Reservoir engineers benefit from a good understanding of reservoir simulation. While most engineers rely on commercial software packages for the calculations, it can be impossible to evaluate the validity of results without a solid foundation in the underlying principles. Basic Applied Reservoir Simulation provides comprehensive coverage of simulation. It begins with the fundamentals of numerical simulation, moving to field applications and more complex topics. Each chapter includes a project section that relates to the implementation of the topics discussed in that chapter. Includes 157 solved examples and 178 exercises.

A mathematical description of non-Newtonian fluids, in particular, emulsions, is of special importance now that most of the enhanced oil recovery methods are being modelled in increasing detail. Only recently a few characteristics of emulsion flow have been incorporated in some of the simulators. Nearly all enhanced oil recovery processes involve emulsion formation and flow in some form or other. Representation of such flow in mathematical models is still inadequate. This paper investigates the rheology of emulsions, their formation in porous media, and subsequent flow, from a mathematical standpoint A critical evaluation of several models describing the flow of pseudoplastic fluids in porous media is presented. The models are expressed in a unified form that makes it possible to detect differences between the various models. The assumptions underlying the various models are discussed in detail. Furthermore, the paper gives a summary of the rheology and in situ formation of emulsions, the role of a variety of other factors responsible for emulsification in porous media, and it introduces a flow model for both Newtonian and non-Newtonian emulsions that is practical, and especially suitable for use in numerical simulation of EOR processes. Introduction Two-thirds or the world's crude oil and three-quarters of the U.S. crude oil is produced in an emulsion form(1,3). Emulsified oil is produced from oil/tar sands undergoing thermal recovery. New methods of secondary recovery that use high viscosity emulsions have been developed(2.4). Filtration of water using porous material also involves dilute concentrations of dispersed oil in water(4,5). These factors and others(6,7) have promoted interest in research related to the now behaviour of non-Newtonian fluids in porous media fur a quarter of a century. The fact that nearly all enhanced oil recovery methods involve emulsion formation and flow coupled with the wide-spread acceptance of reservoir simulation as a valuable tool in the development and optimization of oil recovery from petroleum reservoirs, have contributed to incorporating a few characteristics of emulsion flow in a number of simulators. Mathematical modelling of emulsion flow in porous media calls for the understanding of the rheology of emulsions and the formation of emulsion in oil reservoirs. Emulsion flow in porous media can be modelled through non-Newtonian rheology. as discussed in this paper. A more comprehensive approach would require phase behaviour of the emulsion system and drop size distribution to account for mobility changes in response to drop entrapment. Nature and Rheology of Emulsions An emulsion is a dispersion of one liquid (internal or dispensed phase) with another (external or continuous phase) in the presence of surface -active agents (emulsifiers) (8). The volume fraction of the dispersed phase is called emulsion quality, θ. The emulsion consists of an oil-soluble portion and water-soluble portion. By virtue of its special structure the emulsifier aids in reducing the interfacial tension between the two liquids involved enabling an easier formation of an extended interface and in preventing the coalescence of the dispersed particles once emulsion is formed. There are two types of emulsion water-in-oil (W/O) and oil-in-water (O/W) emulsions.

The computation of flowing-well bottomhole pressure from the pressure of the block containing the well or of well flow rate when the flowing bottomhole pressure is specified are important considerations in reservoir simulation. While this problem has been addressed by several authors, some important aspects of the problem are not treated adequately in the literature.We present an analytical method for computing the wellblock factors (constants of the PI) for a well located anywhere in a square or rectangular block (aspect ratio between V2 and 2). Equations for well geometric factors and well fraction constants are given for gridblocks of various types, contairiing a single well, encountered in reservoir simulation studies. The equations given in this paper can be used for both block-centered and pointdistributed grids in five-and nine-point two-dimensional (2D) , finite-difference formulations. The radial flow assumption used in deriving the equations in this paper is not always strictly valid; however, for most practical situations it provides an adequate approximation for nearwell flow. IntroductionHandling of wells in reservoir simulators presents several difficulties that require special considerations. These difficulties generally can be divided into two classes.1. Problems arise because the block size usually is large compared to the size of the well, and hence the pressure of the block computed by the reservoir simulator is not a good approximation for the well pressure.2. Problems can be caused by the complex interaction (coupling) between the reservoir and the wellbore in both injection and production wells.Some aspects of this second problem are discussed by Settari and Aziz I and Williamson and Chappelear, 2,3 and other important aspects remain unresolved. This paper, however, deals with only the first problem-the problem of relating well-block pressure in the finite-difference model to the well pressure. The discussion is further restricted to single-phase 2D areal models, without any direct consideration of three-dimensional (3D) and crosssectional flow problems. In the absence of more accurate models, well factors derived from single-phase flow considerations may be used even when two-or three-phase flow exists near the well.

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