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Techniques described in this page are classic methods for describing immiscible displacement assuming equilibrium between injected gas and displaced oil phases while accounting for differing physical characteristics of the fluids, the effects of reservoir heterogeneities, and injection/production well configurations. Included are modifications to typical displacement equations, evaluating sweep efficiency, and calculating performance. In simple calculations, the reservoir is treated in terms of average properties for volume of rock, and production performance is described on the basis of an average well. Black-oil-type reservoir simulation models use essentially these same techniques but, by means of 1D, 2D, or 3D cell arrays, account for areal and vertical variations in rock and fluid properties, well-to-well gravity effects, and individual well characteristics. More complex compositional models account for nonequilibrium conditions between injected and displaced fluids and can be used to describe individual well streams in terms of the compositions of the produced fluids.
This page discusses various aspects of gas reservoir performance, primarily to determine initial gas in place and how much is recoverable. The equations developed can used to form the basis of forecasting future production rates by capturing the relationship between cumulative fluid production and average reservoir pressure. Material-balance equations provide a relationship between original fluids in place, cumulative fluid production, and average reservoir pressure. This equation is the basis for the p/z-vs.-Gp Reservoir engineers have often used pressure contour maps or some approximate methods to determine field average reservoir pressure for p/z analysis. Usually, however, individual well pressures are based on extrapolation of pressure buildup tests or from long shut-in periods. In either case, the average pressure measured does not represent a point value, but rather is the average value within the well's effective drainage volume (see Estimating drainage shapes).
This page discusses the primary manner in which the immiscible gas/oil displacement process has been used in qualitative terms. This is the use of gas injection high on structure to displace oil downdip toward the production wells that are completed low in the oil column. In many cases, an original gas cap was present, so the gas was injected into that gas cap interval (see Figure 1 for cross-sectional view of anticlinal reservoir with gas cap over oil column with dip angle α and thickness h). In this situation, the force of gravity is at work, trying to stabilize the downward gas/oil displacement process by keeping the gas on top of the oil and counteracting the unstable gas/oil viscous displacement process. If the oil production rate is kept below the critical rate, then the gas/oil contact (GOC) will move downward at a uniform rate.
The Merriam-Webster Dictionary defines simulate as assuming the appearance of without the reality. Simulation of petroleum reservoir performance refers to the construction and operation of a model whose behavior assumes the appearance of actual reservoir behavior. The model itself is either physical (for example, a laboratory sandpack) or mathematical. A mathematical model is a set of equations that, subject to certain assumptions, describes the physical processes active in the reservoir. Although the model itself obviously lacks the reality of the reservoir, the behavior of a valid model simulates--assumes the appearance of--the actual reservoir. The purpose of simulation is estimation of field performance (e.g., oil recovery) under one or more producing schemes. Whereas the field can be produced only once, at considerable expense, a model can be produced or run many times at low expense over a short period of time. Observation of model results that represent different producing ...
Reservoir simulation is a widely used tool for making decisions on the development of new fields, the location of infill wells, and the implementation of enhanced recovery projects. It is the focal point of an integrated effort of geosciences, petrophysics, reservoir, production and facilities engineering, computer science, and economics. Geoscientists using seismic, well-log, outcrop analog data and mathematical models are able to develop geological models containing millions of cells. These models characterize complex geological features including faults, pinchouts, shales, and channels. Simulation of the reservoir at the fine geologic scale, however, is usually not undertaken except in limited cases.
Historically, reservoir simulation has accounted for rock mechanics by simple use of a time-invariant rock compressibility cR, spatially constant or variable. In reality, rock mechanics is intimately coupled with fluid flow. Rock mechanics is coupled with fluid flow in two aspects. Therefore, rigorous reservoir simulation should include simultaneous solution of multiphase flow and stresses as well as the appropriate dependencies between these processes. While these couplings physically exist to some extent in all reservoirs, they can be often ignored or approximated when the reservoir behaves elastically.
PVT considerations are important in setting up the proper parameters when undergoing reservoir simulation. Phase behavior of a mixture with known composition consists of defining the number of phases, phase amounts, phase compositions, phase properties (molecular weight, density, and viscosity), and the interfacial tension (IFT) between phases. In addition to defining the phase behavior of mixtures at a specific reservoir pressure, knowing the derivatives of all phase properties with respect to pressure and composition is important in reservoir simulation. With either approach, the PVT quantities required by a reservoir simulator are essentially the same. Modern reservoir simulators are usually written with a general compositional formulation, whereas black-oil PVT properties are converted internally to a two-component "compositional" model; the two components are surface gas and surface oil. A reservoir simulator keeps track of overall composition in each computational grid cell as a function of time. The phase fluxes and component movement within the reservoir are greatly affected by phase behavior (e.g., the mobility of each phase and which components are carried in each phase).
Upscaling, or homogenization, is substituting a heterogeneous property region consisting of fine grid cells with an equivalent homogeneous region made up of a single coarse-grid cell with an effective property value. Upscaling is performed for each of the cells in the coarse grid and for each of the grid properties needed in the reservoir flow-simulation model. Therefore, the upscaling process is essentially an averaging procedure in which the static and dynamic characteristics of a fine-scale model are to be approximated by that of a coarse-scale model. A conceptual illustration of the upscaling process is shown in Figure 1. Typically, 3D geological models contain detailed descriptions of the reservoir that can be hard to capture properly with a significantly coarser model. Therefore, it would be preferable if upscaling could be avoided. Currently, an average-sized flow simulation model consists of approximately 100,000 active grid cells. This is to ensure that the CPU consumption of a simulation run will be reasonable (i.e., within practical limits).
Geostatistical reservoir-modeling technologies depart from traditional deterministic modeling methods through consideration of spatial statistics and uncertainties. Geostatistical models typically examine closely the numerous solutions that satisfy the constraints imposed by the data. Using these tools, we can assess the uncertainty in the models, the unknown that inevitably results from never having enough data. Reservoir characterization encompasses all techniques and methods that improve our understanding of the geologic, geochemical, and petrophysical controls of fluid flow. It is a continuous process that begins with the field discovery and all the way through to the last phases of production and abandonment.
The linear equation solver is an important component in a reservoir simulator. It is used in the Newton step to solve the discretized nonlinear partial differential equations. These equations describe mass balances on the individual components treated in the model. For nonisothermal problems, an energy balance is added to the system. The matrix problem involves solving Ax b, where A is typically a large sparse matrix, b is the right-side vector, and x is the vector of unknowns.