Mohammed E. Osman

Pressure analysis of a fractured well in multilayered reservoirs

Abstract Hydraulic or naturally fractured wells located in multilayered reservoirs are common. However, no techniques are available to analyze well testing-data for such systems. In this study a mathematical model was developed to present the pressure behavior of a fractured well located in multilayered reservoirs. It was found that the pressure functions (build-up or draw-down) and fractional production-rate are mainly controlled by the fracture half-lengths in different layers during early time, and by the reservoir transmissibility during late times. The effect of storativity is insignificant. For the system understudy, it might be difficult to use the pressure derivative in determining reservoir parameters. The nature of the fracture was found to affect the time to the end of linear flow period. Also, the reservoir characteristics can be determined using Muskat and MDH plots while Horner plots can not be used. The techniques resented in this study can be used to determine reservoir characteristics using draw-down and/or build-up testing-data.

Effect of boundary conditions on pressure behavior of finite-conductivity fractures in bounded stratified reservoirs

In this study, a mathematical model was developed to model the pressure behavior of a well located in a bounded multilayer reservoir and crossed by a finite-conductivity vertical fracture. It was found that the dimensionless pressure function and its derivative strongly depend on fracture conductivity and fracture extension during early times. The effect of reservoir heterogeneity on the pressure function is negligible compared to that on the pressure derivative. Both functions exhibit four flow periods: bilinear, formation linear, pseudoradial and pseudosteady-state which are separated by transition periods. One or more of these flow periods may be missing. Data obtained from a long test and which are characterized by a unit slope line indicate that the well is intercepted by deeply extended fractures. It has been found that the fractional production rates of different layers are a good measure of reservoir and fracture characteristics. Flowmeter survey data can be used to eliminate the non-uniqueness problem when using the type curves presented in this study.

Architecture of a multipurpose simulator

Abstract This paper presents the development of a multipurpose simulator with the general model describing a four-component, three-phase (oil, aqua, gas), multi-dimensional, finite-difference polymer injection simulator. The model uses a block-centered grid and a seven-point finite-difference scheme. Fluid saturations and pressure distributions are obtained from a fully implicit formulation using Newtons method, whereas polymer concentration is obtained, in a subsequent step, explicitly using the method of cascade. Practical features of the present simulator include: (1) a truly multipurpose simulation; and (2) ease of preparing a batch data file required for the simulator. A novel and simple procedure is implemented to reduce the general model of the polymer injection simulator (polymer, oil, aqua, and gas) to: (1) three-phase black-oil simulator (oil, water, and gas); (2) two-phase black-oil simulators (oil and water, oil and gas, or water and gas); (3) two-phase polymer injection simulator (polymer, oil, and aqua); and (4) one-phase simulators (oil, water, or gas) with only the relevant equations being solved at the matrix level for each simulator. Guidelines for other practical features are also presented. The simulator was tested and verified using a polymer injection test problem and a gas injection bench mark test problem both reported in the literature. The simulator was also used to model a field case and some results are highlighted.

A NEW TECHNIQUE TO PREDICT MULTILAYERED RESERVOIR CHARACTERISTICS USING PULSE TESTING DATA

In this study, a mathematical model was developed to present pulse and interference testing for multilayered reservoirs. It was found that apparent storage calculated from pulse testing data is always less than or equal to the actual storage of the reservoir and that apparent transmissibility is always greater than or equal to the actual transmissibility. For short cycle intervals, the fractional production rate from a particular layer is not proportional to its transmissibility fraction. The effect of storage variation on fractional production rate is negligible. Wellbore damage affects both apparent transmissibility and storage. Less accurate estimation reservoir characteristics is obtained using pulse-test data as the contrast in reservoir properties increases and vice versa. A new approach is suggested to use data of single well test as well pulse test to estimate properties of individual layers. The approach is demonstrated by a three-layer numerical example.

A New Conventional Method of Analysis for Well Tests in Hydraulically Fractured Wells Using Downhole Pressures and Sandface Rates

Analysis of variable flow rate tests has been given special attention recently because, in many cases, it is impractical to keep a flow rate constant long enough to perform a drawdown test. Also, in many other drawdown and buildup tests, the early data are influenced by wellbore storage effects, and the duration of these effects can be quite long for low-permeability reservoirs. For hydraulically fractured wells, the early-time period represents linear flow. Current methods of analysis of multirate tests, in fractured wells, use both conventional and rate-normalized type-curve matching for the pseudoradial flow period; and only rate-normalized type-curve analysis for the linear flow period. None of the current methods use a direct approach to analyze the linear flow data. This paper presents a mathematical model which describes drawdown and buildup tests in hydraulically fractured wells. A new conventional and simple method of analysis based on this model is presented for drawdown and buildup tests in oil and gas wells. This new method uses a direct approach to analyze the linear flow data and combines it with the conventional analysis for pseudoradial flow data. It does not require a priori knowledge of the fracture type (uniform-flux or infinite-conductivity); in fact it predicts the fracture type. This method is useful for the analysis of simultaneously measured downhole pressure and sandface rate data. Data of three well tests reported in the literature were analyzed by the new method and the results including the comparison with those obtained by other methods are presented and discussed.

A new method for pressure test analysis of a vertically fractured well producing commingled zones in bounded square reservoirs

Abstract Although hydraulically or naturally fractured wells located in stratified bounded reservoirs are common, reliable techniques available to analyze the pressure test data for such reservoirs are lacking. This paper presents a mathematical model that describes the pressure behavior of a vertically fractured well located in a stratified, bounded, square reservoir. The fracture can be either a uniform flux or an infinite conductivity fracture. It was found that the dimensionless pressure function and its derivative and the fractional production rate from the different layers are mainly controlled by the fracture penetration into the formation, and that transmissibility and storativity affect the fractional production rate and the pressure derivative but have little effect on the dimensionless pressure function. Type curves of dimensionless pressure and dimensionless pressure derivative can be used to evaluate the reservoir characteristics. The selection of the appropriate type curve is guided by the behavior of the layer fractional production rate obtained from flow rate survey carried out during well testing. Type curves for uniform flux and infinite conductivity fractures exhibit similar features. Two examples are presented to demonstrate the application of the new method of analysis presented in this paper.