INTRODUCTION Well tests have been used for many years for evaluating reservoir characteristics, and numerous methods of interpretation have been proposed in the past. A number of these methods have become very popular, and are usually referred to as 'conventional'. In the last ten years, many others have been developed, that are often called 'modern', but the relationship between 'conventional' and 'modern' well test interpretation methods is not always clear to the practicing reservoir engineer. To add to the confusion, some methods have become the subject of much controversy, and conflicting reports have been published on what they can achieve. This is especially true of the 'type-curve matching' technique, which was first introduced in the oil literature in 19701, for analyzing data from wells with wellbore storage and skin effects. This method, also called 'log-log analysis', was supposed to supplement 'conventional' techniques with useful qualitative and quantitative information. In recent years, however, it was suggested that this technique be only used in emergency or as a checking device, after more conventional methods have failed.2,3 The relationship between 'conventional' and 'modern' interpretation methods is examined in detail in this paper. It is shown that type-curve matching is a general approach to well test interpretation, but its practical efficiency depends very much on the specific type-curves that are used. This point is illustrated with a new type-curve for wells with wellbore storage and skin, which appears to be more efficient than the ones already available in the literature. METHODOLOGY OF WELL TEST INTERPRETATION The Concept of Model The principles governing the analysis of well tests are more easily understood when one considers well test interpretation as a special pattern recognition problem. In a well test, a known signal (for instance, the constant withdrawal of reservoir fluid) is applied to an unknown system (the reservoir) and the response of that system (the change in reservoir pressure) is measured during the test. The purpose of well test interpretation is to identify the system, knowing only the input and output signals, and possibly some other reservoir characteristics, such as boundary or initial conditions, shape of drainage area, etc. This type of problem is known in mathematics as the inverse problem. Its solution involves the search of a well-defined theoretical reservoir, whose response to the same input signal is as close as possible to that of the actual reservoir. The response of the theoretical reservoir is computed for specific initial and boundary conditions (direct problem), that must correspond to the actual ones, when they are known. Interpretation thus relies on models, whose characteristics are assumed to represent the characteristics of the actual reservoir. If the wrong model is selected, then the parameters calculated for the actual reservoir will not be correct. On the other hand, the solution of the inverse problem is usually not unique : i.e., it is possible to find several reservoir configurations that would yield similar responses to a given input signal. However, when the number and the range of output signal measurements increase, the number of alternative solutions is greatly reduced. The Concept of Model The principles governing the analysis of well tests are more easily understood when one considers well test interpretation as a special pattern recognition problem. In a well test, a known signal (for instance, the constant withdrawal of reservoir fluid) is applied to an unknown system (the reservoir) and the response of that system (the change in reservoir pressure) is measured during the test. The purpose of well test interpretation is to identify the system, knowing only the input and output signals, and possibly some other reservoir characteristics, such as boundary or initial conditions, shape of drainage area, etc. This type of problem is known in mathematics as the inverse problem. Its solution involves the search of a well-defined theoretical reservoir, whose response to the same input signal is as close as possible to that of the actual reservoir. The response of the theoretical reservoir is computed for specific initial and boundary conditions (direct problem), that must correspond to the actual ones, when they are known. Interpretation thus relies on models, whose characteristics are assumed to represent the characteristics of the actual reservoir. If the wrong model is selected, then the parameters calculated for the actual reservoir will not be correct. On the other hand, the solution of the inverse problem is usually not unique : i.e., it is possible to find several reservoir configurations that would yield similar responses to a given input signal. However, when the number and the range of output signal measurements increase, the number of alternative solutions is greatly reduced.

This paper presents the results of a theoretical study on the thermal behavior of a hot water storage system in an aquifer using a single well. It is shown that the storage efficiency and temperature are controlled by a limited number of dimensionless groups that depend on the aquifer's physical characteristics and the storage operating parameters. A numerical model is checked against analytical solutions and is then used to evaluate the variation with time of the well temperature during production periods for symmetrical cycles (production volume and flowrate equal to injection volume and flowrate). From these results, type curves are plotted for several sets of dimensionless parameters, covering the range of practical applications. Effects of unequal injection and production periods, standby periods, and other operating conditions are also investigated. Practical recommendations are made for efficient storage projects. INTRODUCTIONThe depletion of classical resources in fossil fuels combined with high inflation rates has recently enhanced interest in developing the exploitation of alternate energy sources and in improving efficiency in the use of energy in general. Along these lines, hot water storage in permeable geological layers appears particularly attractive, for it provides a way of transferring energy from a period of low consumption where it is being produced, into peak hours or seasons.The most important parameters in a heat storage project are (1) the recovery factor (i.e., the ratio of the quantity of energy recovered to that injected) which determines the project economic feasibility and (2) the energy (or temperature) level in the recovered water and its variation during production, which conditions the type of surface utilization. These parameters depend upon the storage physical characteristics (aquifer reservoir thickness, thermal conductivity, heat capacity, etc.) and operating conditions (production and injection rates, duration of injection and production cycles, etc.).In order to facilitate rapid technical evaluations of heat storage projects, and to assess their economic feasibility without engaging into heavy investments, a general study was undertaken of the various parameters that would influence the behavior of such systems. The study, restricted to the case where the same borehole is used for hot water injection and production, included both a theoretical investigation and a field experiment. The theoretical results, which were used to construct type curves convenient for practical applications, are presented hereinafter. Results and analysis of the field experiment are the subject of a companion paper. ScoPE OF STUDYThe theoretical study is concerned with storage of hot water under liquid phase (sensible energy storage) in relatively deep aqufers. Compared with that in shallow aquifers,• Now with Flopetrol, 245 deep aquifer storage appears advantageous because (1) regional groundwater flow being usually negligible, the injected hot water is not displaced, (2) thickness of overburde...

Ten successive in situ experimental investigations of hot water storage by a single well and a pair of wells (doublet) were conducted in 1976-1977 at Bonnaud, Jura, in a confined aquifer 2.5 m thick. The injected volumes ranged from 500-1700 m 3. Temperature profiles were measured daily in 12 boreholes distributed along two perpendicular axes within 13 m of the injection well. Individual temperatures were measured by ten thermistors placed in the caprock. The results are discussed and used to calibrate two mathematical models. An axisymmetric model allows the calibration of average values of the parameters, while a three-dimensional model is used to determine their spatial variation in the horizontal plane. The latter model leads to the identification of a nonhomogeneous transmissibility field which fully accounts for both hydraulic and thermal contour curves. The models, which were matched against particular experiments, proved accurate when simulating other periods. Evidence is given of the importance to the recovery ratio of thermal dispersion in the aquifer and of the water content of the caprock. In a final section, experimental results of single well storage at Bonnaud, Campuget, and Auburn are compared with general type curves derived in the companion paper. They prove to yield adequate predictions of water temperature during the production phases.

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