure involves matching a log-log plot of test data (drawdown versus time) to analytic or semi-analytic solutions that are based on a model of the production well as a line source of constant strength in an infinite reservoir. However, variable discharge well test conditions may arise under a variety of conditions, such as existing well-field production schedules, step-drawdown tests, and influence of the pumping water level on the production rate. It is very desirable to have the capability to reliably interpret data from the tests. In fact, the present study was prompted by a set of recent geothermal well test data in which due to various mechanical problems, the flow rate during the first 70 hours of production varied widely and could not effectively be treated as a mean constant rate. The present paper reports the development of a general technique of analyzing well tests with variable flow rates. This method will make it possible to do well test analyses when a constant discharge flow rate is difficult to maintain, and permit detection of boundaries even in situations where there is …

The useful lifetime of a geothermal resource is usually calculated by assuming fluid will be produced from and reinjected into a uniform porous medium. However, most geothermal systems are found in fractured rock. If the reinjection and production wells intersect connected fractures, then reinjected fluid may cool the production wells much sooner than would be predicted from calculations of flow in a porous medium. We have developed a “quick and dirty” method for calculating how much sooner that cooling will occur (Kasameyer and Schroeder, 1975, 1976). In this paper, we discuss the basic assumptions of the method, and show how it can be applied to the Salton Geothermal Field, the Raft River System, and to reinjection of supersaturated fluids. 6 refs., 6 figs.

Surface geophysical techniques are readily adaptable to exploration for and evaluation of geothermal reservoirs because existing equipment and interpretive models can be used. In contrast, the application of borehole geophysics for these same purposes requires the development of equipment to operate dependably in the very hostile environment of some geothermal wells. After equipment ahs been developed and tested, its response must be calibrated with respect to required parameters such as lithology and porosity. This is difficult in geologic environments where there is practically no experience in well-log interpretation. The desired final products are reliable data to guide exploration for geothermal systems, and to aid in reservoir evaluation, modeling, and development, in the ways in which well logs are routinely used in the petroleum industry. Researchers in geothermal exploration are still some years from achieving the level of application already attained in petroleum exploration and development. This deficiency is receiving some attention from the U.S. Energy Research and Development Agency (ERDA) and the U.S. Geological Survey. The two agencies cosponsored a workshop on Geophysical Measurements in Geothermal Wells in September 1975 (Baker, Baker, and Hughen, 1975). Sandia Laboratories had previously summarized the state-of-the-art in a report on “Well-Logging Technology and Geothermal …

Most of the theoretical study on heat and mass transfer in geothermal reservoirs has been based on numerical method. Recently at the 1975 NSF Workshop on Geothermal Reservoir Engineering, Cheng presented a number of analytical solutions based on boundary layer approximations which are valid for porous media at high Rayleigh numbers. according to various estimates the Rayleigh number for the Wairakei geothermal field in New Zealand is in the range of 1000-5000, which is typical for a viable geothermal field consisting of a highly permeable formation and a heat source at sufficiently high temperature. The basic assumption of boundary layer theory is that heat convective heat transfer takes place in a thin porous layer adjacent to heated or cooled surfaces. Indeed, numerical solutions suggest that temperature and velocity boundary layers do exist in porous media at high Rayleigh numbers. It is worth mentioning that the large velocity gradient existing near the heated or cooled surfaces is not due to viscosity but is induced by the buoyancy effects. The present paper is a summary of the work that we have done on the analytical solutions of heat and mass transfer in a porous medium based on the boundary layer approximations since …

A set of P-V-T-X data for the highly saline fluids encountered in some geothermal reservoirs is an important prerequisite to the modeling of the chemical and physical behavior of geothermal reservoirs. However, very limited data at the temperatures and pressures encountered in the geothermal systems are available (Potter, 1976). In this paper, we present relatively simple workable models which can be used to predict accurately both the density and vapor pressure of complex brines at elevated temperatures. Together these models yield a parametric equation of state for the vapor-saturated geothermal brine. 15 refs.

It is obvious from this study that elevated levels of gaseous air pollutants (CO, NO, NO/sub 2/, and SO/sub 2/) and particulate sulfur and nitrogen compounds are present in indoor environments with gas cooking and heating appliances. High levels of CO and NO/sub 2/ approach or exceed promulgated and proposed ambient air quality standards. Such findings certainly indicate a potential impact of combustion-generated indoor air pollution on human health; and if borne out by further work, they may ultimately have a large impact on the future design of epidemiological studies, on energy conservation strategies for buildings, and on the need for more stringent control of air pollution from indoor combustion sources.

Geothermal power conversion cycles are compared with respect to recovery of the available wellhead power. The cycles compared are flash steam, in which steam turbines are driven by steam separated from one or more flash states; binary, in which heat is transferred from flashed steam to an organic turbine cycle; and dual steam, in which two-phase expanders are driven by the flashing steam-brine mixture and steam turbines by the separated steam. Expander efficiencies assumed are 0.7 for steam turbines, 0.8 for organic turbines, and 0.6 for two-phase expanders. The fraction of available wellhead power delivered by each cycle is found to be about the same at all brine temperatures: 0.65 with one stage and 0.7 with four stages for dual stream; 0.4 with one stage and 0.6 with four stages for flash steam; 0.5 for binary; and 0.3 with one stage and 0.5 with four stages for flash binary.

The basis on which charges are calculated for use of computers at LBL is explained. CPU time, I/O requirements, and memory utilized are among the primary factors considered. (RWR)

The following paper is an abstract of a report under completion at the Lawrence Berkeley Laboratory (Assens, 1977); the main purpose of this report is to (1) provide a mathematical derivation of the equations describing the transfer of heat, mass and momentum in a geothermal brine reservoir (especially when heat or mass sources are present), and (2) help in the choice of the dependent variables best suited for solving these equations numerically. 3 figs., 18 refs., 1 tab.

The East Mesa KGRA is located in an area of anomalously high heat flow on the east flank of the Salton Trough, at the southeast corner of the Imperial Valley of California (see Fig. 1). Ten producing wells have been drilled within the East Mesa KGRA, including three by Republic Geothermal in the northern portion, five by the U.S Bureau of Reclamation in the central area, and two by Magma Power Co. to the south (see Fig. 2). The intent of this presentation is primarily to illustrate an approach to reserve determination applicable to Republic’s lease area. The approach is analogous to a volumetric calculation for determination of conventional oil and gas reserves. First, the total initial heat content (enthalpy) of the reservoir was calculated between a bottom of 9000 feet and a top defined by the 300ºF surface. Second, an estimate was made of the portion of this initial heat content that can be expected to be recovered during the economic producing life of the area by using reservoir simulation studies of a single five-spot reinjection pattern. Lastly, a conversion efficiency was developed that relates the heat content of the produced water to the electrical energy output. 11 refs., …

In recent analyses of the hot-water system at Wairakei, New Zealand (Mercer, Pinder, and Donaldson, 1975) and the vapor-dominated system at Larderello, Italy (Petracco and Squarci, 1975), it has been suggested that large quantities of cold water are entering the reservoir by flowing down from the surface and then horizontally into the reservoir because of decreased reservoir pressures. It is also suggested that decreased reservoir pressures should increase these downward flows above their pre-exploitation levels. In order to estimate the effects of vertical flows on the temperature distribution, two idealized problems are analyzed in this paper. In both problems, the initial condition is a linear temperature increase with depth, and the flow starts at time equal to zero. In the first problem, the flow is through a semi-confining layer with the temperature fixed at the top and bottom of the layer. In the second problem, the flow is into a half-space with the surface temperature fixed. The magnitudes of the effects for the two cases considered suggest that monitoring temperatures in undisturbed wells on the margins of producing geothermal areas should give a measure of the change in the fairly local recharge. If the amount of total recharge is known, …

Although the corrosion and scaling problems associated with handling geothermal fluids are well known, the effects of hydrothermal reactions are often overlooked in geothermal reservoir modeling. Water-rock chemistry can be expected to affect the evolution of a reservoir in at least three ways: (a) the heats of reaction may contribute directly to the energy production, (b) the viscosity and thermodynamic properties of water are affected by the dissolved solids—this is especially important in two-phase regimes, and (c) the porosity and permeability change with time due to dissolving and precipitation as well as due to the volume change associated with alteration. In the case of alteration reactions, the reaction rate is not limited by solubility and, depending on the alteration rate, significant chemical energy may be extracted. One of the objectives of our experimental program is to determine alteration rates in typical reservoir rocks, and thus assess the importance of such reactions to the total thermal regime. The changes in porosity and permeability associated with both dissolving and alteration reactions are easily incorporated into standard finite difference schemes commonly used in numerical reservoir modeling; the paper illustrates this with a system of equations incorporating the dissolution and precipitation of SiO{sub 2}. …

Bioconversion of food processing wastes is receiving increased attention with the realization that waste components represent an available and utilizable resource for conversion to useful products. Liquid wastes are characterized as dilute streams containing sugars, starches, proteins, and fats. Solid wastes are generally cellulosic, but may contain other biopolymers. The greatest potential for economic bioconversion is represented by processes to convert cellulose to glucose, glucose to alcohol and protein, starch to invert sugar, and dilute waste streams to methane by anaerobic digestion. Microbial or enzymatic processes to accomplish these conversions are described.

Hydrogen fusion will require a mixture of liquefied or frozen D/sub 2/ and T/sub 2/. The equilibrium constant of the mixture describes the composition of this fuel. We have calculated the equilibrium constant, K/sub DT/, for the reaction D/sub 2/ + T/sub 2/ = 2DT in the 4.2-100 K temperature range. The results agree well with previous calculations at 25, 50, and 100 K. No calculations at temperatures below 25 K have been previously published. In the 16.7 to 33.3 K temperature range, which includes the triple point, K/sub DT/ can be represented by K = 2.995 exp (-10.82/T). The values of the analogous equilibrium constants for H/sub 2/--D/sub 2/ and H/sub 2/--T/sub 2/ are also given in the 4.2 to 50 K temperature range.

Two methods of dust-flux measurements are discussed which have been utilized to estimate aerosol plutonium deposition and resuspension. In previous studies the methods were found to be sufficiently detailed to permit parameterization of dust-flux to the erodibility of the soil, and a seventh-power dependency of dust-flux (or plutonium flux) to wind speed was observed in worst case conditions. The eddy-correlation method is technically more difficult, requires high-speed data acquisition, and requires an instrument response time better than one second, but the eddy-correlation method has been shown feasible with new fast-response sensors, and it is more useful in limited areas because it can be used as a probe. The flux-gradient method is limited by critical assumptions and is more bulky, but the method is more commonly used and accepted. The best approach is to use both methods simultaneously. It is suggested that several questions should be investigated by the methods, such as saltation stimulation of dust-flux, simultaneous suspension and deposition, foliar deposition and trapping, erodibility of crusted surfaces, and horizontally heterogeneous erodibility.

The method of Kaufman and coworkers is used to provide an estimate of isothermal sections of the Al--Li--Mg system. One starts by calculating the lattice stability of the constituents, the binary interaction coefficients and the binary compound parameters. In the computations, thermodynamic data, when available, were coupled with measured phase diagrams to provide thermodynamically self-consistent liquidus and solidus curves for the binary systems. Standard enthalpies of formation and entropies of formation were calculated for the reported compounds. The binary system Li--Mg illustrates the use of such calculations in selecting the most reliable representation of the phase diagram. The calculated binary data were used to compute the phase diagram of Li--Al--Mg, assuming that no ternary compounds exist. 4 tables, 7 figures, 29 references. (GHT)

A reliable static formation temperature is valuable in determining casing depths, establishing geothermal gradients, analyzing logs and estimating fluid potential for geothermal reservoirs. The conventional drilling mud fluid systems associated with geothermal well drilling distort the static formation temperature near the wellbore because the circulating mud temperature is normally much less than the static formation temperature. As a result, a wellbore temperature recorded during drilling operations does not reflect the static formation condition. The use of a Horner-type temperature buildup plot, similar to the conventional pressure buildup method, has been suggested for estimating static formation temperature. The method has proven satisfactory in a number of oil and gas field cases. Recently, Dowdle and Cobb investigated the conditions under which the Horner temperature plot can be used to yield representative static formation temperatures. They concluded that the method is reliable if both the wellbore temperature gradient changes very slowly and the mud circulation time is short. However, in geothermal operations, temperature gradients are usually more extreme and longer circulation times are required to cool the wellbore sufficiently for logging. Therefore, the method has proved to be less reliable. As an alternative solution, dimensionless Horner temperature type curves have been developed for …

The widespread, economic utilization of geothermal energy is at least partly dependent on efficient methods for stimulation of geothermal wells and formations. The principal problem is temperature, which imposes chemical, physical and mechanical limitations on equipment and stimulation fluids. The restrictions become particularly serious when formation temperatures exceed the 350º to 400ºF range which of course are the better geothermal zones. Ironically, one stimulation technique which has lost favor in oil and gas fields offers promise geothermally. Explosive fracturing, particularly bore shooting, can be used to fracture formations adjacent to the well bore. For true stimulation, only bore shooting offers economic viability today in high temperature wells. Nevertheless, it is a long step from economic and technical feasibility to commercial reality; a major element in that step is the development of safe hardware and field operational procedures. Therefore, certain conditions must be met in order to qualify an explosive stimulation system for routine commercial use. These conditions will insure that the explosive charges cannot cause massive damage or injury to personnel above ground in case of an accident, and also will minimize the potential for serious damage to a well in the event of a mishap. Fortunately, these conditions are …

The purpose of this paper is to illustrate and discuss practical application of pressure buildup test theory in The Geysers steam reservoir, where the theory has been used to make qualitative interpretations about such things as fracture geometry and boundary conditions. Quantitative estimates of reservoir permeability are made on a routine basis. Quantitative estimation of porosity using pressure buildup analysis requires a very accurate knowledge of reservoir geometry, so this application must be approached with caution, since the reservoir is still being delineated by exploratory drilling. The pressure buildup can conveniently be divided up into three general periods for purposes of discussion: (1) short-time, (2) radial flow, and (3) late-time. During short-time, pressure buildup is dominated by either wellbore storage and skin effect, linear flow along a fracture plane, or a combination of these. After these short-time effects die out, pressure becomes a linear function of the logarithm of time. This semi-log straight period will be called radial flow for purposes of discussion in this paper. At late-time, pressure departs from semi-log straight in various ways depending upon boundary conditions. Any or all of the above three periods typical of pressure buildup behavior at wells in The Geysers reservoir may …

In this investigation, we are primarily concerned with modeling fluid flow through vertical cracks that were created for the purpose of extracting heat from hot, dry rock masses. The basic equation for the two-dimensional problem of fluid flow through a crack is presented and an approximate solution is found. The basic equation is a non-linear, Cauchy-singular integro-differential equation. Moderately simple formulae for the crack opening displacement and the effective pressure difference between the crack tips are derived. The results are valid for arbitrary vertical cracks, provided that the fluid injection and removal points are not placed too close to the crack tips. (A more complete treatment of this problem is given by us in a paper to appear in the Journal of Geophysical Research.) There are two corrections that can be made to our results. One of these is for the influence of the earth’s surface. Another correction takes into account the force in the vertical direction produced at the crack walls by the fluid pressure because the crack walls are not vertical when the crack is filled with fluid. It can be shown (Weertman and Chang, Ref. 6) that both of these corrections are negligibly small. We conclude from …

Geoheat is now being extracted for electrical power generation from natural hydrothermal resources in thermally active regions on the basis of free flowing boreholes. This type of operation may be termed as free geoheat production. The Reykjavik District Heating System is a low-temperature operation where large scale resource stimulation by borehole pumping is being applied. These free and stimulated production methods are based on the presence of natural fluid conducting openings in the resource formations and on a natural recharge of the withdrawn fluid. One can also envision forced geoheat extraction systems (FGES) with an artificial recharge of the heat extracting fluid which flows to some extent through artificial openings created by hydraulic fracturing or other pressurizing operations. For the operation of such systems to be successful, the openings have to provide adequate contact areas or contact volumes between the fluid and the rock such that a sufficient amount of heat can be extracted from the hot formations. In this paper, we will discuss a number of economical and physical aspects of FGES with emphasis on heat extraction from sheetlike natural fluid conductors in volcanic formations such as sufficiently open (conducting) fault zones, dikes and formation contacts. We envision applications …

The Bureau of Reclamation has established an ongoing program for the analysis and evaluation of the East Mesa Geothermal Field. This presentation will discuss the recent history of the field including testing methods and results. Future testing plans will also be discussed. 6 refs., 3 tabs., 4 figs.

For reservoir engineers in private industry, a geothermal project begins when a potential geothermal prospect is being evaluated for leasing. The reservoir engineer must be involved with the exploitation and land acquisition groups, and with the exploration and initial drilling program. The reservoir engineer must contribute information to the environmental impact analysis, and is challenged to determine how large his reserves are within the shortest possible time and with the minimum amount of wells and testing. Needs are described for temperature tools as sensitive as those for bottomhole pressure measurement, for analysis of chemical data for its implications about reservoir performance, for more complete understanding of the effects of water injection into reservoirs, and for techniques that minimize water injection’s detrimental effects. The engineering going on in the field is highly complementary to the current research activity.