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Abstract Material balance calculations often referred to as â??zero-dimensionalâ?¿ reservoir evaluations have been used extensively in petroleum and geothermal engineering. This paper presents a Havlena and Odeh-type material balance depletion model for two-phase reservoirs incorporating adsorption phenomena. A straight line, formed between groups of thermodynamic and adsorption properties of water and the cumulative production history provides the initial-fluid-in-place and the size of the vapor-dominated â??steam capâ?¿. Adsorption phenomena were found by Economides and Miller as the controlling mechanism in the depletion of vapor-dominated geothermal reservoirs. A material balance for vapor-dominated geothermal reservoirs, demonstrating the importance of adsorption phenomena is also presented. A straight line provides the initial-fluid-in-place. Introduction The general approach to the material balance depletion model was first suggested by Schilthuis. The equation provides a volumetric balance between the expansion of reservoir fluids as a result of the cumulative production. Havlena and Odeh using the Schilthuis approach developed linear expressions of the material balance equation for a variety of cases including undersaturated, gas cap drive and solution gas drive reservoirs. A similar development for the two-phase geothermal reservoir still be presented in this paper. Studies of reservoir and production behavior of vapor-dominated geothermal systems have focused on estimates of resource size. Whiting and Ramey presented an application of material and energy balances to geothermal steam production. Ramey applying conventional techniques for natural gas reservoirs, attempted to estimate the reserves of steam-in-place. Economides and Miller using the experimental results of Hsieh in which the importance and magnitude of adsorption was demonstrated, introduced a new approach for material balance calculation of vapor-dominated systems. As it will be shown here desorption is the controlling mechanism in the depletion of vapor-dominated geothermal systems and the major variable in their material balance calculations. The Form of the Material Balance Equation for a Two-Phase Geothermal Reservoir As in the Havlena and Odeh approach a volume balance in reservoir cubic feet (m) may be written (in their work they used reservoir barrels): Underground withdrawal (ft, m)=Expansion of liquid water and boiled off water (ft, m) +Expansion of steam cap (ft, m) +Expansion of desorbed water (ft, m) +Reduction in the pore volume (ft, m) The reduction in the pore volume will be neglected in the case of two-phase and vapor-dominated systems as has been demonstrated by Havlena and Odeh for saturated reservoirs. Figure 1 is a schematic depiction of the two-phase geothermal model used in this analysis.
- Energy > Oil & Gas > Upstream (1.00)
- Energy > Renewable > Geothermal > Geothermal Resource (0.31)
Single-Well and Multiwell Pressure Interference Analysis
Economides, M.J. (U. of Alaska) | Ogbe, D.O. (U. of Alaska)
SPE Members Abstract The purpose of an interference test analysis is to provide reservoir characteristics such as permeability, porosity and areal extent. Reservoir porosity and areal extent. Reservoir anisotropy and areal extent. Reservoir anisotropy may be identified and measured. A drawback of interference testing is that it requires one or more potentially productivity wells to be shut-in. However, productivity wells to be shut-in. However, this well test is superior to single-well drawdown or buildup because it often supplies results that reflect the characteristics of a much larger region of the reservoir. This paper presents a comprehensive review of the available analytical model and is supplemented by several real field problems and the associated interpretations. Guidelines are provided for the selection of the provided for the selection of the appropriate model, and criteria for interference well test design are outlined. Introduction The need to have detailed reservoir characteristics has become increasingly important in various reservoirs of the world. Well testing methods, especially pressure transient tests, are being employed pressure transient tests, are being employed routinely to obtain these detailed reservoir descriptions. Of the several pressure transient testing methods available to the reservoir engineer, single-well and multi-well interference tests have become popular. This popularity can be attributed to significant improvements in pressure recording devices, and in computer hardware and software. Both of these factors have led to the development of several mathematical models for the design, conduct and interpretation of interference tests. Interference tests have been found to reveal important information on reservoir transmissivity and storativity. Additionally, interference testing can provide qualitative indications of reservoir provide qualitative indications of reservoir heterogeneities and communication between two or more wells (or zones). In the early 1940's, after the pioneer work of Theis on the solution of unsteady-state pressure response at any time and location in a reservoir, several studies (See Guyton, Jacob ad King Hubbert) were reported on interference testing in the area of groundwater hydrology. In the petroleum literature, early works on interference testing and interwell communications were presented by Elkins and Muskat. Since then methods for analyzing interference test data were provided by Mortada, Tiab and Kumar, and Earlougher and Ramey. The reader is referred to a detailed review of the literature on interference and pulse testing recently presented by Kamal. presented by Kamal. At present, the reservoir engineer has five generalized models for the interpretation of interference tests. These include:Simple analytical model such as the line source solution for radial flow. Pressure drawdown/buildup interference type curves are available for the analysis of test data measured from two wells in a large homogeneous reservoir. An analytical model, which is a direct extension of the line source solution has been developed for simple anisotropic reservoirs (See Ramey, 1975). Given the interference test data from four wells, the direction of the principal axes of permeability and the magnitude of the permeabilities may be calculated. p. 745
- Overview (0.68)
- Research Report > Experimental Study (0.46)
- Energy > Oil & Gas > Upstream (1.00)
- Government > Regional Government > North America Government > United States Government (0.46)
- North America > United States > New Mexico > Permian Basin > Maljamar Field > San Andreas Formation (0.99)
- North America > United States > New Mexico > Permian Basin > Maljamar Field > Grayburg Formation (0.99)
- North America > United States > New Mexico > Permian Basin > Maljamar Field > Abo Formation (0.99)
- Europe > France > Paris Basin (0.99)
Pressure Transient Analysis for Single Well/Reservoir Pressure Transient Analysis for Single Well/Reservoir Configurations (Considering Partial Penetration, Mixed Boundary, Wellbore Storage, and Skin Effects) Abstract This work presents a set of solutions for pressure transients analysis demonstrating the flexibility of Green's functions in solving a wide range of problems. problems. The impact of partial completions and off centered wells is presented along with a first-time incorporation of wellbore storage and skin effects. Custom type-curves tailored to fit any well, reservoir and boundary configuration may be generated using the methods outlined here. An associated computer model is fully interactive and can be run on a small computer, readily available to most reservoir engineers. Introduction Green's functions have been used by a number of investigators to describe reservoir pressure transients in petroleum and geothermal reservoirs. Wegner (1983) developed an automated procedure to generate analytical solutions for a variety of boundary configurations. He compiled, in a concise form, various existing Green's functions. His computer code provides "custom type curves", suited to each well as completed in each reservoir. A small desk-top computer could run it, creating a fully interactive scheme. In order to rationalize the present work, a general presentation of the conventional approach used in pressure transients analysis is offered. The more direct and more easily understood solutions, are those in Laplace space, first presented by van Everdingen and Hurst (1949) and which are used by most investigators of pressure transients analysis. The main drawback from these methods is the difficulty to extend the results obtained for a particular geometry, to a generally similar, but different type of geometry or boundary conditions. This means that for each individual problem, some analytical work is required and more importantly, from an operational point of view, it is necessary that different cases should be treated differently. This is essential in identifying the trends of the pressure response and a major step towards pressure response and a major step towards the uniqueness of the solution. Another drawback, that has not been clearly pinpointed in the literature is the problem related to the inversion of the problem related to the inversion of the Laplace solutions. Once the solution to a particular problem is obtained in Laplace particular problem is obtained in Laplace space, it needs to be transformed back in the real time domain. Two main approaches have been used so far: an analytical inversion using Mellin's formula and a numerical inversion of the Laplace transform. Stablest (1970) developed a numerical algorithm that has been used widely. The use of Mellin's formula requires substantial and complex analytical work. It has the advantage of providing closed form solutions, usually involving infinite intergrals. However, there is no systematic treatment of the inversion in the petroleum literature. Each inversion petroleum literature. Each inversion attempt must be studied carefully and independently, thus forbidding the use of a simple computer code. In the past, the Stablest algorithm has been considered, as the panacea for too many times. P. 387
- North America > United States > Alaska (0.28)
- North America > United States > Texas (0.28)
Members SPE-AIME Abstract The prominent examples of linear flow behavior in the well test literature relate to linear flow within or to a fracture penetrated by a producing well. The resulting pressure transients generally are exhibited in the early portion of a well test and are followed by infinite-acting radial flow behavior and/or boundary effects. In this paper, the linear flow occurs in the formation, which has a predominantly linear shape. Analysis of interference, drawdown, and build up tests is described in theory and illustrated by practical examples. The necessary equations for practical examples. The necessary equations for the analysis are provided for testing gas, geothermal steam, and oil wells. In elongated linear flow systems, the pressure transient behavior associated with linear flow occurs late in the drawdown or build up test. The type curves provided in this work show that this pressure behavior is readily distinguishable from pressure behavior is readily distinguishable from conventional well tests, particularly in interference tests. Introduction Interest in the linear flow geometry was for a long time limited to application T related to water influx. The paper by Miller provided solutions for the pressure distributions in a semi-infinite or finite length linear aquifer assuming water influx into the oil zone at a constant flow rate. More recently, Ehlig-Economides, et al. developed methods for analyzing geothermal well tests in a predominantly linear flow system. This work was motivated by the presence of parallel linear faults predominant in geothermal regions such as the one shown in Figure 1. Methods for interference analysis and for drawdown testing of geothermal steam wells were presented. Currently, the linear flow geometry is cited as a fairly common occurrence in low permeability gas fields. Kohlhaas, del Giudice, and Abbott provided a case study of linear flow behavior for provided a case study of linear flow behavior for a gas well completed in a channel-like reservoir. They also provided equations for analyzing the linear flow portion of drawdown and buildup tests. Stright and Gordon examined rate decline behavior in gas wells in the Piceance Basin in Northwest Colorado which exhibited apparent linear flow behavior. In one case, the well penetrated a fracture in a low permeability marine sand in which a number of long permeability marine sand in which a number of long natural fractures are present and appear to be related to extensive faulting in the area. In another case, the well was completed in a long narrow sand body as evidenced by outcrops in the same area. A recent paper by Nutakki and Mattar provided solutions for drawdown versus time for the linear flow geometry which are identical to the work done by Ehlig-Economides and Economides for geothermal steam wells. However, the method of analysis, which made use of a "pseudo-skin" factor, was distinctly different. In this paper, the previous methods of interference and drawdown analysis for geothermal wells in a lienar flow system are reintroduced with additional coefficients for oil and gas well testing. In a subsequent paper, the draw down and buildup analysis of fractured wells in the predominantly linear flow system will be presented in detail. THEORY In Figure 1, the geological map from an unidentified geothermal region shows linear faults running parallel for several hundred feet. If the regional parallel for several hundred feet. If the regional faults provide impermeable boundaries to flow, then a particular well may drain a volume best described as a long narrow channel. In Figure 2 schematic diagrams of other types of depositional environments show possible reservoir geometries which would result in predominantly linear flow. P. 153
Abstract The rheological properties of Prudhoe Bay oil, as with any other mixture of hydrocarbons, are markedly affected by the lowering of temperature. The Transalaska pipeline traversing the state in a North/South direction is subjected to severe ambient temperatures during the winter months. A prolonged flow interruption would result in inevitable heat losses from the trapped crude oil. The temperature decline would cause a significant alteration of the flow behavior. A fundamental heat transfer study and laboratory measurements were combined in order to forecast the rheological response and subsequent start-up requirements of Prudhoe Bay oil in gathering lines and in the Transalaska pipeline. Introduction The Prudhoe Bay reservoir is the largest reservoir discovered in North America. The recoverable reserves are estimated at 9.7 × 10(9) bbl (1.54 × 10(9) m3) while the recoverable gas reserves are estimated at 26 × 10(12) SCF (7.36 × 10(11) m3). The Transalaska pipeline, roughly 800 miles long, joins the North Slope fields with the port of Valdez. The flow rate is 1.68 × 10(6) bpd (2.8 × 10(5) m3/d) (November 1982). During the winter months, the unburied portion of the pipeline (roughly one-half of the total length) is subjected to ambient temperatures that may reach -70F (-57C). The flowing temperature of 140F (60C) is sustained through a 4" thick insulation and the addition of kinetic energy through the various pumping stations. About eighty percent of Alaska is underlain by permafrost. The entire North Slope and much of the state's western half are in a "continuous zone" of permafrost, where the phenomenon is found nearly everywhere. The seasonally frozen active layer is commonly only a foot thick in these regions, but the underlying permafrost is more than a thousand feet thick in many places. Most of the rest of the state is in a "discontinuous zone", where permafrost is progressively mo-re sporadic from north to south, diminishing to progressively mo-re sporadic from north to south, diminishing to isolated, small masses of permanently frozen ground. Major soil engineering problems arise where permafrost occurs in poorly drained, fine-grained soils, especially silts and clays which are "thaw-unstable". Such soil generally contains large amounts of ice. The volume of ice can be much greater than the void volume of the thawed soil. In fact, while the soil may be pure, thawing would produce excess moisture. The result can be pure, thawing would produce excess moisture. The result can be loss of strength, settlement, and soil containing so much moisture that it becomes mobile. These possibilities were accounted for in the design of the pipeline. In much of the discontinuous zone, the permafrost is just below 32F, and the addition of as little as half a degree in some places will induce thawing. This is termed "warm permafrost" as compared to the "cold permafrost" of the North Slope. In order to keep the permafrost stable around the pipeline, about half of its length is erected above ground on a unique system of vertical supports (VSM's) which permit the oil to be moved through the pipeline without disturbing the stability of the permafrost below the line. permafrost below the line. An interruption of the flow would result in the lowering of the fluid temperature with the subsequent elevation in viscosity. Further decline in temperature would result in the gelling or even waxing of the oil. Perkins and Turner calculated the starting behavior of Prudhoe Bay crude based on laboratory measurements. They found that several factors affected the yield strength of Prudhoe Bay oil. p. 427
- Well Drilling > Drilling Fluids and Materials > Drilling fluid selection and formulation (chemistry, properties) (1.00)
- Reservoir Description and Dynamics (1.00)
- Production and Well Operations > Well & Reservoir Surveillance and Monitoring > Production logging (1.00)
- Production and Well Operations > Well & Reservoir Surveillance and Monitoring > Downhole and wellsite flow metering (0.84)