Summary This paper describes a control-volume finite-element (CVFE) method incorporating linear triangular elements for the simulation of thermal multiphase flow in porous media. The technique adopts the usual finite-element shape functions to evaluate flow potentials at the control-volume boundaries and uses the conservation equations for each control volume. The main advantage of the CVFE method over the finite-difference method is in the representation of complex reservoir geometries. In addition, desirable features, such as local grid refinement for near-well resolution, can be achieved simply and consistently. The control-volume approach enforces local mass conservation and permits a direct physical interpretation of the resulting discrete equations. These are significant advantages over the classical Petrov-Galerkin or variational finite-element methods. The method was implemented in a general-purpose thermal simulator. Numerical examples compare the proposed method with five-point and nine-point finite-difference schemes in terms of grid-orientation effects and run time. The CVFE method was found to reduce grid-orientation effects significantly. At the same time, computational cost was much lower than for the nine-point scheme. The geometric flexibility of the method also is demonstrated. Introduction In many reservoir simulation problems, a flexible discretization method is extremely useful in the definition of complex reservoir geometries and discontinuities (such as faults) and in enhancing the resolution near the wells. The use of Cartesian grids with finite-difference methods has created difficulties and/or complexities in the definition of complex geometries or grid refinements.1-6 It is desirable to adopt the intrinsic grid flexibility of the finite-element method. However, combining upstream weighting with the usual finite-element method for the multiphase multidimensional flow problem presents difficulties. Although asymmetric weighting procedures like the Petrov-Galerkin method7 have been introduced to deal with the convective terms in the mixed convective-diffusive flow problems, such methods are in general not mass-conservative in the local sense. On the other hand, local mass conservation is a specific requirement of the control-volume methods. In addition, reservoir simulation problems can be very complex, involving multiphase mass and heat flow with interphase transfers and chemical reactions. The mass-conservative aspect of the control-volume methods is a distinct advantage in the programming and testing of these simulators. The CVFE method was proposed in computational fluid dynamics for solving the Navier-Stokes equations,8,9 where flexible gridding and local mass, momentum, and energy conservation are achieved. In this paper, a CVFE procedure for the reservoir flow equations is developed where flexible grid geometry is obtained without sacrificing the advantageous attributes of the control-volume finite-difference method. The derivation shows that the use of the perpendicular-bisection10 grid and the seven-point finite-difference method11 are special cases of this discretization method. Recently, Forsyth12 applied a CVFE method to the local-mesh-refinement problem by providing a smooth transition between the coarse and fine grids. As discussed in detail later, a proper choice of the triangular finite-element mesh is crucial to the reduction of grid-orientation effects. The construction of a CVFE grid by triangulation with one of the diagonals of each rectangle in a Cartesian grid (as in Ref. 12) will result in a five-point discretization scheme because the diagonal flow terms for this grid are identically equal to zero. The method results in a set of discretized conservative equations where the Jacobian construction for Newton's method and the upstream weighting of mobilities can be done in the usual way. For the incompressible single-phase flow problem, the method gives the same stiffness matrix as the Petrov-Galerkin weighted-residual finite-element method when linear shape functions are used. The criterion for maintaining positive transmissibility coefficients of a general anisotropic system also is derived. A number of examples are included to demonstrate the geometric flexibility, non-grid-orientation characteristics, and efficiency of the proposed method. p. 349-357
Summary Electrical preheating has been proposed as a method of overcoming many of the problems inherent in using a steamdrive in very viscous oil reservoirs-such as the Athabasca oil sands of Alberta, Canada. A numerical simulator was developed to study the process of electrically heating oil reservoirs consisting of several layers with different electrical resistivities. This simulator was used to study the effects of electrode placement on the final temperature contours resulting from electrically heating realistic reservoirs. Three cases illustrating the development of a hot-oil communication path low in the formation are described. Introduction The recovery of oil from heavy-oil and oil-sand deposits is hindered primarily by the high viscosity of the reservoir oil. For example, the intrinsic viscosity of the bitumen in the Athabasca oil-sand deposit has been estimated to be more than 1000 Pa.s [1× 10 6 cp]. The application of heat is the simplest and most efficient way of lowering bitumen viscosity. The methods of heating the reservoir oil include well-known fluid-injection methods-such as cyclic steam stimulation, steam-flooding, and fire-flooding-and the newer techniques of heating the reservoir with electromagnetic energy. Steam injection and fireflooding techniques are now applied commercially to heavy-oil deposits, but they are still technically difficult and usually uneconomical in very viscous oil-sand deposits. All fluid-injection methods in oil- sand deposits are faced with (1) very low initial injectivity, (2) difficulty in establishing communication paths between wells, (3) poor control of injected fluid movement, (4) reservoir inhomogeneity, (5) steam override, and (6) a very poor mobility ratio leading to a poor sweep efficiency. Electromagnetic heating techniques, which heat the reservoir by means of the ohm losses of electric current flowing in the connate water and the oil of the reservoir, can overcome many of these difficulties. Because no fluid is injected, low initial injectivity is not a problem. Heating occurs both near the well and deep into the problem. Heating occurs both near the well and deep into the formation. In addition, with proper attention to the reservoir lithology and electromagnetic properties, the reservoir may be heated relatively uniformly. Production may occur during or immediately after electromagnetic heating if the formation pressure is sufficient, or electromagnetic heating may be used to preheat the formation for a steamflood or fireflood. The disadvantages of electromagnetic heating should be weighed against the advantages. First, electromagnetic energy is more costly than the same amount of steam energy. The additional cost of the electricity for the same amount of steam energy, however, is usually a small fraction of the total cost of the recovery scheme, and the electrical energy may be directed more efficiently into the formation. Second, electrically insulating all or part of the tubing, casing, and wellhead is necessary to protect the operating personnel and to prevent short circuits. The well completion technology for electromagnetic heating has been developed for some of the simpler heating procedures, but much work remains to be done in this area. procedures, but much work remains to be done in this area. The three types of electromagnetic heating usually considered are radio frequency heating, induction heating, and low-frequency conduction heating. This paper discusses only low-frequency (60-Hz [60-cycle/sec]) electrical heating and reports on our construction and use of the MEGAERA numerical simulator. Several simulation cases are presented to illustrate the simulator's flexibility for studying the electrical heating of the Athabasca oil- sand deposits and to show how the oil-sand formation can be heated almost uniformly with the more conductive adjacent formations as extended electrodes. These results are an improvement over the previously reported electrical heating predictions because actual multilayered reservoir lithologies and properties of the Athabasca oil-sand deposit were used. The simulator and results are described after a short review of the low-frequency electrical heating literature. Previous Work Previous Work Refs. 2 through 5 report on the selective electrical reservoir heating process. SPERE p. 76
An implicit three-dimensional electrothermal simulator has been developed to numerically model multi-phase electric-preheat steam-drive (EPSD) processes in the Athabasca deposit. Two versions of the model are discussed. In the first version (Model 1), the electric preheat phase of process is modelled assuming that fluid expansion and flow can be neglected. The second model (Model 2) accounts for the flow of oil, water, and steam, as well as heat transfer due to conduction and convection during both the electric preheat and steam-drive phases of the recovery process. Data from two simple two-dimensional reservoir simulations using both models are presented and compared. The results suggest that in most circumstances the expansion and flow of fluids during the electric preheat may have negligible effect on the temperature distributions established in the reservoir, and hence, that the computationally less complex Model 1 is generally adequate for simulating EPSD processes in the Athabasca deposit. Finally, an EPSD process in a representative reservoir is simulated using a 1 ha repeated 5-spot pattern with an electric preheat of 365 days. The preheat is followed by a combination of steam and hot waterflooding extending for a period of approximately eight years. Cumulative recovery is shown to be about 60% original-oil-in-place (OOIP) at an OSR of 0.42. Introduction Large portions of the Athabasca oil sand deposits of Alberta have porosities, oil saturations and pay thicknesses that should make them excellent candidates for economical steamflooding. However, to inject steam and produce bitumen continuously at practical rates it is necessary to have some initial fluid communication between injector and producer wells. Under in situ conditions the reservoir fluids in these formations are virtually immobile. In an electric-preheat steam-drive (EPSD) process the reservoir is first selectively heated electrically so as to lower the viscosity of the oil along predetermined paths between wells. Fluid mobilities along these heated interwell channels are generally several hundred times greater than in the original reservoir, and steam can be injected at satisfactory rates, at pressures well below fracture pressure. Electrode wells (which may also be required to serve as injectors or producers), excited at power frequency), are located with due consideration given to reservoir lithology and electrical properties so as to cause current to pass through the regions that are desired to be heated. Electric current flows primarily through the interconnected water paths in the oil sand and the electrical power dissipated along these filamentary paths is rapidly transferred to the surrounding bitumen and to the sand matrix. Detailed considerations for the selection and placement of electrode wells for various reservoir lithologies have been previously reported(1–3). As well, a considerable literature relating to the numerical and physical modelling of electric-preheat processes has developed(1–16). Recently the economics of such processes have been examined by the Alberta Oil Sands Technology and Research Authority(17) and by Petrotec Systems Inc. of Denver(18). Few of the referenced articles consider the problem of fluid flow during electrical preheating(4, 6, 7, 12, 15, 16, 17). Only three of these(12, 15, 17) specifically address modelling of the electric-preheat steam-drive process.
The ability to accurately simulate and optimize fully integrated oil and gas fields is of critical importance in the development and operation of an asset. To this end, a novel and comprehensive framework for simulating fields comprised of connected reservoirs, wells, and production facilities is presented. Individual field components may be connected to each other through physical equipment such as pipes, and operations may be subject to field-wide constraints, such as limits on total production of green house gases. The proposed framework allows for simulation of the evolution of such a field, optimization of the field under various constraint choices, and planning and scheduling of the entire field operations. The framework is founded on representing each component using appropriate sets of Models, Equations and Variables (MEV) combined with a common Physical Property Manager that ensures a consistent calculation methodology, and uses grid-level partitioning to support parallelism. The MEV system operates in concert with customized nonlinear and linear equation solvers to generate updated values for variables in all the different sub-systems, regardless of their originating component. Optimizers in the system manipulate the same variables employed in the MEV solution process to assemble objective functions, act on decision variables, and satisfy constraints. These variables may also be parameterized to support uncertainty analysis or design possibilities. The componentized nature of the equation set allows the ability to plug in alternate custom technologies to replace or augment capabilities. The framework supports multiple fidelities for modelling the components, and enables the use of different coupling styles between them. Choices range from using simple proxy models for certain components, to explicit one- and two-way coupling of more rigorous models, up to solving a fully coupled, detailed field representation. It will be demonstrated that this approach allows for efficient simulation of the combined systems under different constraints.
Summary The RESCUE consortium formed in 1995 in response to the requirement to transfer the structural framework, 3D gridded models, and associated well data from "geomodels to upscalers." RESCUE developed a data standard and libraries that allowed multiple vendors to support subsurface projects across the geoscience and engineering domains. To date, more than 20 of the sponsoring petroleum companies and application vendors have integrated RESCUE into their applications. In late 2008, the consortium began a transition to a much more flexible standard: RESQML™. RESQML joins with WITSML™ and PRODML™ as the latest XML-based data-transfer standards managed by Energistics. The V1.0 developer's release of the RESQML data standard was published in December 2010, followed by a fully commercial V1.1 release in October 2011. We expect vendor applications using RESQML V1.1 to be available commercially in 2012. RESQML has been designed to support Interaction with real-time production and drilling domains Transfer of gigacell reservoir-simulation models, as are currently in use in some areas of the world, together with static reservoir models, which may be several orders of magnitude larger Lossless data transfer for complex grids, especially for nonstandard connectivity Retention of the geologic and geophysical meta-data associated with 3D grids Data standards to support flexible and iterative multivendor subsurface workflows across geology, geophysics, and engineering As an example of the latter, workflows that support fault-seal analysis or 4D-seismic interpretation benefit greatly from the integration of data, metadata, and interpretations from multiple geophysical, geologic, and engineering applications into a coherent subsurface model. Such integration is not possible for a single application or vendor. In this paper, we will present our objectives, challenges, and work plan for 3D/4D-reservoir-model exchange. Details of the technical design defined by participating petroleum oil companies and software vendors will be shared to demonstrate the efficiency of the RESQML standard.
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