L.B. Cunha

Uncertainty Assessment of SAGD Performance Using a Proxy Model Based on Butler's Theory

Steam Assisted Gravity Drainage (SAGD) is an efficient method for thermal recovery of bitumen from the vast reserves available worldwide and particularly from the oil sands in western Canada. Flow simulators are available for predicting SAGD performance and are used to support reservoir management decisions; however, the high computational time associated with the use of such complex flow simulation makes it impractical for all locations especially when reservoir uncertainty and variable operational parameters are included in the making decision process. The use of a simpler analytical model as a proxy for the reservoir simulator is shown to be a feasible alternative to flow simulation. A proxy model based on the Butler’s SAGD theory is developed to predict the oil flow rate, cumulative oil production and cumulative steam injection profiles during both: the rising and spreading steam chamber periods for a confined SAGD well pair. Modifying factors are used to fit the proxy to flow simulation results to account for conformance and reservoir heterogeneity among other factors. A critical aspect of the proxy model is a realistic parameterization of geological heterogeneity. Monte Carlo Simulation (MCS) and the proxy model permit an efficient transfer of the uncertainty in reservoir and operational parameters through to performance variables such as oil production and steam oil ratio. An example application for a single well pair showed the efficiency of the methodology in terms of computation time. The results permit improved reservoir management of complex SAGD projects. This paper has been published as SPE 115662.

Investigation of a Stochastic Optimization Method for Automatic History Matching of SAGD Processes

Western Canada has large reserves of heavy crude oild and biturmen The Steam-Asssited Gravity Drainage (SAGD) process that couples a steam-based in situ recovery method with horizontal well technology, has emerged as an economic and effieint way to produce the shallow heavy oil reservoirs in Westen Canada. Numerical reservoir simulation is used to predict reservoir performance. However, prior to the prediction phase, integration of production data into the reservoir model by means of history matching is the key stage in the numerical simulation workflow. Research and development of efficient history matching techniques for the SAGD process is important. An automated technique to assist in the history matching phase of the SAGD process is implemented and tested. The developed technique is based on a global optimization method known as Simultaneous Perturbation Stochastic Approximation (SPSA). This technique is easy to implement, robust with respect to non-optimal solutions, can be easily parallelized and the shown an excellent performance for the solution of complex optimization problems in different fields of science and engineering. The reservoir paramenters are estimated at reservoir scale by solving an inverse problem. At each iteration, selected reservoir parameters are adjusted. Then, a commercial thermal reservoir simulator is used to evaluate the impact of these new parameters on the field production data. Finally, after comparing the simulated production curves to the field data, a decision is made to keep or reject the altered parameters tested. This research is preliminary. Although the results are not ready for commercial implementation, the ideas and results presented here should prove interesting and fuel development in this important subject area. A Matlab (1) code, coupled with a reservoir simulator, is implemented to use the SPSA technique to study the optimization of a SAGD process. A symthetic case that considers average reservoir and fluid properties present in Alberta heavy oil reservoirs is presented to highlight the advantages and disadvantages of the technique.

A study of the gravity assisted tertiary gas injection processes

Gravity assisted tertiary gas injection processes can produce a large amount of incremental tertiary oil from water drive oil reservoirs. These processes include the Double Displacement Process (DDP) and the Second Contact Water Displacement (SCWD) process. A transparent sandpack micromodel was developed to conduct a pore-level observation to investigate the microscopic mechanisms of the DDP and the SCWD processes. Observation of the two processes confirmed that oil films play a very important role in achieving high recovery efficiencies in the DDP. In the SCWD process, trapped gas reduces the possibility of residual oil being trapped in the centre of the pores in the second water flood. Moreover, reservoir simulations at reservoir scale were performed to investigate the macroscopic level mechanisms of the two processes. The results have shown that both processes are efficient methods to recover waterflood residual oil.

Economic Analysis for Enhanced CO Injection and Sequestration Using Horizontal Wells

Carbon dioxide flooding has been recognized widely as one of the most effective enhanced oil recovery processes applicable for light to medium oil reservoirs. Moreover, the injection of CO 2 into an oil reservoir is a promising technology for reducing greenhouse emissions while increasing the ultimate recovery of oil. Numerical reservoir simulation is an important and inexpensive tool for designing EOR CO 2 projects and predicting optimal operational parameters. In this work, reservoir simulations performed with a compositional simulator were applied to investigate the macroscopic mechanisms of a CO 2 injection process. Horizontal injectors were used to increase injectivity. Compared to traditional vertical wells, horizontal wells are more attractive to improve CO 2 flooding economics by increasing injection rate, improving areal sweep and increasing CO 2 storage. The effects of several important parameters on the performance of the CO 2 process were studied to optimize the process. Operational parameters such as different production schemes, the injector pressure and injection rate were investigated to determine the optimal operating conditions for simultaneous objectives of higher recovery and higher CO 2 storage. The application of CO 2 flooding using horizontal wells can shorten project life, which is critical to its economics. The simulation results served as the basic input parameters for the economic analysis performed. Furthermore, net present value (NPV) and profitability index results were used to optimize the profitability of the project and to compare the CO 2 application using vertical and horizontal wells. The analysis used actual design parameters, including equipment and operating costs. The evaluation emphasized the importance of reservoir characteristics, optimum design of operation parameters and economic factors in the economic feasibility of CO 2 injection projects for enhanced oil recovery and sequestration.

A multi-scale approach to improve reservoir characterization and forecasting: the Albacora Field (deep-water offshore Brazil) study

The Upper Albian Namorado Sandstone is one of the reservoirs of the Albacora Field, located in the Campos Basin, deep-water offshore Brazil. It is a sand-rich turbidite system where the most important controls on permeability are calcite cementation, thin beds of non-reservoir lithologies and some north–south trending faults. A major multidisciplinary reservoir characterization project was conducted to improve the reservoir description using all available data. In this paper, we focus on how the effect of rock heterogeneities were represented in the fluid flow model and on the performance obtained from this model. The basic idea was to define a hierarchical model of facies established on the basis of three main work scales: porous systems (thin sections and core sample scale); composite facies (whole core and log scale); and seismic facies (interwell to field scale). An up-scaling technique, based on the geopseudo concept, was used to generate the effective petrophysical properties for the fluid-flow simulation model. A Markov–Bayes geostatistical simulation method was applied in facies stochastic modelling. The sophisticated model that was built allowed very fast history matching.

Investigations of Interfacial Coupling Phenomena and its Impact on Recovery Factor

It is well known that Darcy’s equation was developed on the basis of experiments involving single-phase flow through porous media. To account for multiphase flow, Darcy’s equation was modified by Muskat et al.(6) into a form that has been widely used in petroleum reservoir engineering. However, as pointed out by several researchers(1, 3, 7-13), the modified equation can not give accurate recovery predictions when used to simulate multiphase flow in petroleum reservoirs. This is because, in multiphase flow, the presence of one fluid affects the flow of the other fluids; that is, interfacial coupling effects (viscous and capillary coupling effects) influence the flow. The viscous coupling effect, first identified by Yuster(14), refers to the coupling that arises due to the viscous drag exerted by one fluid on the other when they flow through the same porous medium, and it is usually associated with the mobility of the fluids(5). The capillary coupling effect, recently postulated by Babchin and Yuan(15) and by Bentsen(16), refers to the coupling that arises due to coupling, through the capillary function(2), of pressure across the interfaces of the fluids. Moreover, counter-current experimental data(17-19) has been used to show that Muskat’s extension of Darcy’s equation does not correctly describe the physics of multiphase flow through porous media, because the magnitude of the relative permeabilities for a given phase obtained from countercurrent flow is always less than that acquired from a co-current experiment conducted in the same porous medium. To closely capture the physics of flow, Bentsen(1, 2), Ayub and Bentsen(3), Ayub(4) and Ayodele(5) developed a set of modified transport equations that incorporate interfacial coupling and hydrodynamic effects. In the following sections, a one-dimensional form of these modified transport equations is solved numerically by developing an Interfacial Coupling Simulator (ICS). Simulation results are compared with immiscible displacement experimental data and some conclusions are drawn as well. Abstract

Proxy Models for Fast Transfer of Static Uncertainty to Reservoir Performance Uncertainty

Petroleum reservoirs are heterogeneous and, therefore, uncertain. Heterogeneity and uncertainty are important for reservoir management. The transfer of geologic uncertainty through process performance is commonly achieved with flow simulation; however, full physics flow simulation requires significant professional and computer time. A proxy model tuned to the specific recovery process provides a means to quickly predict performance uncertainty caused by multiple geologic models and uncertain operating conditions. A limited number of flow simulation runs are used to calibrate the proxy, then calculations proceed quickly. The classical response surface approach is also illustrated. Details are given to the application of proxy models to the steam-assisted gravity drainage process. A proxy model based on the Butler steam-assisted gravity drainage theory is developed to predict the oil flow rate, cumulative oil production, and cumulative steam injection profiles during the rising and spreading steam chamber periods of a steam-assisted gravity drainage well pair. A synthetic example shows the efficiency of the methodology in terms of computation time and predictability.

Preservation of Multiple Point Structure when Conditioning by Kriging

The idea of conditioning by kriging is well known in theory and practice. It has been used for conditioning the realizations from unconditional simulation techniques such as the moving average and the turning bands simulation approaches. The basis of the conditioning by kriging approach is to use the same variogram for both the unconditional simulation and the kriging. In this paper, the focus is on using kriging for conditioning of more complex unconditional simulations. Unconditional simulated realizations with multiple point structure are generated for posterior conditioning. Two sets of data are used for kriging. After conditioning, the simulated values at data locations are the real data values, so the local data is honored. Beyond the range of correlation, the simulated values are the unconditional simulated values, which mean the multiple point structure can be preserved. The results obtained in this work show that conditioning by kriging is a simple, easy and reliable way to account for data with complex multiple point structures. Both continuous and categorical variables are used to show the performance of the conditioning by kriging approach. Moreover, kriging with different sets of data demonstrates that the multiple point structures are well preserved after conditioning.

Experimental and Numerical Quantification and Verification of Interfacial Coupling in Two-Phase Porous Media Flow

Interfacial coupling in two-phase porous media flow was investigated analytically and numerically. Modified forms of Darcys equation, which incorporated interfacial coupling (viscous and capillary coupling) and hydrodynamic effects, were formulated. A numerical scheme was developed to solve the equations and was codified into a standalone numerical simulator using the Java TM programming language. From the results of the analyses carried out, the parameter that controls the amount of viscous coupling was, theoretically and experimentally, found to have maximum values of 2 and 0.001, respectively, in order to account for the effect of viscous coupling. A comparison of analytical and experimental results shows that the transport equations give a good description of flow. The viscous coupling and capillary coupling effects are very small and can be neglected in horizontal, cocurrent flow. In horizontal, countercurrent flow, the capillary coupling was found to have a more significant effect than viscous coupling, which can be neglected. The hydrodynamic effects are found to be insignificant in horizontal, cocurrent and countercurrent flow. For vertical flow, analytical results show that viscous coupling effects are insignificant. Due to the limitations and non-availability of a complete set of vertical flow experimental data, the applicability of the capillary coupling concept could not be verified fully using the modified set of transport equations. Hence, the modified set of transport equation is yet to be verified for vertical flow.

A Lagrangian Approach for Oil Recovery in Two-Phase Porous Media Flow

This paper deals with a fully implicit finite difference scheme for the numerical solution of the Lagrangian form of the porous media fractional flow equation. It covers the theoretical background, description of mathematical formulations, basic assumptions in the models, normalization and transformation between Lagrangian and Eulerian formulations, specification of boundary conditions, discretization and solution method. Some numerical examples are described and the results compared favourably with co-current immiscible displacement data. The solution presented is more efficient than the finite element solution method in terms of requiring less matrix computation effort and it is much more stable than the explicit finite difference solution methods that have been presented in the literature. Due to the ease of formulation and use, the simulation algorithm presented can be used to formulate laboratory numerical simulators that can be used routinely for co-current flow numerical studies.