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
This paper describes an electrical model and its application to the analysis of four reservoirs in Saudi Arabia. The model has 2,501 mesh points and represents 35,000 sq miles of the Arab-D member. Details of modeling such as mesh size, control problems and standards of performance in matching reservoir history are discussed. The particular performance match achieved for the Arad-D member is presented. Details such as permeability barriers, aquifer depletion and interference between oil fields are given. The performance match realized in the Abqaiq pool is presented in detail. Introduction The resistor-capacitor network and associated control equipment described in this paper comprise an electrical analog of a reservoir system. Similar equipment has been used to study the transient response of reservoirs for many years. The unique feature of the model and application to be described is the extremely large size of the model and reservoir system, and the detail observed in simulating the reservoir with the model. The Arabian American Oil Co. first became interested in analog computers for simulation of oil reservoirs in 1949. Since that time, several models have been developed, each more elaborate and refined so that the reservoir system might be more closely simulated. The current model is the latest in a series designed, built and operated by the Field Research Laboratory of Socony Mobil Oil Co. in collaboration with Aramco. It has been and continues to be used to study the regional performance of the Arab-D member limestone reservoir. The Arab-D member is one of the Middle East's most prolific producing horizons. THE MODEL The theory of simulating a reservoir system with an electrical system has been presented in the literature. Therefore, this paper will not discuss the theoretical aspect of the problem except to point out the correspondence between the fluid system and electrical system, as shown in Table 1.In general, the complete model is made up of input devices, output devices, central control and a resistance- capacitance (RC) network. At times, the RC network alone is referred to as the "model". However, it should be evident from the text which meaning is attached to the word "model". A discussion of the equipment follows. THE RESISTANCE-CAPACITANCE NETWORK The RC network consists of 2,501 capacitance decades interconnected through 4,900 resistance decades. The components are arranged to form a rectangular network of 2,501 mesh points in a 41- X 61-mesh array. Imposing the mesh grid system on the continuous reservoir system divides the reservoir into discrete areal segments. These discrete segments may be of various sizes. More precisely, the mesh size need not be uniform throughout the model. The RC network is fabricated in two sections which are connected at the top, An inside view of the "tunnel" formed by the two sections is shown in Fig. 1. The height and width of the tunnel are shown in the figure. Numerals appear along the bottom and along the back opening of the tunnel. These numbers denote the x and y coordinate positions of mesh points. Fig. 2 presents a rear view of one-half the model. The length dimensions of the model, as well as a rear view of the capacitor decades, are shown in this figure. The control dials used in adjusting the resistance and capacitance values on the model can be seen in the enlarged portion of the model shown in Fig. 3.The electrical capacity at any mesh point can range from 0 to 1.0 microfarads set to the nearest tenth of a microfarad. The electric resistance connecting any two mesh points can range from 0 to 9,990,000 ohms set to the nearest 1,000 ohms. External capacitors may be added to any or all mesh points if the need arises. The values of electrical resistance and capacitance are adjusted manually by manipulating the two types of decade units. INPUT EQUIPMENT A considerable quantity of equipment is used to control the input to the RC network. TABLE 1 - CORRESPONDENCE BETWEEN FLUID AND ELECTRICAL SYSTEMS Fluid System Electrical System Item Units Item UnitsReservoir Pressure psi Voltage Volts Reservoir Production Reservoir B/D Current MicroamperesRate orInjectionRate Fluid Capacitance Reservoir bbl/psi Electrical MicrofaradsCapacitance Transmissibility, darcy-ft Electrical Mhos/cp Conductivity Real Time Months Model Time Seconds JPT P. 1275^
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.