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William E. Brigham

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Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Annual Technical Conference and Exhibition, September 27–30, 1998

Paper Number: SPE-49021-MS

Abstract

Abstract In the first part of this study, the accuracy of the JBN technique for the determination of heavy oil/water relative permeabilities, and the effect of temperature on relative permeabilities is examined by giving numerical as well as experimental examples. Using the JBN technique leads to a false temperature dependence of relative permeability curves. In the second part, we present unsteady state relative permeability experiments with initial brine saturation at differing temperatures conducted using South Belridge sand and heavy oil. A new three step experimental technique and an analysis procedure were developed to test the effect of temperature on relative permeabilities. In this technique, an ambient temperature unsteady-state relative permeability run is conducted in the first stage, and following that the temperature is increased twice (i.e. 1220F and 1500F). Two phase saturation profiles along the sand pack are measured using a CT scanner. A commercial black oil simulator, coupled with a global optimization code is then used to estimate two phase relative permeabilities. Experimental saturation profiles, differential pressure and recovery data collected from both the ambient and higher temperature data are used in the numerical model. It has been observed that a single set of relative permeability curves can represent both the ambient and high temperature parts of the experiment. This suggests that relative permeability is not a function of temperature at least for the systems and temperature ranges tested P. 329

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Annual Technical Conference and Exhibition, September 26–29, 1982

Paper Number: SPE-11071-MS

Abstract

Abstract Relative permeability is perhaps the most important parameter in describing underground flow behavior of immiscible fluids. In recent years, thermal recovery methods have gained in importance. This requires an understanding of temperature effects on flow characteristics of reservoir fluids. This paper presents an experimental study dealing with temperature effects on relative permeabilities of oil-water systems. Results indicate that the curves are independent of temperature as are the end point saturations. There is a decrease in "practical" residual oil with temperature saturation due to a change in the shape of the fractional flow curve. Introduction Relative permeability curves basically represent multiphase flow of fluids as controlled by the interaction of viscous and capillary forces within a porous medium. Altering temperature can cause changes in the relative levels of these two forces. This, in turn, may affect the flow characteristics of the different fluids within the porous medium. Temperature effects on relative permeabilities were first studied by Wilson who observed no temperature dependence. Following that, a number of studies were conducted that showed distinct changes in end point saturations. All these studies observed a decrease in the residual oil saturation, , with an increase in temperature. Those that studied changes in irreducible water saturation, , found it to increase with temperature. One reason given for these changes was an increase in water-wetness of the porous media with an increase in temperature. Lo and Mungan conducted steady state runs to determine relative permeabilities. They observed that if the viscosity ratio remained constant, relative permeability curves were independent of temperature. permeability curves were independent of temperature. The purpose of this study was to determine the effect of temperature on relative permeabilities and to provide explanations for any observed effects. Further, dependence of or on initial water saturation was also studied. EQUIPMENT AND PROCEDURE The schematic diagram of the equipment is shown in Fig. 1. The system consists of a Ruska constant-rate, positive-displacement pump that can independently flow oil from on cylinder and water from the other. Lines from both these cylinders enter an air bath that is capable of maintaining a constant temperature (+/- 0.4F) up to 650F. Once inside the air bath, both lines flow through heating coils and capillary tube viscometers, the latter to measure fluid viscosities at temperature and pressure. After the viscometers, the lines flow into a four-way switching valve that is controlled from outside the air bath. This valve is capable of withstanding temperatures up to 750F and pressures up to 500 psia. One of the outlets from this valve goes out of the air bath, through a condenser and a back-pressure regulator, and into a collection vessel. The other outlet goes into the core which is composed of Ottawa sand packed in a stainless steel tube. Bypassing is prevented by applying a confining pressure on the sand through a movable end plug. The core holder itself is pressure on the sand through a movable end plug. The core holder itself is capable of withstanding 10,000 psia confining pressure. On leaving the core, the fluid is cooled in a condenser, then flows through a thick-walled glass capillary metering tube and finally into a pressure bomb. The porous medium used in this study was unconsolidated Ottawa sand (mesh size 170–200). The pack has a diameter of 1 in. and a length of 7 in. The sand was subjected to a confining pressure of 2000 psi. A pore pressure of 200 psi was used in the runs to keep the fluids in liquid phase pressure of 200 psi was used in the runs to keep the fluids in liquid phase at high temperatures. Figure 2 shows a schematic of the glass tube that is used to determine the oil produced. The metering technique assumes that the oil and water flow as independent slugs. This is true for pure systems that do not contain emulsion-forming agents. A light emitting diode (LED) source is used to provide light from one side of the tube and a photoelectric cell receives the light on the other side after it has passed through the tube walls and the fluid flowing within.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Annual Technical Conference and Exhibition, September 21–24, 1980

Paper Number: SPE-9294-MS

Abstract

Introduction The subject of well test analysis is one of great interest in Petroleum Engineering and the large number of publications bear witness to the considerable effort directed at obtaining a better understanding of the subject. The majority of the reported research assumes a radial flow profile which is valid for most test situations. There are certain well test situations which can be more adequately modelled by assuming a spherical flow profile, e.g. vertical interference testing and wireline formation testing. However few papers have been published on spherical flow. In single-well pressure transient tests, the presence of wellbore storage has long been recognised presence of wellbore storage has long been recognised to have adverse effects on the analysis of the test results which can lead to erroneous interpretations if the period dominated by wellbore storage is not properly identified. The purpose of this paper is to properly identified. The purpose of this paper is to present a theoretical analysis of how wellbore storage present a theoretical analysis of how wellbore storage can influence transient pressure analysis in systems characterised by spherical flow geometry. Type curve methods have been used to apply this theory. The problem to be considered is the flow of slightly compressible (small pressure gradient) single phase fluid in an ideal spherical system, i.e. the phase fluid in an ideal spherical system, i.e. the flow is assumed to be perfectly spherical to a well of radius r in an isotropic medium with the effects of gravitational forces being negligible. Since the prime concern is the consideration of pressure transients at short times when outer boundary effects are not seen, the reservoir is assumed to be infinite in extent. The initial condition for an infinite medium can then be taken as a constant pressure, p, at a radius greater or equal to the wellbore radius, r. The inner boundary condition will be taken as production at constant surface rate from a wellbore production at constant surface rate from a wellbore of finite volume with significant wellbore storage. Since the reservoir is assumed to be infinite, the outer boundary condition implies that the pressure drop equal zero at all time. THEORY The basic, partial differential equation describing the flow of a slightly compressible fluid in a homogeneous porous medium, governed by spherical geometry, can be stated as: (1) where the porosity, compressibility and mobility are assumed to be constant and where gravitational effects can be neglected. The various dimensionless variables are defined in field units as follows: dimensionless radius, (2) dimensionless time, (3) dimensionless pressure (4) where rsw is defined as the pseudo spherical wellbore radius and depends upon many factors such as wellbore condition, type of well completions, i.e. either partially or fully completed, etc. partially or fully completed, etc.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Fall Meeting of the Society of Petroleum Engineers of AIME, October 6–9, 1974

Paper Number: SPE-5055-A

Abstract

Introduction Pulse testing, as a practical method of reservoir analysis, was introduced into petroleum engineering literature by Johnson et al. in 1966. Since then, several authors have discussed, expanded on, or applied some of the basic concepts of horizontal pulse testing. Pulse testing as originally formulated by Johnson et al. can provide two pieces of information from which the reservoir transmissibility (T = krh/Î¼) and storage (S = Î¦cth) can be obtained. It does not address itself to the problem of evaluating the in-situ vertical permeability, which is important in reservoir processes where there is appreciable vertical flow. It has been recognized that vertical interference testing has considerable promise for simultaneous evaluation of the horizontal and vertical permeability; however, no one has considered the use of multipulse tests and the Johnson gradient method for this purpose. This is despite the inherent advantages of multipulse testing over the other techniques. The objective of this paper is twofold: to examine the behavior of multipulse pressure transients in a vertically pulsed slab reservoir, noting the effect of the finite characteristics of the reservoir, and to generate correlation curves, based on known pressure response characteristics, for interpreting dynamic data from pulse-tested reservoirs.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Fall Meeting of the Society of Petroleum Engineers of AIME, October 6–9, 1974

Paper Number: SPE-5055-B

Abstract

Introduction Most of the published literature on pulse testing has concentrated on the analysis of pulse tests in infinite domains. Few known comprehensive analyses have been made on tests in finite-acting domains. This is despite the known fact that pulse test results based on the simple infinite model are subject to serious errors if boundary effects are present. This paper is an illustration of the practical application of the theoretical model presented by Falade and Brigham on "The Dynamics of Vertical Pulse Testing in a Slab Reservoir" with special considerations for the boundary effects. Review of Model The transient pressure response due to equal and alternating periods of shut-in and injection (or production) into a test well during vertical pulse testing in a slab reservoir can be described as follows.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Fall Meeting of the Society of Petroleum Engineers of AIME, September 30–October 3, 1973

Paper Number: SPE-4585-MS

Abstract

ABSTRACT Often, in flow through porous media, the mixing characteristics of the flowing fluids are defined by the diffusivity equation. Solutions of this equation are available for linear flow and close approximations are available for radial flow. In this paper, one of the radial flow approximation methods has been generalized to a variety of geometries. The solution is assumed to be in the form of an error function; and equations are derived for the standard deviation, i.e., the argument of the error function. By breaking the flow system into segments and by repeated use of these solutions, mixing can be calculated in a large variety of flow systems. For example, equations can be used to calculate tracer flow behavior in reservoirs and mixing in vertical miscible displacement. INTRODUCTION In the absence of viscous fingering, the equations defining mixing in a linear miscible displacement are well known.