Matching the Performance of Saudi Arabian Oil Fields with an Electrical Model
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Matching the Performance of Saudi Arabian Oil Fields With an Electrical Model W. L. WAHL L. D. MULLINS SOCONY MOBIL OIL CO., INC. R. H. BARHAM DALLAS, TEX. MEMBERS AIME W. R. BARTlETT ARABIAN AMERICAN OIL CO. MEMBER AIME DHAHRAN, SAUDI ARABIA ABSTRACT devices, output devices, central control and a resistance Downloaded from http://onepetro.org/JPT/article-pdf/14/11/1275/2214599/spe-414-pa.pdf by guest on 02 October 2021 capacitance (RC) network. At times, the RC network This paper describes an electrical model and its appli alone is referred to as the "model". However, it should be cation to the analysis of four reservoirs in Saudi Arabia. evident from the text which meaning is attached to the The model has 2,501 mesh points and represents 35,000 word "model". A discussion of the equipment follows. sq miles of the Arab-D member. Details of modeling such as mesh size, control problems and standards of perfor THE RESISTANCE·CAPACITANCE NETWORK mance in matching reservoir history are discussed. The The RC network consists of 2,501 capacitance decades particular performance match achieved for the Arab-D interconnected through 4,900 resistance decades. The com member is presented. Details such as permeability barriers, ponents are arranged to form a rectangular network of aquifer depletion and interference between oil fields are 2,501 mesh points in a 41- X 61-mesh array. Imposing given. The performance match realized in the Abqaiq the mesh grid system on the continuous reservoir system pool is presented in detail. divides the reservoir into discrete areal segments. These discrete segments may be of various sizes. More precisely, INTRODUCTION the mesh size need not be uniform throughout the model. The resistor-capacitor network and associated control The RC network is fabricated in two sections which equipment described in this paper comprise an electrical are connected at the top. An inside view of the "tunnel" analog of a reservoir system. Similar equipment has been formed by the two sections is shown in Fig. 1. The height used to study the transient response of reservoirs for many and width of the tunnel are shown in the figure. Numerals years. The unique feature of the model and application appear along the bottom and along the back opening of to be described is the extremely large size of the model the tunnel. These numbers denote the x and yeo-ordinate and reservoir system, and the detail observed in simulating positions of mesh points. Fig. 2 presents a rear view of the reservoir with the model. one-half the model. The length dimensions of the model, as well as a rear view of the capacitor decades, are shown The Arabian American Oil Co. first became interested in this figure. The control dials used in adjusting the resist in analog computers for simulation of oil reservoirs in ance and capacitance values on the model can be seen 1949. Since that time, several models have been developed, in the enlarged portion of the model shown in Fig. 3. each more elaborate and refined so that the reservoir sys tem might be more closely simulated. The current model The electrical capacity at any mesh point can range is the latest in a series designed, built and operated by from 0 to 1.0 microfarads set to the nearest tenth of a the Field Research Laboratory of Socony Mobil Oil Co. microfarad. The electric resistance connecting any two in collaboration with Aramco. It has been and continues mesh points can range from 0 to 9,990,000 ohms set to to be used to study the regional performance of the the nearest 1,000 ohms. External capacitors may be added Arab-D member limestone reservoir. The Arab-D member to any or all mesh points if the need arises. The values of is one of the Middle East's most prolific producing hori electrical resistance and capacitance are adjusted manually zons .. by manipUlating the two types of decade units. INPUT EQUIPMENT THE MODEL A considerable quantity of equipment is used to control The theory of simulating a reservoir system with an the input to the RC network. These input devices are electrical system has been presented in the literature.'-5 Therefore, this paper will not discuss the theoretical as TABLE l-CORRESPONDENCE BETWEEN flUID AND ELECTRICAL SYSTEMS pect of the problem except to point out the correspondence Fluid System Electrical System between the fluid system and electrical system, as shown Item Units Item 'Units in Table 1. Reservoir Pressure psi Voltage Volts In general, the complete model is made up of input Reservoir Production Reservoir BID Current Microamperes Rate or I niection Rate Original manuscript received in Society of Petroleum Engineers office Fluid Capacitance :Reservoir bbl/psi EI&etrical Microfarads July 10, 1962. Revised manuscript received Oct. 3, 1962. Paper pre Capacitance sented at 37th Annual Fall Meeting of SPE held Oct. 7-10, 1962, in Transmissibility kh/ f.L. darcy·1t Electrical Mhos Los Angeles, Calif. /cp Conductivity 'References given at end of paper. SPE 414 Real Time Months Model Time Seconds NOVEMBER, 1962 1275 necessary to control currents which are the analog of well from the memory unit to a time-dependent rate controller. production rates. For simplicity, the input equipment em It appears here as a step function of voltage to control ployed will be discussed briefly according to type. the current withdrawn from (or supplied to) a mesh point of the model. Upon completion of the data transfer Programmed Time-Dependent Rate Controllers from the memory unit to the controller, another card is read. The new rate is again stored in the memory unit for Controllers of this type are used primarily during the use at the next command from central control. history portion of a reservoir study. They generate step Fig. 4 shows 34 of the time-dependent rate controllers functions of current vs time from a predetermined pro (left side of the relay rack) together with 34 memory gram. Each 2.5 seconds (the basic model time interval), units (right side of rack). Also shown is an IBM repro a new rate can be generated. These rates are proportional ducer used to read the cards. A total of 102 time-depend to the average well production or injection rates for the ent controllers is available for use with the model. All period of time (weeks, months, etc.) equivalent to the can be used as either production or injection controllers. 2.5-second interval. The rate of production (or injection) for a particular Pressure-Dependent Rate Controllers well or group of wells is punched into IBM cards. Upon command from central control, * a card is read by an A relay rack containing 126 pressure-dependent rate IBM reproducer and the digital information is stored in controllers can be seen at the end of the "tunnel" shown a memory unit. Two and one-half seconds later (upon in Fig. 1. Of this number, 108 can be used only as production-rate controllers, while the remaining 18 can command from central control), the rate is transferred Downloaded from http://onepetro.org/JPT/article-pdf/14/11/1275/2214599/spe-414-pa.pdf by guest on 02 October 2021 be used as either production or injection controllers. «The central-control equipment is discussed later. For this type of controller, the current withdrawn (or injected) is a linear function of the voltage at a mesh point on the RC network. A variable resistor is placed between the mesh point and a point of zero potential. FIG. 3- O:-lTR0L DIALS U E:D IN ADJUSTING RE [STANCl: AND APA ITANCf; VALUE ON THE 10nEL. FIG. 4--TIME-DEPENDENT RATE CONTROLLERS AND MEMORY U NITS LOCATED ON THE RELAY RACK (LEFT), AND IBM REPRODUCER FIG. 2-REAR VIEW OF THE MODEL. U SED TO READ CARDS (RIGHT). 1276 JOURNAL OF PETROLEUM TECHNOLOGY Thus, as the voltage difference between the two points of a digital computer. The digital computer is programmed decreases, the current through the resistor decreases. The to convert the coded data in the cards to pressure, pro resistor value determines the slope of a graph of current duction rates and injection rates. These pressures, pro vs voltage difference. Also incorporated in the pressure duction rates, etc., may then be tabulated from the digi dependent controllers is a device whereby the intercept tal-computer output. of the afore-mentioned graph can be made greater than or less than zero. CENTRAL CONTROL This type of controller is very useful when predicting future reservoir performance. In such cases, the produc The central control (see Fig. 6) is the "brain" of the tion rates of existing and proposed wells can be described analog computer. It is here that the very accurate 2.5- by linear functions of static reservoir pressure. This func second time period is generated. During the first few mil tional relationship between production rate and static res liseconds of each time period, central control issues a ervoir pressure is represented and generated by the pres chain of commands to cemrol the "read-in" and "read sure-dependent controller. out" equipment. The read-in circuits are interlocked in such a way that most equipment malfunctions will be detected and the computer stopped. To provide further Constant-Rate Controllers observation of computer performance or reproducibility, Constant-rate controllers are practically self-explanatory. two additional potentiometers are used to monitor the The production or injection rate is constant with time total net current being withdrawn from the model. Any deviation from the regular curve drawn by these poten and independent of the voltage at a mesh point.