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Numerical investigations on compressible non-linear fluid flow associated with a stress -sensitive fractured reservoir


Abstract: This paper emphasizes on the development of an improved mathematical model to understand the single-phase gas flow in a coupled matrix-fracture fluid mass exchange in a stress-sensitive reservoir a...
Topics: Fluid dynamics (61%), Flow (mathematics) (53%)
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Ren-Shi Nie1, Fan Xiaohui1, Min Li1, Zhangxin Chen2  +4 moreInstitutions (3)
Abstract: Transient flow of geofluids caused by a well production in a subsurface formation is a phenomenon of enormous importance in hydrology, geosciences and engineering. Geofluid transient flow has been proved to be a nonlinear physical process dominated by QPG (quadratic pressure gradient). Much research has indicated that neglecting a QPG term in flow models by assuming small pressure gradients can cause significant errors in predicted pressures. Despite the existence and importance of QPG, limited research on nonlinear QPG models has been performed when compared with the traditional linear flow models. On the basis of the previous linear and nonlinear QPG models, a comprehensive geofluid flow model for a well in a subsurface formation was established and solved. A general solution method for this model and its general solutions were obtained for vertical and horizontal wells in ordinary, fractured and fractured-vuggy formations. Next, flow regimes and typical transient flow characteristics were thoroughly analyzed by using a series of standard type curves. Then, the differences in type curves between linear and nonlinear QPG models were qualitatively and quantitatively studied. Afterwards, model validations and production predictions were performed. This comprehensive model contained various specific modeling situations. Some modeling situations that were reported in the previous studies were well-reviewed in this paper. The other previously unreported modelling situations were firstly studied and exhibited in this paper. At the end, the existing problems pending to be solved were put forward and future work on nonlinear QPG models was suggested. This paper is very helpful in understanding the QPG-dominated transient flow behavior more profoundly.

2 citations


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Journal ArticleDOI
Abstract: An idealized model has been developed for the purpose of studying the characteristic behavioroja permeable medium which contains regions which contribute sigizificantly to tbe pore volume O! the system but contribute negligibly to the flow capacity; e.g., a naturally fractured or vugular reservoir, Vnsteady-state flow in this model reservoir has been investigated analytically. The pressure buiid-up performance has been examined insomedetait; and, a technique foranalyzing tbebuild.up data to evaluate the desired parameters has been suggested. The use of this ap$roacb in the interpretation of field data has been discussed. As a result of this study, the following general conclusions can be drawn: 1. Two parameters are sufficient to characterize the deviation of the behavior of a medium with “double porosity ”from that of a homogeneously porous medium. 2. These Parameters can be evaluated by the proper analy~is of pressure buildup data ob~ained from adequately designed tests. 3. Since the build-up curve associated with this type of porous system is similar to that obtained from a stratified reservoir, an unambiguous interpretation is not possible without additional information. 4, Dif@rencing methods which utilize pressure data from the /inal stages of a buik-kp test should be used with extreme caution. INTRODUCTION In order to plan a sound exploitation program or a successful secondary-recovery pro ject, sufficient reliable information concerning the nature of the reservoir-fluid system must be available. Sincef it is evident chat an adequate description of the reservoir rock is necessary if this condition is to be fulfilled, the present investigation was undertaken for the purpose of improving the fluid-flow characterization, based on normally available data, ofs particular porous medium. DISCUSSION OF THE PROBLEM For many years it was widely assumed that, for the purpose of making engineering studies, two psram. . -. . Origlml manuscriptreceived fn eociaty of Petroleum Ertatneere offiae AUS. 17, 1962.Revieed manuscriptreceived.March21, 1963. P eper pr+$eented at the Fetl Meeting of the %ciot Y of. Petreleum Enginsera In Lo= Ar@Ies on Oct. 7-10, 1962. ‘ . GULF RESEARCH d DEVELOPMENT CO. PITTSBURGH, PA, eters were sufficient to desckibe the single-phase flow properties of a prodttcing formation, i.e., the absolute permeability and the effective porosity. It : later became evident that the concept of directional permeability was of more thin academic interest; consequently, the de$ee of permeability anisotropy and the orientation of the principal axes of permeability were accepted as basic parameters governing reservoir performance. 1,2 More recently, 3“6 it was recognized that at least one additional parameter was required to depict the behavior of a porous system containing region,s which contributed significantly to the pore volume but contributed negligibly to the flow capacity. Microscopically, these regions could be “dead-end” or “storage” pores or, microscopically, they could be discrete volumes of lowpermeability inatrix rock combined with natural fissures in a reservoir. It is obvious thst some provision for the ;.ncIusion of all the indicated parameters, as weIl as their spatial vstiations$ must be made if a truly useful, conceptual model of a reaetvoir is to be developed. A dichotomy Qf the internaI voids of reservoir rocks has been suggested, r~s These two classes of porosity can be described as follows: a. Primary porosity is intergranular and controlled by deposition and Iithification. It ie highly intercoririected arid “usually can be correlated with permeability since it is largely dependent on the geometry, size distribution and spatial distribution of the grains. The void systems of sands, sandstones and oolitic limestones are typical of this type. b. Secondary porosity is foramenular and is controlled by fracturing, jointing and/or solution in circulating water although it may be modified by infilling as a result of precipitation. It is not highly interconnected and usually cannot be correlated with permeability. Solution channels or vugular voids developed during weathering or buriaI in sedimentary basins are indigenous to carbonate rocks such as limestones or dolomites. Joints or fissures which occur in massive, extensive formations composed of shale, siltstone, schist, limestone or dolomite are generally vertical, and they are ascribed to tensional failure, during mechanical deformation (the permeability associated with this type of void system is often anisotropic). Shrinkage cracks are the result 1 ~ef&ence. aiven atendof p@er. ‘-

3,065 citations


Journal ArticleDOI

2,286 citations


"Numerical investigations on compres..." refers background in this paper

  • ...Barenblatt, Zheltov, and Kochina (1960) introduced the dual-continuum formulation for the first time....

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Book
15 Mar 2000-
Abstract: Fundamentals of Reservoir Fluid Behavior Reservoir-Fluid Properties Laboratory Analysis of Reservoir Fluids Fundamentals of Rock Properties Relative Permeability Concepts Fundamentals of Reservoir Fluid Flow Oil Well Performance Gas Well Performance Gas and Water Coning Water Influx Oil Recovery Mechanisms and the Material Balance Equation Predicting Oil Reservoir Performance Gas Reservoirs Principles of Waterflooding Vapor-Liquid Phase Equilibria Decline and Type Curve Analysis Index

903 citations


"Numerical investigations on compres..." refers background in this paper

  • ...Around 60% of the world’s proven oil reserves and nearly 40% of the world’s gas reserves are trapped in naturally fractured carbonate reservoirs as against the conventional sandstone reservoirs (Ahmed 2010)....

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Journal ArticleDOI

560 citations


"Numerical investigations on compres..." refers background or methods in this paper

  • ...Kazemi (1969) developed a numerical model to understand the transient nature of the fluid mass exchange between the rock-matrix and fracture....

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  • ...The flow mass exchange from the rock-matrix to fracture was analyzed by a pseudo-steady state coupling term, which is a function of the difference between the average pressure in the rock-matrix and average pressure in the fracture (Kazemi 1969)....

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Journal ArticleDOI

460 citations


"Numerical investigations on compres..." refers methods in this paper

  • ...(26) The gas viscosity is calculated using the correlation given by (Lee, Gonzalez, and Eakin 1966) In Eq....

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