A 3-D field scale steam injection simulator is developed and tested. The three-dimensional multi-phase mass and energy flow equations are based on compositional balances. A fully implicit numerical solution method is implemented in the solution of the nonlinear system of equations. The model solves for (nhcd+5) primary variables simultaneously where n, denotes the number of hydrocarbon components permissible. The accuracy and efficiency of the model is verified and benchmarked against the compositional problem of the Fourth SPE Comparative Solution Project: Comparison of Steam Injection Simulators. Large computational time and extensive hardware facility requirements are the two major sources of difficulty on compositional simulation of hydrocarbon reservoirs. Nonetheless, it is important to include the correct physics of the problem to be modeled in fine details. The problem is aggravated more by the highly nonlinear nature of most of the improved oil recovery operations requiring computationally demanding, numerically stable fully implicit solutions. Although explicit formulations or semi-implicit formulations are computationally less demanding, they cannot adequately handle highly nonlinear nature of the chemistry and physics encountered in most of the oil recovery operations making their application almost impossible for this class of problems. In this paper by investigating a trade-off between the degree of implicitness and stability as well as a required level of accuracy of the results and computational time, we present a sensitivity analysis of the research results obtained by solving the mathematical model via various implicit formulations with different sets and numbers of primary variables. Understanding the relationship between the degree of implicitness and the accuracy of the simulation results will help in deciding on the degree of refinement of the grid blocks and level of detail of the actual problem representation in the simulation model. In order to speed up the simulator, for each of the implicit formulations implemented, various primary variable/equation alignment schemes are considered in the construction of the Jacobian. The simulator is tested using a wide range of compiler/CPU combinations. While performing well on a certain computational environment the very same alignment may result in logarithmically singular Jacobian on another compiler/CPU combination. An analysis on the round off error dependence of the mathematical stability of the Jacobian as a function of primary variable/equation alignment schemes is presented. Accordingly, a set of criteria for the optimum primary variable/equation alignment is proposed to increase the efficiency of the model. To the authors' knowledge, the model presented in this paper is one of the more implicit models reported in the literature. The developed simulator is found to be strongly stable and internally consistent even for the most dynamic and stiff systems as the ones studied in this research. This is benchmarked by the model's ability in accommodating large average time step sizes of over 50 days and its high average convergence rates of less than three Newtonian iterations per time step. Introduction Steam injection has been successfully implemented in oil reservoirs as an EOR method. Approximately 70% of oil produced through EOR methods is by steam injection. There are three predominant forces acting on a reservoir fluid system. These are viscous, gravitational, and capillary forces. All of the recovery techniques target these forces to increase oil production through different mechanisms. In a steam injection operation. it is possible to take advantage of all the acting forces. The success of a steam injection operation depends on designing and applying the most optimum recovery operations as much in detail as possible as to how the aforementioned forces and mechanisms are controlled. During the steam injection into an oil reservoir dramatic temperature and pressure changes, which in turn cause compositional changes in the fluid phases, take place. Obviously, changing the composition of liquid and gas hydrocarbon phases and their net effects can be more adequately represented by a compositional model rather than a non-compositional model. There are numerous studies about the subject. The Fourth SPE Comparative Solution Project compares the commercial steam injection simulators used by the participating six organizations. There are three independent problems studied; two of the problems fall into the "black-oil" type simulation category, and the third one is a compositional problem. Only three of the participating six organizations submitted results for the compositional problem. The project presents selected results submitted by the participating organizations, and in general indicates good agreement. However, still there are some considerable discrepancies. P. 269

A numerical simulator for steam displacement of oil from naturally fracturedreservoirs is developed and tested.The three-dimensional and three phasefield scale model employs a compositional dual-porosity/dual-permeabilitymathematical formulation.Capillary, gravitational and viscous forces areaccounted for in the mathematical model.Using a fully implicit solutionscheme, the model solves for (2nHC+10) primary variables simultaneously, wherenHC is the number of hydrocarbon components.All reservoir parameters areformulated as functions of all the primary variables.The model islinearized using Newton-Raphson method, and the system of linear equations issolved by a direct and an iterative solver.The model is verified againstthe Fourth and Sixth SPE Comparative Solution Projects.The model ishighly stable for the studied extremely dynamic and stiff problems, accommodating large time steps with two to three Newtonian iterations.Thesimulations are carried out up to ten years to test the features of the modelfor long periods of steam injection in naturally fractured systems. Fluid exchange between the fracture and the matrix blocks due to thegravitational, capillary and viscous forces is investigated for a range ofnaturally fractured reservoirs with different matrix block sizes and capillarypressures.Relative effects and relative magnitutes of these acting forceson the displacement of the matrix oil are analysed in these naturally fracturedsystems undergoing steam injection.This comprehensive and comparativeanalysis is conducted using different realizations of the studied naturallyfractured systems such as the dual-permeability and the dual-porositymodels. The steam injection operations are carried out for long periods oftime.The low initial pressures in the studied fractured systemsfacilitate zooming in on and observing how, in particular, the capillary andgravitational forces work, and testing the model under more strained conditionsin a naturally fractured reservoir undergoing a steam injection operation. Introduction Modeling fluid flow in naturally fractured reservoirs, particularlyaccounting for the matrix/fracture fluid exchange, has been an extremelychallenging problem for the researchers[1–6].Steam injection in naturallyfractured reservoirs provides even a more difficult problem numerically and interms of accounting for the gravitational, capillary and viscous forces in thematrix/fracture fluid exchange.It is important to understand how thecontinuously changing roles of these capillary and gravitational forces and theresulting fluid displacement mechanisms work during an entire steam injectionoperation in a naturally fractured reservoir. The single-phase pressure transient anlysis and isothermal multi-phase fluidflow studies form a major part of research conducted in the area of naturallyfractured reservoirs.In this study, the research is focused on the actingforces in the matrix/fracture flow potential in a field scale study of streaminjection operation in a naturally fractured reservoir.A naturallyfracture reservoir with a relatively lower initial formation pressure isinvestigated in order to better focus on and understand the relative roles ofthe capillary and the gravitational forces on the steam displacement of oilfrom the matrix blocks. In this research, a comparative analysis is employed regarding the effectsof the viscous forces, gravitational forces and the matrix capillary pressureterms in the matrix/fracture potential expression on the steam displacement ofthe matrix oil in a range of naturally fractured reservoirs.Thiscomprehensive investigation should provide us with more understanding on therelative interactions among the acting forces in the matrix/fracture flowpotential, and also their relative effects on the fluid flow mechanisms betweenthe matrix and the fracture systems. A wide range of approaches is present in the literature in order to accountfor the effects of gravitational and the capillary forces[7–13].In thisresearch, unmodified capillary pressure and relative permeability values areused in both of the dual-porosity and the dual-permeability models of thenaturally fractured reservoir.The present investigation should contributeto the determination of level of confidence in designing optimum steaminjection operations in naturally fractured reservoirs.

fax 01-972-952-9435. AbstractThis research effort discusses the effects of a comprehensive range of fluid, rock-fluid and operational properties on the efficiency of steam injection in naturally fractured reservoirs with heavy oil. For this purpose, a fully implicit dualporosity/dual-permeability simulator is developed, and the model is applied to an inverted nine-spot pattern in a naturally fractured reservoir with heavy oil. The effects of the reservoir and operational properties on the steam displacement of heavy oil are studied comparatively in naturally fractured reservoirs with and without interacting matrix blocks and in approximate single porosity realizations of these naturally fractured reservoirs.The field scale numerical model is three-dimensional and three phase accounting for capillary, gravitational and viscous forces. The model solves for (n HC +5) primary variables simultaneously, where n HC is the number of hydrocarbon components. The fully implicit model formulates all reservoir and operational parameters as functions of all the primary variables. The model is linearized using the Newton-Raphson method. A direct and an iterative solver is used in the solution of the system of linear equations.The simulations of steam injection in naturally fractured systems are carried out for long periods of time in order to test the features of the model under strained conditions. The model is verified against the Fourth and Sixth SPE Comparative Solution Projects.This study should help in screening naturally fractured reservoirs for steam injection, and in designing steam injection operations in these reservoirs.The comparative analysis of the effects of reservoir and the operational parameters in naturally fractured reservoirs should provide insight into the range of confidence of heavy oil recovery from naturally fractured reservoirs by steam injection.

This study presents development and verification of a field scale compositional and non-isothermal numerical simulator for CO2 sequestration in naturally fractured systems/coalbeds. The main body of the model is three-dimensional, and four-phase mass and energy flow equations are based on compositional balances. Dual-permeability approach is used for the mathematical formulation of the problem. Single-porosity and dual-porosity approaches, subsets of the dual-permeability formulation, are considered as the second and the third approaches in the mathematical formulation of the problem. The model accounts for fluid displacement due to capillary, viscous, gravitational forces and diffusion. The field-scale simulator is developed using a fully implicit numerical solution considering the highly non-linear nature of the problem. The proposed formulation assumes (potential) nonlinearity for all the reservoir and operational parameters with respect to all primary variables identified. (2nhc+10) primary variables for each grid block are solved simultaneously, where nhc denotes the number of hydrocarbon components permissible. A direct solver is used for the resulting system of linear equations. The present model is verified and benchmarked against two SPE Comparative Solution Projects; the Sixth SPE Comparative Solution Project: A Comparison of Dual-Porosity Simulators1, and the compositional problem of the Fourth SPE Comparative Solution Project: Comparison of Steam Injection Simulators2. In addition to these two benchmark problems, the model is tested and verified against a coal seam degasification problem from the literature3. The present study is capable of handling the ever-changing relative effects of the various dominant forces on the establishment of fluid displacement mechanisms. The model formulation also accounts for complex fluid flow problems involving thermal effects, injection and production of fluids of different compositions as well as various composite fluid systems encountered in a given system. Having formulated sorption phenomena as a function of composition, pressure and temperature, various sorption mechanisms in coal seams would be studied by the present model. The developed model is very flexible and capable of enveloping a number of different reservoir domains and different types of problems. As a result the present study should enable us test various hypothesis leading to improved conceptualization and modeling of fluid flow in naturally fractured geological systems. Introduction Naturally fractured formations are very common all around the world and important sources of oil, gas, water and geothermal energy, and are related to critical environmental issues as well. These environmental problems include CO2 sequestration and contaminant disposal (including nuclear waste) into geological formations. Development and management of such reservoirs depend on the use of numerical simulators. The sequestration of CO2 into the subsurface has enormous potential for helping to stabilize the atmospheric concentrations of greenhouse gases. Carbon taxes provide immediate incentives for advancing the necessary technologies. Moreover, more than 80% of oil reservoirs worldwide might be suitable for CO2 injection based upon oil-recovery criteria alone4. Several potential disposal targets could be depleted and undepleted oil and gas reservoirs, deep saline aquifers, salt caverns and coalbeds. Coalbeds are particularly attractive when coal seam gas is displaced and produced by CO2 sequestration, thus, significantly improving the economics of such disposal. CO2 is physically adsorbed by coal and hence safe from rapid and catastrophic releases. These considerations make coalbed sequestration very attractive for on-shore disposal of CO2. The sorption phenomenon in coal seams is a strong function of composition of the sorbed gas and has to be modeled accordingly. In addition, temperature dependence of sorption of gases on solids is one of the considerations that need to be addressed in modeling of CO2 sequestration operations5,6,7,8.

Steam injection in naturally fractured reservoirs provides an extremely challenging problem as well as a potentially effective and efficient improved oil recovery method.Coupling of the two distinct and contrasting matrix and fracture systems results in a highly non-linear problem, and it gets even more complicated as a result of steep changes in fluid properties due to the thermal effects of steam injection.Modeling and designing an optimum steam injection operation in such systems requires an accurate characterization and representation of a naturally fractured reservoir and steam injection operation parameters and dynamics. In this research effort, a thermal dual-permeability/dual-porosity numerical model is developed for the problem.The multi-phase fully implicit model is three dimensional and compositional, accounting for viscous, capillary and gravitational forces.The model incorporates detailed anisotropic and heterogeneous reservoir property description, and formulates all reservoir and operational parameters as functions of all the primary variables, (2nHC+10), where nHC is the number of hydrocarbon components.The multi-layer production and injection wells are coupled to the reservoir fully implicitly.Both an iterative and a direct solver are employed in the solution of the resulting system of linear equations.The present model is verified and benchmarked against two SPE Projects. A comprehensive and comparative study is conducted in order to understand the relative effects of naturally fractured system and injection operation properties on the oil recovery performance.This comparative sensitivity analysis is performed using the dual-permeability, the dual-porosity and the approximate conventional single-porosity model. In search of some practical guidelines, each reservoir system and operational property is studied in a range of naturally fractured reservoirs such as with different matrix block sizes, fracture/matrix permeability ratios and capillary pressures.The present study should help us better understand fluid flow dynamics, design optimum recovery operations and determine range of confidence for an oil recovery operation in naturally fractured reservoirs undergoing steam injection Introduction As one of the heterogeneous systems, the naturally fractured reservoirs have been an active research subject1.The difficulty in modeling of naturally fractured reservoirs arises from the capillary discontinuity at the fracture/matrix interface.The parameters governing fluid flow dynamics in naturally fractured reservoirs are different than those of single porous systems.Highly non-linear nature of steam injection compounds the existing problems of modelling naturally fractured reservoirs undergoing steam injection[2,3,4]. A major part of research interest in the naturally fractured reservoirs has focused on single-phase pressure transient analysis.The multi-phase fluid flow studies in naturally fractured reservoirs include black oil and compositional simulation, most of which is directed towards waterflooding.Some of the existing thermal simulators are applied to naturally fractured hydrocarbon reservoirs[5], and some others have had specialized applications in geothermal reservoirs[6], and carbonate reservoirs[7].In some cases, conventional steam injection models[8] are employed to model naturally fractured reservoirs. Extensive research efforts are directed towards understanding the flow mechanisms and parameters governing fluid flow in naturally fractured reservoirs[9,10,11].These studies are both numerical and experimental in nature.However, it is still generally accepted that further research is needed for a better understanding of mechanisms of mass and heat flow in the naturally fractured reservoirs.