Abeeb A. Awotunde

Reservoir Description with Integrated Multiwell Data Using Two-Dimensional Wavelets

Inferring reservoir data from dynamic production data has long been done through matching the production history. However, proper integration of available production history has always been a challenge. Different production history data such as well pressure and water cut often occur at different scales making their joint inversion difficult. Furthermore, production data obtained from the same well or even the same reservoir are often correlated making a significant portion of the dataset redundant. Thirdly, the massiveness of the data recorded from wells in a large reservoir over a long period of time makes the nonlinear inversion of such data computational demanding. In this paper, we propose the integration of multiwell production data using wavelet transform. The method involves the use of a two-dimensional wavelet transformation of the data space in order to integrate multiple production data and reduce the correlation between multiwell data. Multiple datasets from different wells, representing different production responses (pressure, water cut, etc.), were treated as a single matrix of data rather than separate vectors that assume no correlation amongst datasets. This enabled us to transform the multiwell production data into a two-dimensional wavelet domain and subsequently select the most important wavelets for history match. By minimizing the square of the Frobenius norm of the residual matrix we were able to match the calculated response to the observed response. We derived the relationship that allows us to replace a conventional minimization of the sum of squares of the l2 norms of multi-objective functions with the minimization of the square of the Frobenius norm of the integrated data. The usefulness of the approach is demonstrated using two examples. The approach proved very effective at reducing correlation between multiwell data. In addition, the method helped to reduce the cost of computing sensitivity coefficients. However, the method gave poor prediction of water cut when the datasets were not scaled before inverse modeling.

Sensitivity studies and stochastic optimization of CO2 foam flooding

The use of CO 2 foam flooding for enhanced oil recovery is increasingly becoming common. In this type of enhanced oil recovery, the surfactant is dissolved into CO 2 to form foam and the CO 2 foam is injected alternately with water to improve the sweep efficiency of the flood. However, many parameters affect the effectiveness of this CO 2 flood. Some of these parameters are the concentration of surfactant dissolved in the CO 2, the ratio of the foam injection time to the water injection time (cycle ratio), etc. Large savings in cost can be realized if these parameters are carefully selected. In this work, we optimized CO 2 foam flooding by estimating the parameters that affect the flooding using stochastic optimization algorithms. First, we performed some sensitivity studies to determine the extent of influence of different parameters of the CO 2 foam flood. From the sensitivity studies, we were able to reduce the number of parameters to be optimized to three (cycle ratio, surfactant concentration, and well locations) that have significant effects on the flood. Subsequently, we adopted two optimization algorithms to estimate the three parameters.

A multiresolution adjoint sensitivity analysis of time-lapse saturation maps

Improvements in seismic data acquisition and processing have made seismic technology a viable source of information for locating hydrocarbon deposits and also for describing the spatial variability of reservoir parameters. While three-dimensional seismic technology is already a well-established means of locating hydrocarbon deposits, the 4D (or time-lapse) seismic is gradually becoming a source of reservoir parameter description. In particular, time-lapse seismic is increasingly becoming a useful source of information about fluid migration and pressure changes in the reservoir. In recent years, time-lapse seismic data or saturation maps derived from such data have been used to estimate spatial distribution of reservoir parameters through history matching. However, successful application of the method to accurate description of reservoir parameter variability remains a challenge. Some major challenges in the application of time-lapse seismic data in reservoir model history match are the poor resolution of the seismic data, uncertainty associated with the maps of changes in saturation derived from the seismic data, and the massiveness of the data or the associated saturation maps. Repeat seismic data are blurred or low-resolution maps of trends in reservoir responses to production and injection activities. These trends are influenced by reservoir property distribution and when used judiciously, constitute a good source of information that can help in reducing the uncertainty associated with reservoir parameter estimates. The maps of changes in reservoir saturation or pressure obtained from repeat seismic data are themselves fraught with uncertainties and care must be taken when using these maps to estimate reservoir parameters. Furthermore, obtaining the most useful information from a voluminous seismic data set is challenging and is still an active area of research. In this work, we present the use of the wavelet transform to integrate maps of changes in reservoir saturation derived from time-lapse seismic data into reservoir model history matching. The work involves transforming the saturation-change map into a wavelet space and then history matching some carefully selected wavelets to obtain estimates of reservoir parameters. Three sample applications based on synthetic data are used to show the suitability of the approach. Comparison is made to conventional approach in which the saturation-change map is not transformed into wavelets before matching.

Generalized field-development optimization with well-control zonation

Of concern in the development of oil fields is the problem of determining the optimal locations of wells and the optimal controls to place on the wells. Extraction of hydrocarbon resources from petroleum reservoirs in a cost-effective manner requires that the producers and injectors be placed at optimal locations and that optimal controls be imposed on the wells. While the optimization of well locations and well controls plays an important role in ensuring that the net present value of the project is maximized, optimization of other factors such as well type and number of wells also plays important roles in increasing the profitability of investments. Until very recently, improving the net worth of hydrocarbon assets has been focused primarily on optimizing the well locations or well controls, mostly manually. In recent times, automatic optimization using either gradient-based algorithms or stochastic (global) optimization algorithms has become increasingly popular. A well-control zonation (WCZ) approach to estimating optimal well locations, well rates, well type, and well number is proposed. Our approach uses a set of well coordinates and a set of well-control variables as the optimization parameters. However, one of the well-control variables has its search range extended to cover three parts, one part denoting the region where the well is an injector, a second part denoting the region where there is no well, and a third part denoting the region where the well is a producer. By this, the optimization algorithm is able to match every member in the set of well coordinates to three possibilities within the search space of well controls: an injector, a no-well situation, or a producer. The optimization was performed using differential evolution, and two sample applications were presented to show the effectiveness of the method. Results obtained show that the method is able to reduce the number of optimization variables needed and also to identify simultaneously, optimal well locations, optimal well controls, optimal well type, and the optimum number of wells. Also, comparison of results with the mixed integer nonlinear linear programming (MINLP) approach shows that the WCZ approach mostly outperformed the MINLP approach.

Improvement of Levenberg-Marquardt algorithm during history fitting for reservoir simulation

Abstract In order to estimate reservoir parameters more effectively by history fitting, DE (Differential Evolution) was proposed to estimate the optimum damping factor so that the standard Levenberg-Marquardt algorithm was improved, and the improved algorithm was validated by analysis of examples. The standard LM algorithm uses trial-and-error method to estimate the damping factor and is less reliable for large scale inverse problems. DE can solve this problem and eliminate the use of line search for an appropriate step length. The improved Levenberg-Marquardt algorithm was applied to match the histories of two synthetic reservoir models with different scales, and compared with other algorithms. The results show that: DE speeds up the convergence rate of the LM algorithm and reduces the residual errors, making the algorithm suitable for not only small and medium scale inverse problems, but also large scale inverse problems; if the iteration termination criteria of LM algorithm is preset, the improved algorithm will save the number of iterations and reduce the total time greatly needed for the LM algorithm, leading to higher efficiency of history matching.

A CUDA based parallel multi-phase oil reservoir simulator

Abstract Forward Reservoir Simulation (FRS) is a challenging process that models fluid flow and mass transfer in porous media to draw conclusions about the behavior of certain flow variables and well responses. Besides the operational cost associated with matrix assembly, FRS repeatedly solves huge and computationally expensive sparse, ill-conditioned and unsymmetrical linear system. Moreover, as the computation for practical reservoir dimensions lasts for long times, speeding up the process by taking advantage of parallel platforms is indispensable. By considering the state of art advances in massively parallel computing and the accompanying parallel architecture, this work aims primarily at developing a CUDA-based parallel simulator for oil reservoir. In addition to the initial reported 33 times speed gain compared to the serial version, running experiments showed that BiCGSTAB is a stable and fast solver which could be incorporated in such simulations instead of the more expensive, storage demanding and usually utilized GMRES.

Optimal parameters selection for SAGD and VAPEX processes

Steam Assisted Gravity Drainage (SAGD) and Solvent Vapor Extraction (VAPEX), both of the techniques have been proved to be successful for the exploitation of heavy oil reservoirs. Field development of heavy oil reservoirs requires careful determination of optimal parameters, well locations and control setting of producers and injectors. In recent years, field development decisions based on sensitivity studies have been shifting toward automated optimization. In this paper, we present the optimal parameter selection for SAGD and VAPEX. We performed the search of optimum parameters; the vertical separation between injector and producer, well controls and well locations. All these parameters have been simultaneously optimized to study and compare the performance of both processes. Also, we present an efficient method to constrain horizontal wells to preset minimum well spacing constraints. This method was then applied to constrain the well spacing between different peers of horizontal wells in the SAGD and VAPEX processes. The particle swarm optimization was used as an optimizer to determine the optimum parameters. The results indicated that the method could successfully determine the optimal parameters while satisfying the spacing constraint imposed by the user. The comparison of the results showed the better performance of SAGD over VAPEX process.

Self-adaptive differential evolution with a novel adaptation technique and its application to optimize ES-SAGD recovery process

Abstract Differential evolution (DE) algorithm has shown good performance in many optimization problems. However, its control parameters greatly affect its performance and require many trials to determine the optimum values of control parameters for each specific optimization problem. In this paper, we present a self-adaptive DE with a new adaptation technique to improve the solution quality as well as increase the speed of convergence with a reduction in the computational cost. The proposed approach, called modified self-adaptive differential evolution (MSaDE), employs a new success-rate indicator of the strategies used to generate the trial vectors in conventional self-adaptive differential evolution (SaDE) algorithm. The proposed method has been tested on 22 benchmark problems and on the expanded solvent steam-assisted gravity drainage (ES-SAGD) recovery process. The results show that a significant speed-up is achieved in the exploitation and exploration capabilities of the self-adaptive DE algorithm.

Sensitivity-based upscaling for history matching of reservoir models

Simulation of reservoir flow processes at the finest scale is computationally expensive and in some cases impractical. Consequently, upscaling of several fine-scale grid blocks into fewer coarse-scale grids has become an integral part of reservoir simulation for most reservoirs. This is because as the number of grid blocks increases, the number of flow equations increases and this increases, in large proportion, the time required for solving flow problems. Although we can adopt parallel computation to share the load, a large number of grid blocks still pose significant computational challenges. Thus, upscaling acts as a bridge between the reservoir scale and the simulation scale. However as the upscaling ratio is increased, the accuracy of the numerical simulation is reduced; hence, there is a need to keep a balance between the two. In this work, we present a sensitivity-based upscaling technique that is applicable during history matching. This method involves partial homogenization of the reservoir model based on the model reduction pattern obtained from analysis of the sensitivity matrix. The technique is based on wavelet transformation and reduction of the data and model spaces as presented in the 2Dwp–wk approach. In the 2Dwp–wk approach, a set of wavelets of measured data is first selected and then a reduced model space composed of important wavelets is gradually built during the first few iterations of nonlinear regression. The building of the reduced model space is done by thresholding the full wavelet sensitivity matrix. The pattern of permeability distribution in the reservoir resulting from the thresholding of the full wavelet sensitivity matrix is used to determine the neighboring grids that are upscaled. In essence, neighboring grid blocks having the same permeability values due to model space reduction are combined into a single grid block in the simulation model, thus integrating upscaling with wavelet multiscale inverse modeling. We apply the method to estimate the parameters of two synthetic reservoirs. The history matching results obtained using this sensitivity-based upscaling are in very close agreement with the match provided by fine-scale inverse analysis. The reliability of the technique is evaluated using various scenarios and almost all the cases considered have shown very good results. The technique speeds up the history matching process without seriously compromising the accuracy of the estimates.