Layer | Fill | Outline |
---|
Map layers
Theme | Visible | Selectable | Appearance | Zoom Range (now: 0) |
---|
Fill | Stroke |
---|---|
Collaborating Authors
Results
Abstract This paper describes the design of FLEX, an object-oriented, flexible grid, black-oil reservoir simulator helps in dealing with the complexity of this problem. This approach is particularly useful because of the difficulties associated with generation and use of flexible grid geometries (like Voronoi, median, boundary adapting grids, etc.). The entire problem is divided into subsystems like geometry, gridnodes, gridnode connectivity, grid, reservoir fluid flow, and matrix. Each of these subsystems have objects which are closely related. The dependency of these subsystems is established. A detailed analysis of each subsystem leads to identifying the classes, which are a set of objects having similar behavior. Attributes and behavior of the classes are assigned. After establishing relationships between the classes, they are arranged into hierarchies. About one hundred major classes have been identified and designed to achieve the desired behavior from FLEX. The programming language used is C++. Introduction Reservoir simulators are inherently complex. A simulator has to deal with issues such as reservoir and grid geometry, fluids, flow calculation, matrix computations, several well and production constraints, visualization, etc. The most important feature of FLEX, a black oil simulator, is its ability to handle complexities arising from flexible grids. Verma and Aziz (1996) give a description of flexible grids in reservoir simulation. The flexibility in grids increases geometrical complexities as well as complexities in flow calculation. These complexities need sophisticated data structures (and associated procedures) to simplify the problem. It is expected that FLEX will change with time to incorporate new features. One of the important considerations in designing the simulator is the ease with which the simulator can be expected to handle new problems. All these factors combined to make the development process of FLEX quite complex. This paper describes the advantages of using an object-oriented approach for the development of reservoir simulators. The philosophy followed in designing FLEX is that advocated by Booch (1994) and Cheriton (1995). Basic Features of FLEX FLEX solves flow equations based on the control volume formulation (see Verma and Aziz, 1996). It uses the Newton-Raphson method to iteratively solve for the variables. A connection-based approach is employed to form the Jacobian matrix and the residual vector (see Lim, Shiozer and Aziz, 1995 and Verma and Aziz, 1996). Presently the simulator is developed to handle only two immiscible phases. The gridnodes can be located so that they represent reservoir geometry, wells, faults, etc. Figure 1 is an example of the flexible grid generation capabilities of FLEX. Why Object-Oriented? An object-oriented approach was followed in the design of FLEX to handle the complexities associated with a flexible grid simulator, and to provide for future enhancements.
SPE Members Abstract To simulate steam injection in fractured reservoirs either double porosity or double permeability models are used. Both incorporate a matrix-fracture transfer term in the mass and energy balances. Due to the difficulty in modeling the physical processes taking place in the matrix-fracture transfer and the lack of experimental data, the matrix-fracture transfer term is not fully understood. This is especially true for nonisothermal processes. Fine grid simulation results are used to design a 3-D laboratory matrix-fracture model to study the matrix-fracture transfer function for steam injection. A CT-Scanner will be used to measure the three-phase insitu saturations in the fractured model. The flow parameters were determined by using the results of several simulation runs. Among these are the steam injection rate, maximum expected pressure in the system and the number and the locations of the injection and production wells needed to clean and saturate the model for each run. Analytical heat transfer models were used to determine the heat losses from the model. Fine grid simulations were used to investigate the sensitivities of the flow process to matrix-fracture properties such as capillary pressure and relative permeability. The simulations showed that matrix water-oil capillary pressure increased the oil recovery by increasing the water imbibition rate. On the other hand, fracture water-oil capillary pressure decreased the water imbibition rate and recovery. Matrix gas-oil capillary pressure had no effect on the oil recovery but fracture gas-oil capillary pressure had a positive effect on recovery by allowing flow of steam into the matrix thus increasing oil mobility. The effect of matrix relative permeability was found to be less important. The experimental design was modified based on the numerical results. We give details of the experimental apparatus and show some results from preliminary experiments. Introduction Several flow models have been developed in the literature for isothermal processes in fractured media. The models used in thermal simulators are generally extensions of models for isothermal processes. They are classified into two groups, dual porosity and dual permeability models. All dual porosity models assume that fractures constitute the main path for fluid flow, and matrix blocks act as sources or sinks to the fracture network. In the basic dual porosity model, matrix and fracture communicate through a single exchange term in the flow equations. Kazemi et al. (1976) developed a three-dimensional 2-phase model to simulate such a fractured system. The simulator equations are two-phase extensions of the single-phase equations derived by Warren and Root (1963) Thomas et al. (1983) extended the model to 3-phase flow in fractured systems. In the multiple interacting continua model which is a different type of dual porosity model, the matrix is divided into nested volume elements which communicate with each other. In this model, flow of fluid and heat between matrix and fracture is transient. The model was first used in geothermal reservoir simulation by Pruess and Narasimhan (1985). Oilman (1986) applied this model to hydrocarbon reservoirs. Pruess and Wu (1989) developed a semianalytical model to simulate matrix-fracture transient flow. Dutra and Aziz, (1992) developed an analytical transfer function, which results in a model having the same form as single-porosity models. P. 49^
SPE Members Abstract Numerical reservoir simulation commonly divides naturally fractured reservoirs into matrix and fracture systems. The high permeability fractures are usually entirely responsible for flow between blocks and flow to the wells. The flow in these fractures is modeled using Darcy's law and its extension to multiphase flow by means of relative permeabilities. The influence and measurement of fracture relative permeability for two-phase flow in fractured porous media have not been studied extensively. Transfer of fluids between the matrix and fractures is known to be one of the most important mechanisms of fluid movement in these reservoirs. Therefore, matrix/fracture fluid transfer, matrix and fracture two-phase flow, and interactions among them must be better understood for accurate simulation of oil recovery from naturally fractured reservoirs. Experimental and numerical work on two-phase flow in fractured porous media has been initiated. The process considered is oil displacement by water in fractured porous media. Fine grid simulations of two-phase flow through a fractured core were performed in order to design the experiments and to study the effects of several key variables. These variables included fracture relative permeability, matrix/fracture capillary pressure, and matrix wettability. This paper presents the results obtained from the sensitivity analysis using fine grid simulations. The numerical computations show that fracture relative permeabilities and wettability become important only at low capillary numbers. A dimensionless capillary number at which the fracture relative permeabilities become an important factor was estimated to be 20. The concept of a limiting capillary number may be extended to determine when fracture relative permeabilities are of influence in field scale simulations of naturally fractured reservoirs. Fracture capillary pressure was observed to have a negative effect on water imbibition, reducing the efficiency of the oil recovery. At high capillary numbers, i.e. when capillary forces are more important, water moves faster inside the matrix than in the fracture which results in high oil recovery. At lower capillary numbers, i.e. when viscous forces are more important, water channels rapidly through the fracture with a low recovery efficiency. Comparison of simulations of similar fractured and unfractured systems shows that at high capillary numbers the recovery is higher for the fractured core. At low capillary numbers the unfractured core exhibits higher recovery. Introduction Dual-porosity, dual-permeability formulations are commonly used to model multiphase flow in naturally fractured reservoirs (NFR). The discretized flow equations for this type of model are as follows: (1) where the subscript denotes a given phase (oil, gas or water), m denotes matrix, and f stands for fracture. P. 605^
Abstract This paper describes a scheme for combining reservoir constituents into fewer pseudo components for compositional studies. The algorithm is based upon the minimization of the errors introduced in the predicted phase saturations. It requires the generation of a second derivative matrix of the phase saturation with respect to moles present at phase saturation with respect to moles present at various expected reservoir conditions, which are then used to calculate the simple correlation coefficient matrix and to establish the criterion for combining the reservoir constituents. Once determined, the properties of pseudo components are calculated using Lee and Kesler's mixing rule. The interaction parameters required for the two constant equation of state models are calculated using simple mixing rules. The utility of the proposed scheme is demonstrated by comparing predicted phase saturations for the lumped scheme with the saturations obtained using the full original compositions for three widely different reservoir oils. A one dimensional gas cycling process is also simulated to show that the lumped scheme gives an adequate description of the process. Introduction In numerical modelling of many gas/solvent injection processes, one is confronted with devising a suitable scheme for combining the existing large number of hydrocarbon and non-hydrocarbon components into fewer components. These components must be grouped together so that the predicted phase behaviour is not altered significantly and the important features of the process remain intact. In the past, the lumping of reservoir fluid components has been primarily based upon the true boiling point analysis. The components boiling within a narrow range are combined together. This approach does not yield the minimum number of components required to provide a good approximation of the reservoir constituents, and generally a very large number of components is required. Lee et al proposed a more systematic approach, in which various physics-chemical properties, such as molecular weight, density, viscosity, etc., are plotted against the average boiling points for plotted against the average boiling points for different oil fractions. The slopes of these curves, normalized by dividing with the maximum value, are used to determine similarity among the fractions. Fractions with similar slopes are combined into pseudo components. pseudo components. Although Lee et al's scheme results in a satisfactory lumping of some crude oil fractions, it lacks any theoretical basis. Besides, the method requires a large amount of experimental data which normally are not available. Hong has recently suggested a simple approach to the lumping of components. The method, based on a trial and error procedure, computes the phase diagram using a small number of pseudo components. The number of components is, then, systematically increased until a satisfactory match between predicted and experimental phase envelopes is achieved. The main drawback of this method is that it may be quite time consuming, depending upon the reservoir constituents and the prevailing operating conditions. In this paper, a statistical approach is suggested to properly combine the reservoir constituents. The basis of the scheme is the observation that phase saturations play the dominant role in the simulation of reservoirs, due to their strong influence on phase mobility, and reservoir components should be grouped together so as to minimize the errors introduced in the prediction of phase saturations. The theoretical development of the scheme is described below.