Adel Malallah

A Multiscale Approach to Production Data Integration Using Streamline Models

We propose a multiscale approach to data integration that accounts for the varying resolving power of different data types from the very outset. Starting with a very coarse description, we match the production response at the wells by recursively refining the reservoir grid. A multiphase streamline simulator is utilized for modeling fluid flow in the reservoir. The well data is then integrated using conventional geostatistics, for example sequential simulation methods. There are several advantages to our proposed approach. First, we explicitly account for the resolution of the production response by refining the grid only up to a level sufficient to match the data, avoiding over-parameterization and incorporation of artificial regularization constraints. Second, production data is integrated at a coarse-scale with fewer parameters, which makes the method significantly faster compared to direct fine-scale inversion of the production data. Third, decomposition of the inverse problem by scale greatly facilitates the convergence of iterative descent techniques to the global solution, particularly in the presence of multiple local minima. Finally, the streamline approach allows for parameter sensitivities to be computed analytically using a single simulation run and thus, further enhancing the computational speed. The proposed approach has been applied to synthetic as well as field examples. The synthetic examples illustrate the validity of the approach and also address several key issues such as convergence of the algorithm, computational efficiency, and advantages of the multiscale approach compared to conventional methods. The field example is from the Goldsmith San Andres Unit (GSAU) in West Texas and includes multiple patterns consisting of 11 injectors and 31 producers. Using well log data and water-cut history from producing wells, we characterize the permeability distribution, thus demonstrating the feasibility of the proposed approach for large-scale field applications.

Prediction of Water Influx of Edge-Water Drive Reservoirs Using Nonparametric Optimal Transformations

The accurate estimation of water influx into a petroleum reservoir is very important in many reservoir engineering applications, such as material balance calculation, design of pressure maintenance programs, and advanced reservoir simulation studies. These applications have heavily relied on the classical work of van Everdingen and Hurst for finite and infinite edge-water drive reservoirs. However, for both types of water drive reservoirs, the calculation of water influx is not a straight forward task. Table lookup and interpolation between time entries are needed, and furthermore for finite aquifers, interpolation between tables may be also required. The paper presents nonparametric optimal transformations models for the prediction of dimensionless water-influx and dimensionless pressure drop for finite and infinite edge-water drive reservoirs using Graphical Alternating Conditional Expectation (GRACE). In order to achieve maximum efficiency, all the terms involved in the models are used in dimensionless form. GRACE transformations are totally data driven and do not assume any a priori functional form. The results of the various cases are in excellent agreement with the original tables of van Everdingen and Hurst. Introduction Petroleum reservoirs are often surrounded from the edge or the bottom by water aquifers that support the reservoir pressure through water influx. In response to a pressure drop in the petroleum reservoir, the water aquifer reacts to offset, or retard, pressure decline by providing a source of water influx or encroachment. To determine the effect that an aquifer has on the oil and gas production, it is important to estimate the amount of water that has entered into the reservoir from the aquifer. Such calculation is not a simple and risk-free task due to the involvement of many unknown parameters. For instance, aquifer pressure, thickness, permeability, porosity, shape, and areal extent are usually all unknown variables. Furthermore, water aquifer models are classified according to the flow geometry as either edge-water or bottom-water drive (Figures 1 and 2). These models have completely different flow behavior. The type of the water aquifer, its size, properties, and the amount of water that it can deliver into the reservoir for a certain pressure drop during a specific period of time affect the entire production life of the reservoir. A good knowledge of the aquifer properties, specifically the amount of water that it can provide into the reservoir, dictates the production schedule and the development strategies that need to be implemented in order to optimize oil recovery. Many authors have presented different models for estimating the water influx. These models apply to different flow regimes, including steady-state, modified steady-state (Schilthius, 1963), pseudo-steady-state (Hurst, 1943; 1958; Leung, 1986), and unsteady-state (Fetkovitch, 1971; Leung, 1988). van Everdingen and Hurst (1949) presented the most commonly used water-influx model. This model is basically a solution of the radial diffusivity equation; hence, it yields an accurate estimate of water encroachment for practically all flow regimes, provided that the flow geometry is actually radial. van Everdingen and Hurst solutions are for both the constant-terminal-rate case and the constant-terminal-pressure case of finite and infinite edge-water aquifers. Coats (1962) developed a model that takes into consideration the vertical flow of water into the reservoir. However, his model has two major drawbacks: (1) the presented solution is for the constant-terminal-rate case only, which permits the calculation of the pressure from a known water influx rather than the reserve, and (2) the model is only applicable to infinite aquifers and

New Approach for Fracture Gradient Prediction Using Nonparametric Optimal Transformations— Field Applications in the Middle East

Abstract Accurate prediction of formation fracture gradient is essential to many petroleum-engineering operations. Proper planning and execution of deep abnormal pressure wells, stimulation treatment, and reservoir exploitation require, among other factors, good estimates of fracture gradient. It has been proven in the literature that most of the available fracture gradient correlations do not provide reliable results when exposed to data away from the geographical region where they were initially developed. A new approach for fracture gradient prediction based on nonparametric optimal transformations is presented. The transformations are totally data driven and do not assume any a priori functional form. The model presents the fracture gradient as a function of pore pressure gradient, rock density, and depth. The data set used in the study consists of more than 21,000 points taken from 16 wells drilled in seven different geologic prospects covering more than 200 mi2. The excellent results obtained from the proposed model establish a new simple tool for fracture gradient calculation that is based on readily accessible parameters. The proposed model is illustrated and validated using several examples from different fields in the Middle East. The results of the various cases confirm that the computed and the measured fracture gradient values are in excellent agreement with an average absolute relative error of 6% and a standard deviation of 0.05 psi/ft.

Characterizing Fluid Saturation Distribution Using Cross-Well Seismic and Well Data: A Geostatistical Study

One of the goals of reservoir characterization, particularly in mature reservoirs, is to identify unswept regions containing high oil saturation for targeted infill drilling or enhanced recovery. A common approach to the problem is to generate high resolution distribution of reservoir properties such as permeability and porosity and then conduct flow simulations to identify regions of high oil saturation. One possible alternative to flow simulations would be to generate spatial distribution of properties that are related to fluid saturations and then infer fluid saturation distribution through the use of appropriate correlations. In this paper we present a field application to infer interwell water saturation distribution by combining crosswell seismic and well data. First, we use a non-parametric transformational approach to correlate sonic velocity with resistivity and porosity at the wells. An iterative procedure using alternating conditional expectations (ACE) forms the basis for this calibration. Next, stochastic cosimulation is carried out to generate conditional realizations of resistivity and porosity in the interwell region. In this cosimulation, cross-well seismic velocity is considered as the secondary data while resistivity and porosity are treated as primary data. Finally, water saturation distribution is deduced from the resistivity and porosity distributions through the use of Archie’s law.

Modeling Inflow Performance Relationships for Wells Producing From Two-Layer Solution-Gas Drive Reservoirs Without Cross-Flow

Abstract Continuous monitoring and accurate anticipation of the present and future performance of the flowing wells and reservoirs constitute the cornerstone elements in the design of optimum field development strategy. It is crucial for the petroleum engineer to possess the appropriate tools that assist in efficiently predicting well behavior, designing artificial lift equipment, forecasting production, and optimizing the entire production system. Inflow performance relationship (IPR) is one of the vital tools required to monitor well performance. Existing inflow performance relationship models are idealistic and mainly designed for homogeneous reservoirs. However, most reservoirs around the world are heterogeneous and composed of layers of different permeabilities. Hence, there is an urgent need for new realistic IPR models that describe the actual reservoir inflow performance behavior more efficiently than the available models. The authors investigate the effects of reservoir heterogeneity on IPR curves for wells producing from two-layer solution-gas drive reservoirs without cross-flow. Furthermore, the results provide the petroleum engineer with two simple yet accurate IPR models for heterogeneous reservoirs. The first model represents the IPR of the well under present flowing conditions, while the second model is used to forecast future well deliverability.

Inflow performance relationships for layered solution-gas drive reservoir

Inflow performance relationship (IPR) is a very important tool to forecast well performance. Existing IPR models are idealistic since they are developed for homogeneous reservoirs; therefore, they are inappropriate for layered systems. Consequently, there is a need for IPR models that efficiently describe layered reservoir performance. This study investigates the effects of reservoir heterogeneity on IPR for layered solution-gas drive reservoirs. Multiphase flow in both two and multilayer reservoirs was simulated. Both fluid cross flow and no fluid cross flow among layers were considered. A stochastic simulation algorithm was used to generate various permeability realisations among layers. Three geostatistical models using uniform, Gaussian, and bimodal probability distributions were used to grasp optimum match between real reservoir behaviour and simulated data. The generated data were scrutinised to develop two accurate IPR equations. The first equation describes the well behaviour under current flowing conditions, whereas the second equation can be used to forecast future well performance.

Modeling Inflow Performance Relationships for Wells Producing from Multi-Layer Solution-Gas Drive Reservoirs

Optimum field development strategy requires good knowledge of anticipated well performance and future flowing condition variation. This practice involves continuous monitoring of surface facility network, wells, and reservoir. Thus, it is crucial for the petroleum engineer to possess the appropriate tools to efficiently forecast well behavior, design artificial lift equipment and stimulation treatments, forecast production, and improve the entire production system optimization. Inflow performance relationship (IPR) is one of the vital tools required to monitor well performance. Currently used inflow performance relationship models are idealistic in nature, mainly developed for homogeneous reservoirs, and not suitable for multi-layer systems with different permeabilities. Consequently, the available IPR relationships do not provide accurate performance of such reservoirs. Thus, there is an urgent need for new realistic IPR models that describe the actual reservoir inflow performance behavior more efficiently than t he available models. This study investigates the effects of reservoir heterogeneity on IPR curves for wells producing from multi-layer solutiongas drive reservoirs. To achieve the desired objectives a stochastic simulation algorithm known as simulated annealing was used to generate various permeability realizations among the stacked layers. The generated data were then thoroughly scrutinized and two simple yet accurate empirical IPR models were developed for heterogeneous two and multi-layer solutiongas drive reservoirs. Introduction In reservoir studies, Inflow Performance Relationship (IPR) of a well is an essential tool to assess the well performance. It indicates the production behavior of a well and it will assist in determining the feasibility of producing a well. The IPR curve visualizes the relationship between the well’s producing bottomhole pressures and its corresponding production rates under a given reservoir condition. The shape of the curve is influenced by many factors such as the reservoir fluid composition, the existence of well zones, and the behavior of the fluid phases under reservoir flowing conditions. Gilbert introduced IPR curves in 1954 and through the years, these curves had several modifications. In 1968, Vogel introduced a mathematical dimensionless model for wells producing in bounded solution-gas drive reservoirs where the average reservoir pressure is less than the bubble-point pressure. Standing (1970, 1971) introduced a modified version of Vogel’s curve to characterize a well performance for damaged wells and different depletion stages. In 1973, Fetkovich showed that the performance curve for an oil well can be expressed by a more general equation similar to that used for a gas well. His developed equation was found to be valid for tests conducted for a variety of reservoir conditions even when the flowing pressures were well above the bubble-point pressure. Through time, IPR curves have been utilized in different applications in the petroleum industry. Weiss et al. (1981) employed a method of individual zone productivity combined with IPR testing to characterize two prolific offshore oil fields. Later, Brown (1982) combined well-inflow performance with tubing intake curves to prepare pressure/flow rate diagrams in order to properly select the best artificial lift method. Chu and Evans (1983) used a computer-based analysis to find the optimum production design for a naturally flowing water drive wells. They developed a group of graphs that are derived based on the performance of IPR, vertical lift, choke, horizontal flow, and the surface equipments thermodynamics. To eliminate the need for conventional multipoint tests, Mishra and Caudle (1984) developed a new method to calculate the IPR curves for stabilized non-Darcy flow in unfractured gas reservoirs. On the other hand, other studies developed dimensionless IPR curves for fractured gas wells with positive, negative or zero skin effect