Matching the Performance of Saudi Arabian Oil Fields With an Electrical Model
Authors: Wahl W.L. , Mullins L.D. , Barham R.H. , Bartlett W.R. 
Published: December 2007

Abstract
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
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