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F.A. Sobbi

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Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Annual Technical Meeting, June 6–8, 1995

Paper Number: PETSOC-95-12

Abstract

Abstract An analytical composite model using non-linear least square regression technique for estimation of real parameters of naturally fractured reservoirs, utilizing well test data is presented. The problem of alteration of fracture properties due to acidizing or damage called by drilling fluid is taken into account by introducing two concentric media of different fractures. In this work correlations amongst fracture permeability and porosity, ω, λ, skin factor and matrix block size together with field examples are also presented. Introduction The double porosity models presented by Barenblatt et al l and many others 2–4 treat naturally fractured reservoirs by superimposing two continua, One for the fracture system and another for the porous matrix. The flow of fluid in the fracture system toward the wellbore is assumed to be radial. This holds only for infinisimal matrix block dimensions. For real cases where the matrix blocks are of finite dimensions, several fee~ the flow in the fractures near the wellbore is linear. It has been shown 5 that the pressure drop in the fractures with linear flow is less than the pressure drop caused by a radial system with a bulk permeability identical to that of the fractures. This is why the analysis of well test data obtained from naturally fractured reservoirs usually show negative skins by semilog analysis. The flow behavior of a two dimensional fracture network with nonporous identical parallelepiped matrix blocks under steady state conditions 5 has shown that the negative skin is proportional to the logarithmic of the matrix block size and the flow system starts exhibiting radial flow behavior from a radial distance of one matrix block from the wellbore. Drilling and workover operations may alter the width of the fractures around the wellbore resulting in two damaged and undamaged zones. The damage zone may be assumed circular and the fractures in this zone of uniform thickness. In order to study the behaviour of the flow system with the above mentioned features a composite model consisting of three regions is considered. Composite systems have been the subject of considerable attention in the petroleum literature. In general, the composite model consists of a well completed in the centre of a circular inner region with fluid and rock properties different from those in an outer region. This approach has been used to study interference between oil fields in a common aquifer of different permeabilities6. A two region composite model has been used to study the behavior of wells intersected by fractures extending over a limited area 7 , It also has been used to study the behavior of wells intersected by infinite conductivity vertical fracture in dual porosity reservoirs 8 . In this work a general flow equation for a composite system consisting of three (inner, intermediate and outer) regions is presented to describe the near wellbore linear flow and the outer radial flow in the two damaged and undamaged regions.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Annual Technical Meeting, June 11–14, 1994

Paper Number: PETSOC-94-16

Abstract

Abstract The reservoir parameters obtained from any transient pressure analysis, reflect average values of the characteristics of the area around the well that has experienced a pressure disturbance due to the change of flow rate at the wellbore. This area is described by an associated radius called the radius of investigation. In the authors&apos; knowledge, no work has been done to examine this radius in fractured or dual porosity reservoirs. This paper describes a new equation for evaluation of the radius of investigation for well tests in such reservoirs under pseudosteady state interporosity flow regime. The results have shown that the radius of investigation in such reservoirs starts increasing in the fracture network proportional to the square root of the fracture conductivity. When the matrix contribution to the flow of fluids starts the rate of advance of the radius decreases until its magnitude reaches a maximum value and remains constant until the total system stabilizes. After this time the radius increases again with a lower rate dependent now on the total system conductivity. Introduction The radius of investigation also called the radius of influence or radius of drainage is defined in many ways by several authors 1,2,3.4.5,6 . In most definitions this radius determines a circular system with a pseudo-steady state pressure istribution around the wellbore, and takes the form as follows: Equation (1) Available In Full Paper where A is a constant and r inv is the radius of investigation. If the start of semi-steady state flow for a homogeneous and symmetrical bounded cylindrical reservoir at a time t De of 0.3 is used, and the parameters are defined in oil field units where, r inv is in feet, t is the time of flowing for a drawdown test or the time of shut-in when Δtp for a buildup test in hrs., K is the formation permeability in mds, φ is the reservoir porosity in fraction and c is the total system compressibility in psi −1 , the constant A becomes 0.029. Odeh and Nabor 7 , by using an RC analyzer obtained A to be 0.0257, and Kazemi 8 from the numerical finite difference solution obtained it to be 0.035. Hurst et al 3 , Van Poolen 5 and Slider 9 separately used the concept of unsteady state radial flow to find out when to switch from infinite acting solution to finite solution of the homogeneous diffusivity equation. By taking the derivative of the difference between the above solutions with respect to time and putting it equal to zero the flowing equation for radius of investigation will be obtained: Equation (2) Available In Full Paper Matthews and Russell 10 picked a time t De of 0.25 intermediate to the two times corresponding to the end of infinite acting and the start of semi-steady state, and obtained the same Eq.2. Muskat 1 , Chatas 11 and Craft and Hawkins 12 by equating the volume of the fluid produced to the expansion of the fluid contained in the drainage area and by considering steady state conditions also obtained the same Eq. 2 for r inv . Note: The paper is missing text between pages 4 and 5. This is the version included in the proceedings. It is priced free of charge.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Annual Technical Meeting, June 11–14, 1994

Paper Number: PETSOC-94-02

Abstract

Abstract An Iranian Asmari reservoir with an initial oil-in-place of about 381 millions m 3 (2.4 billion bbls) and a history of18 years of oil production is studied in this work. The field is a typical Iranian fractured carbonate oil reservoir which has a matrix rock of poor quality and a highly permeable fracture network. The subject of the study was to simulate the reservoir flow performance with an elaborated two-dimensional vertical model capable of simulating nonconventional producing mechanisms such as gravity drainage and block to block interaction. After successful proving of the model capability by reservoir production history the model was used to predict the reservoir behaviour under natural depletion, and to evaluate two ases of pressure maintenance by gas injection. Results showed that in both cases of pressure maintenance, an ultimate additional oil production of about 150 million bbls will be achieved over natural depletion. This additional oil production corresponds to an increase of approximately 6 % of original oil in place. Introduction The oil reservoir under study is an elongated NW-SE anticline symmetrical along its minor axis located in southwest of Iran. The structure plunge to the southeast is more gentle than to the northwest. The productive area is 195 kilometres long and 7.75 kilometres wide at the original WOC located at 1890 meters subsea. Heavy mud losses during drilling, production tests, and good pressure communication between the wells indicate the existence of an active fracture system. The original reservoir pressure at a depth of 1600 loss, was measured to be 210.7 bars about 57 bars above saturation pressure. Commercial oil production commenced in 1973 at a rate of 3100 m 3 /day. The rate was then successively increased as more wells were drilled in the field. During the early time of the field production, a relatively fast pressure drop as shown in Fig. 1 was encountered which is characteristic of an undersaturated reservoir. In 1978 the pressure at the crest had been dropped below the bubble point pressure ausing the liberation of solution gas and the formation of a secondary gas cap. The field was closed-in from 1979 to 1984 during which 0.2 billion m 3 of gas had been injected intermittently. During this period the average reservoir pressure was increased by 20 bars approximately. Then the production started at a rate of 6000–6500 m 3 /D with a gas injection rate of 1.4 million m 3 /D continuously. From 1986 the amount of injected gas was insufficient to maintain the reservoir pressure, therefore the reservoir pressure was lightly declined. Fig. 2 depicts the trend of pressure and the reservoir production history. The producing mechanisms in the fractured reservoirs of Iranian type are substantially different from those in conventional homogeneous reservoirs. Therefore to study their performance special mathematical model should be used. In this study It will be shown that the two-dimensional fractured reservoir model "STACKED BLOCK MODEL" which describes the reservoir as a series of stack of interacting blocks, surrounded by fracture space, can be successfully applied to simulate the performance of the reservoir.