The effects of anisotropic or directional permeability on the areal sweep efficiency and the flow capacity are examined. The paper points out the importance of taking directional permeability into consideration in planning a flood. It analyzes the two-dimensional flow pattern associated with the skewed line drive for a unit mobility ratio. The direct and staggered line drives are treated as special cases of the skewed line drive. Analytical expressions are developed for the areal sweep efficiency at breakthrough and the flow capacity. They are related to the spacing between like wells, the distance between a row of injectors and the nearest row of producers, and the degree of skewness of the line drive. The latter quantity is defined such that it is equal to zero for the direct line drive and equals one-half for the staggered line drive. The a real sweep efficiency and the flow capacity depend also on the orientation of the flood pattern with respect to the principal axis of anisotropy. The paper provides a simple method for determining the a real sweep efficiency and the flow capacity for a formation in which the permeability in the bedding plane is anisotropic. Introduction Directional or anisotropic permeability is manifested by the ability of the formation to conduct fluids more readily along certain preferred directions. This situation occurs in many producing formations and is usually attributed to depositional features in which the sand grains are oriented in a preferred direction. In some cases it results from the formation of a major and a minor fracture system. Directional permeability should be taken into account in many phases of the production and exploration activities. Recognizing its existence in the formation of interest and planning accordingly can lead to increased recovery and substantial savings. For instance, the areal sweep efficiency in a water flood depends to a great extent on the orientation of the flood pattern with respect to the principal axis of permeability. Anisotropic permeability is specified by the directions of its three principal axes and the permeability along each axis. The principal axes of permeability are mutually perpendicular. This paper deals with the areal sweep efficiency at breakthrough and the flow capacity for formations with anisotropic permeability. The flood pattern considered consists of alternate rows of injecting and producing wells. The rows of wells are parallel and form a developed, skewed line drive which is illustrated in Fig. 1. The staggered and direct line drives are treated as special cases of the skewed line drive.

Introduction Linear aquifers, either limited or essentially infinite, may be encountered in reservoir engineering practice. In areas where faulting fixes reservoir boundaries, the fault block reservoir may have an aquifer of limited extent whose geometry is best approximated as linear. An infinite linear aquifer can occur as a regional feature whenever water movement through the aquifer member is constrained to one direction. Such constraints can arise from major faults. facies changes or pinchout of the member. Miller* pointed out that linear aquifers have received only meager attention in the past. He analyzed the performance of finite and infinite aquifers, developed working equations and curves, and presented examples. While Miller's curves may be used fairly easily, a separate one is required for each size of aquifer. In this paper, Miller's equations have been used as a starting point. By modifying them slightly, they can be reduced to a form which yields a single a working curve, applicable to any size of aquifer. Thus, interpolation between curves is eliminated and accuracy is improved. Miller's results for finite aquifers covered only the boundary condition of no flow across the outer aquifer boundary. This paper also includes the case of constant pressure at the outer aquifer boundary. DEVELOPMENT OF EQUATIONS FOR LINEAR AQUIFERS Miller's equations give pressure drop or cumulative influx at the linear aquifer-reservoir boundary as a function of time for the boundary conditions of an infinite aquifer and a finite aquifer with sealed outer boundary. In addition to these equations, those appropriate for the boundary condition of a finite aquifer with constant pressure at the outer boundary have been developed. The approach used in developing these equations was the same as that used by Miller. BOUNDARY CONDITION 1: CONSTANT RATE OF INFLUX ACROSS AQUIFER-RESERVOIR BOUNDARY Infinite Linear Aquifer (1) Finite Linear Aquifer, Constant Pressure at Outer Boundary (2) BOUNDARY CONDITION 2: CONSTANT PRESSURE AT AQUIFER-RESERVOIR BOUNDARY Infinite Linear Aquifer (4) Finite Linear Aquifer, Sealed Outer Boundary (5) Finite Linear Aquifer, Constant Pressure at Outer Boundary (6) These equations are usually put in a form where dimensionless time is defined by (7) Here, x is a reference distance and is usually taken to be a unit distance. However, the choice is really arbitrary, as long as consistency is maintained. We choose x = L; then (8) For finite aquifers, L is the length of aquifer; for infinite cases, it may be considered as an arbitrarily chosen length. The reason for this choice will be clear later when the performances of finite and infinite aquifers are compared. JPT P. 561ˆ

Formation compressibility has long been recognized as an important factor influencing production behavior from overpressured oil and gas reservoirs. However, formation compressibility data are not routinely collected and the use of formation compressibility in reservoir analysis and simulation is often oversimplified. This paper discusses more accurate methods to determine formation compressibility and introduces a new method for analyzing overpressured oil and gas reservoirs which utilizes the variability of formation compressibility with declining reservoir pressure. The newly developed method departs from earlier proposed methods in the use of variable rather than~formation compressibility by employing a "pore volume formation volume factor", Bt, that properly integrates pore volume compressibility effects over the full pressure range of investigation. Using the new concept of Bt, the material balance equation (MBE) can be modified to include the effects of pressure dependent formation compressibility.We find that the formation compressibility in highly overpressured unconsolidated reservoirs can be the same order of magnitude as gas compressibility and significantly higher than oil compressibility. In some types of reservoirs, an order of magnitude change in formation compressibility can occur during drawdown. We show that in many overpressured and/or unconsolidated reservoirs, proper integration of accurate formation compressibilities is important for reserve estimates, determination of drive energies, and overall reservoir development plans. For example, we find that the use of compressibility values in the MBE which are significantly lower than those which exist in the reservoir could suggest a strong water drive where one does not exist.

No abstract

A blotter-type electrolytic model was utilized to prepare flow diagrams for a field test of the in-situ combustion process. It is pointed out that the areal sweep of a combustion pattern is similar to sweep patterns that would be developed at an infinite mobility ratio, which exists (approximately) across a combustion front because of the complete removal of liquids from the sand behind it.The precision of the blotter method was tested by comparison with results obtained by other techniques and was found to be satisfactory. The blotter-type model will not furnish as much information as more elaborate and expensive potentiometric models, but its speed of operation and ease of construction make it a highly satisfactory tool to determine areal sweep patterns. A tabulation of sweep efficiency and mobility ratio is furnished for various well geometries.