Summary In 1962, Vogel proposed an empirical inflow performance relationship (IPR) for solution-gas drive reservoirs based on numerical simulation results. This relationship isEquation and was based on a wide range of rock and fluid properties. This generalized relationship gained almost immediate acceptance in the industry due to its relative ease of use and because it gave reasonable engineering accuracy. This paper presents a theoretical basis for Vogel's IPR based on the physical nature of the multiphase flow system. The resulting analytical IPR follows from a Taylor series expansion of the multiphase flow equations and is verified by computer simulation results. Introduction Predicting the performance of individual oil wells is an important responsibility of the petroleum engineer. Estimates of well performance allow the engineer to determine the optimum production scheme, design production and artificial lift equipment, design stimulation treatments and forecast production for planning purposes. Each of these activities is integral to the efficient operation of producing wells and successful reservoir management. When estimating oilwell performance, engineers often assume that fluid inflow is proportional to the difference between reservoir pressure and wellbore pressure, One of the first relationships to be used based on this assumption was the Productivity Index (PI). This straight-line relationship is derived from Darcy's law for the steady-state incompressible flow of a single-phase fluid and is the ratio of the producing rate to the pressure difference. In equation form, the PI is defined byEquation 1 However, Evinger and Muskat1 pointed out that a straightline relationship should not be expected when two phases, oil and gas, are flowing in the reservoir. They presented theoretical calculations that showed a curved relationship between flow rate and pressure. Their method, however, did not gain wide acceptance by petroleum engineers since it required extensive knowledge of rock and fluid properties. Vogel2 later developed an empirical inflow performance relationship (IPR) for solution-gas drive reservoirs that accounted for the flow of two phases, oil and gas, in the reservoir based on computer simulation results. The resulting IPR equation isEquation 2 Vogel's relationship gained almost immediate use within the industry due to its simplicity and accuracy. The method, which required knowledge only of a single flow rate, flowing wellbore pressure and average reservoir pressure, was easy to use and gave good approximations of the pressure-production behavior of an oil well over a wide range of operating conditions.
A rigorous interporosity flow equation incorporating a time-dependent shape factor is derived and validated for improved dual-porosity modeling of naturally fractured gas-condensate reservoirs. The equation expresses theinterporosity molar rate in terms of the pseudo-pressure gradient in thematrix, fracture surface area, matrix permeability, and a variable matrix-blockshape factor. This approach can accommodate the flow directed from matrix tofractures in a simulator that represents the permeability of the interconnected fractures by a tensor inside each grid-block. This feature distinguishes thismodel from the popular sugar-cube approach to modeling naturally fracturedreservoirs. Compositional simulation is performed to verify the flow equation using thetime-dependent shape factor. Numerical experiments with various matrix-blocksizes indicate that the shape factor varies with time but converges to values derived by Lim and Aziz (1995). The average matrix-pressure location in the matrix block shifts from near the fracture face to the block center as thefluid flows from the matrix into the fracture. This phenomenon indicates that neglecting the time dependency of the shape factor can introduce significant errors in numerical simulation of naturally fractured reservoirs. The time dependency can contribute significantly to fluid production once the pressure front moves through the reservoir along the highly permeable fracture network.This phenomenon is not considered in present commercial simulators that usepseudo-steady state factors. The model equations are expressed in dimensionless form so they can bereadily integrated into current simulators. The dimensionless time used in the proposed method includes pseudo-functions that capture multiphase effects ofthe gas-condensate systems. Applications to single- and multiphase black-oils ystems are also discussed. Introduction Numerical simulation of naturally fractured reservoirs has received significant attention and its application has increased in recent years withthe advent of highly efficient computers. Much of the research on naturally fractured reservoir modeling has focused on accurately representing thematrix-fracture fluid transfers. Various mechanisms, including gravity andcapillary effects,1–3 reinfiltration and capillary continuity of the matrix blocks,4–7 and cocurrent/counter current imbibition phenomena,8–10 have been extensively investigated. However, in spiteof the great level of current model sophistication, the highly anisotropic andheterogeneous nature of a fractured formation makes fractured reservoir modeling a challenging task, frequently with uncertain results inforecasting. Typically, numerical simulation of naturally fractured reservoirs assumesthere are two continua, matrix and fractures, within each grid-block. The flow equations are written for each system with a matrix/fracture transfer function to relate the loss or gain of matrix fluids to or from the fracture. For single-phase fluid flowing through an interconnected fracture system, thefollowing governing equation applies: Equation 1 where the fluid transfer rate per unit volume of rock, q, is commonly calculated as a function of the pressure difference between the matrix and fracture systems, matrix flow capacity and matrix geometry considered through aconstant shape factor.
TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractIn recent years, a technique of separating water downhole to reduce the volume of produced water and decrease the chance of surface pollution has been developed. It is called downhole oil-water separation (DOWS) technology. This technique allows water to be separated in the wellbore and injected into a suitable injection zone downhole while oil with traces of water is produced to the surface.Subsequent to the introduction of the DOWS technology to the oil industry in the 1990's, several trial applications have been undertaken to test the technology. These trials allowed significant information to be collected on the feasibility of the DOWS technology. Through the joint efforts of Argonne National Laboratory, CH2M-Hill, and the Nebraska Oil and Gas Conservation Commission, a comprehensive technical report was issued in January 1999 discussing this technology. Additional reports on trial applications and feasibility studies have been presented by various study groups.This paper reviews the status of and issues surrounding the application of downhole separation technology. This review summarizes the various papers and reports dealing with DOWS technology and its application in the oil and gas industry. This technology has the potential to provide significant reductions in produced water as the technology is adopted by the industry. It can also reduce produced water handling costs and increase oil and gas production in the right application. The wide-spread adoption of DOWS technology is dependent on improving the understanding of the process and its applications throughout the oil and gas industry.
Many petroleum reservoirs are not developed and produced properly. This failure can be the result of poor reservoir operations management. An understanding of reservoir management and its elements is needed to effectively exploit petroleum reservoirs. This paper defines reservoir management and proposes a comprehensive, integrated approach to the management of reservoir operations. The paper does not address the many technical details of reservoir management, nor does it give detailed recommendations for particular operations. It presents a method and approach to making these decisions for any reservoir. Its purpose is to communicate the importance of reservoir management and to present an approach for the development of a reservoir management plan. Introduction The petroleum industry has progressed from an early period of unrestrained production, through a period of maximum production regulated by government constraint into a period of declining production where companies plan to maximize profits based on the current management environment. Thc industry has now moved into a period of challenge. Industry must accept the challenge that a significant amount of oil and gas will remain unrecovered unless improvements are made in reservoir management practices. Petroleum reservoir management is an area that has generated significant discussion within the industry in recent years as reserves have declined, prices have fluctuated and companies have begun to realize the necessity for comprehensive planning in reservoir development. A review of the literature suggests that there are varying conceptions of what reservoir management is and what it involves as evidenced by just a few references. A thorough understanding of the petroleum reservoir management process is important to the proper development and exploitation of oil and process is important to the proper development and exploitation of oil and gas reserves. This paper will define reservoir management, discuss its process and recommend the use of a written reservoir management plan. process and recommend the use of a written reservoir management plan. RESERVOIR MANAGEMENT Petroleum reservoir management is the application of state-of-the-art technology to a known reservoir system within a given management environment. Reservoir management can be thought of as that set of operations and decisions by which a reservoir is identified, measured, produced, developed, monitored and evaluated from its discovery through produced, developed, monitored and evaluated from its discovery through depletion and final abandonment. Figure 1 summarizes the concept of reservoir management A reservoir is managed for a particular purpose and that purpose is accomplished within the management environment using the available tools and technology. Elements of Reservoir Management Reservoir management is not simply the creation of a depletion plan and/or a development plan but rather a comprehensive, integrated strategy for reservoir exploitation. Management is comprehensive in that it requires the three primary components of reservoir management; 1) knowledge about the entity being managed, 2) the management environment, and 3) the available technology. When these three components are integrated, decisions can be made and a strategy developed for achieving management goals. Without an understanding of these components, effective management cannot take place and a comprehensive strategy for achieving management goals will not be developed. Reservoir Knowledge. Knowledge of the system being managed has several dimensions. First is the general nature of the system. A petroleum reservoir is an accumulation of hydrocarbons trapped within a petroleum reservoir is an accumulation of hydrocarbons trapped within a single hydrodynamically-connected geological environment. This general knowledge includes an understanding of fluid movement, rock properties, phase behavior and other basic knowledge. phase behavior and other basic knowledge. P. 327
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