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ECMOR IX - 9th European Conference on the Mathematics of Oil Recovery
- Conference date: 30 Aug 2004 - 02 Sep 2004
- Location: Cannes, France
- Published: 30 August 2004
41 - 60 of 87 results
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A New Fast Fourier Transform Algorithm for Fluid Flow Simulation
Authors L. Ricard, M. Le Ravalec-Dupin, B. Noetinger and Y. GuéguenB005 A NEW FAST FOURIER TRANSFORM ALGORITHM FOR FLUID FLOW SIMULATION Abstract 1 Fluid flow simulators are usually based upon finite difference finite volume or also finite element schemes. As these methods can be CPU-time consuming we develop an alternative approach involving Fast Fourier Transforms to simulate steady-state single-phase flow. In this paper two algorithms are envisioned. They apply to heterogeneous porous media submitted to periodic boundary conditions. Basically the algorithms are designed to solve sequentially the pressure equation in the frequency space. For the first algorithm the convergence rate is proportional to the permeability contrast. It can be pretty
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Multi-Scale Finite-Volume Method for Highly Heterogeneous Porous Media with Shale Layers
More LessB006 MULTI-SCALE FINITE-VOLUME METHOD FOR HIGHLY HETEROGENEOUS POROUS MEDIA WITH SHALE LAYERS Abstract 1 A multi-scale finite-volume (MSFV) method for solving elliptic problem in highly heterogeneous media was recently developed. The goal of the MSFV method is not simply to capture the large-scale effects of the fine-scale heterogeneity but to fully describe the fine-scale velocity field with the original resolution. Thus the MSFV method differs fundamentally from upscaling since it provides an efficient tool for solving large flow problems with fine-scale resolution. The first step in the MSFV method is to compute the effective parameters that are used to solve
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A Finite Element Upscaling Technique Based on the Heterogeneous Multiscale Method
Authors J. Ma and G. CouplesB007 A FINITE ELEMENT UPSCALING TECHNIQUE BASED ON THE HETEROGENEOUS MULTISCALE METHOD Abstract 1 Simulating fluid flow through heterogeneous reservoirs requires the use of upscaling techniques that account for subscale effects but which nevertheless accurately represent the fluid flow behaviors at the reservoir scale. To simulate single-phase fluid flow through a system upscaling often involves estimating the unknown permeability at the coarse scale using information available at the fine scale. Many upscaling methods share a common feature: they define localized fine-scale problems or cell problems and solve them to estimate the permeability at the coarse scale. Cell problems are often
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Comparison of Methods for Downscaling of Coarse Scale Permeability Estimates
Authors A.-A. Grimstad and T. Mannseth1 B008 COMPARISON OF METHODS FOR DOWNSCALING OF COARSE SCALE PERMEABILITY ESTIMATES Alv-Arne Grimstad 1 and Trond Mannseth 1 2 1 RF-Rogaland Research 2 Now with CIPR - Centre for Integrated Petroleum Research University of Bergen Abstract Fine scale reservoir models with all available information integrated are important for predictions of future behavior. Traditionally fine-scale realizations of the geostatistical model are adjusted in some way to integrate production data. Since these data do not support high resolution of the permeability representation strong regularization of the history matching problem is needed. In this paper we study how integration of information may
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Reduced-Order Optimal Control of Waterflooding Using POD
Authors J.F.M. van Doren, R. Markovinovic and J.D. JansenB009 REDUCED-ORDER OPTIMAL CONTROL OF WATERFLOODING USING POD 1 J. VAN DOREN * R. MARKOVINOVI� * AND J.D. JANSEN *+ * Delft University of Technology Dept. of Geotechnology PO box 5028 2600 GA Delft The Netherlands + Shell International Exploration and Production Exploratory Research PO box 60 2280 AB Rijswijk The Netherlands Abstract Model-based optimal control of water flooding generally involves multiple reservoir simulations which makes it into a time-consuming process. Furthermore if the optimization is combined with inversion i.e. with updating of the reservoir model using production data some form of regularization is required to cope with the ill-posedness
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Reduced Representations in Reservoir Simulation – Extending POD to Include More General Optimality Conditions
Authors R. Markovinovic, J.D. Jansen and J.R. RommelseB010 REDUCED REPRESENTATIONS IN RESERVOIR SIMULATION - EXTENDING POD TO INCLUDE MORE GENERAL OPTIMALITY CONDITIONS 1 R. MARKOVINOVI� * J.D. JANSEN *+ AND J.R. ROMMELSE * * Delft University of Technology Dept. of Geotechnology PO box 5028 2600 GA Delft The Netherlands + Shell International Exploration and Production Exploratory Research PO box 60 2280 AB Rijswijk The Netherlands Abstract We consider mathematical reduction methods to generate low-order system representations of high-order reservoir models. In this paper we concentrate on possible extensions of our previous work on the use of proper orthogonal decomposition (POD) for effectively representing the reservoir dynamics (e.g.
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Stochastic Reservoir – The Buckley-Leverett Model
More LessB011 STOCHASTIC RESERVOIR – THE BUCKLEY- LEVERETT MODEL Abstract 1 The stochastic approach has found broad acceptance in weather forecasting global climate modelling or hydrology. In the oil business already in the sixties such tools were used to represent the complex and intricate structure of a porous media. Scheidegger Matheron and Beran were among the people who used such approach to deduce Darcy law at a macroscopic scale the flow being modelized at the microscopic scale by Stokes equation. A modern revival of such an approach more mathematically founded could be the homogenisation theory which was developed since the eighties.
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Stationary Fronts in Hetererogeneous Reservoirs
Authors V. Artus and B. NoetingerB012 STATIONARY FRONTS IN HETEROGENEOUS RESERVOIRS Abstract 1 In this paper we show that the careful study of the two-phase front can improve up-scaling techniques for two phase immiscible flows in heterogeneous reservoirs. A detailed numerical and analytical study of the dynamics of the front shows that stochastic approaches cannot neglect the viscous coupling between the pressure and saturation. A very strong interaction exists between the heterogeneity and the stability or instability of the fluid flow displacement. This coupling is responsible for a qualitative and quantitative change of the form of the large scale equations that must be accounted for
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Macroscopic Simulation of Three Phase Flow Using Consistent Pore-Level Model Relative Permeabilities and Capillary Pressures
Authors K.S. Sorbie, I.S. Ivanova and M.I.J. van DijkeB014 MACROSCOPIC SIMULATION OF THREE PHASE FLOW USING CONSISTENT PORE- LEVEL MODEL RELATIVE PERMEABILITIES AND CAPILLARY PRESSURES Abstract 1 In this paper we perform 1D macroscopic simulations using theoretical three phase relative permeabilities and capillary pressures (3PRPs and 3PCPs) based on simple pore-scale models. These 3PRP models were used to perform a range of 1D three phase macroscopic simulations where “low” and “high” viscosity gas has been injected into a system at constant oil and water saturation. No trapped saturations were allowed in these model calculations in order to clarify the structure of the saturation profiles and the phase paths
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Simulation of Air Injection in Light-Oil Fractured Reservoirs – From the Matrix Block Scale to the Cross-Section Scale by Using a Dual-Porosity Model
Authors P. Delaplace, S. Lacroix, B. Bourbiaux and Y. LagalayeB015 SIMULATION OF AIR INJECTION IN LIGHT-OIL FRACTURED RESERVOIRS – FROM THE MATRIX BLOCK SCALE TO THE CROSS- SECTION SCALE BY USING A DUAL- POROSITY MODEL Abstract Air injection can be an economical alternative for pressure maintenance of fractured reservoirs as it avoids re-injecting a valuable associated gas and/or generating or importing a make-up gas. In addition the oil recovery can be enhanced thanks to the thermal effects associated with oil oxidation. However such an improved recovery method requires a careful assessment of the involved reservoir displacement mechanisms in particular the magnitude and kinetics of matrix-fracture transfers. Considering the situation
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Simulation of Displacement Processes by a LBM VOF-CSF Model
Authors C. Redl and J. SteinerB016 SIMULATION OF DISPLACEMENT PROCESSES BY A LBM VOF-CSF MODEL Abstract 1 The Lattice Boltzmann Method (LBM) is known as a very powerful tool for simulating fluid flow processes in highly complex structures. The structure of porous media can be resolved in detail by means of e.g. computer tomography and afterwards used in the LBM. However most LBM models were restricted to single phase flows or to multiphase flows with only small density differences between the phases. By means of the LBM VOF-CSF (LBM Volume of Fluid- Continuum Surface Force) model it is possible to handle multiphase flows with high
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A Black-Oil and Compositional IMPSAT Simulator with Improved Compositional Convergence
Authors J. Haukås, I. Aavatsmark and M. EspedalB017 A BLACK-OIL AND COMPOSITIONAL IMPSAT SIMULATOR WITH IMPROVED COMPOSITIONAL CONVERGENCE Abstract A unified black-oil and compositional simulator has been developed using an IMPSAT formulation within the framework of the Volume Balance Method. By new ways of determining explicit equations and variables we obtain improved convergence over the traditional compositional formulations. In addition simulator maintenance and development costs are reduced due to the unified formulation. Application of the new formulation to simulation of a multiphase multicomponent problem is presented in the paper. Introduction Reservoir Simulation in General All reservoir simulators solve a set of differential equations. If the reservoir fluids
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Mass Conserving Forward & Adjoint Black-Oil Reservoir Simulation for (Under)Saturated Oil
Authors J.R. Rommelse and C.P.J.W. van KruijsdijkB018 MASS CONSERVING FORWARD & ADJOINT BLACK-OIL RESERVOIR SIMULATION FOR (UNDER)SATURATED OIL 1 J.R. Rommelse & C.P.J.W. van Kruijsdijk Delft University of Technology Department of Geotechnology PO Box 5028 2600 GA Delft The Netherlands Abstract Reservoir simulators that efficiently calculate gradients are not yet widely used because for few control parameters (or little data available) it is feasible to approximate gradients by numerical perturbations. As more parameters need to be handled the need for efficiently calculating gradients increases. In this paper it is shown how to implement a Black-Oil reservoir simulator for (under)saturated oil with gradient capabilities. The usefulness of
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Statistical Moment Equations for Flow in Composite Heterogeneous Porous Media
Authors H. Tchelepi and L. LiB019 STATISTICAL MOMENT EQUATIONS FOR FLOW IN COMPOSITE HETEROGENEOUS POROUS MEDIA Abstract L. Li 1 and H. A. TCHELEPI 2 (1) ChevronTexaco Energy Technology Co. (2) Standard U. We describe a conditional statistical moment equations (CSME) method for quantifying the uncertainty in flow related quantities (pressure and velocity) due to incomplete knowledge (uncertainty) about the permeability field in a composite system. We identify multiple permeability regions in the flow domain. For each region the mean variance and covariance of permeability are specified. We focus on the flow problem; specifically we study the first two statistical moments of pressure for incompressible
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Analysis and Design of Coreflow Experiments
By A.E. FinchamB020 ANALYSIS AND DESIGN OF COREFLOW EXPERIMENTS Abstract 1 T. FINCHAM TOTAL UK Geoscience Research Center 33 Cavendish square LONDON UK Relative permeabilities are empirical factors that are used to correct the single-phase Darcy’s law for application to multiphase flow. The relative permeability of any phase is an increasing function of the phase saturation. Relative permeabilities are important input data for reservoir simulation studies and have a strong influence on reservoir behaviour. There are several different types of laboratory experiments on core samples that are used to find the relative permeability of reservoir rock: unsteady state steady-state centrifuge. To extract
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Toward Reservoir Simulation on Geological Grid Models
Authors J.E. Aarnes and K.-A. LieB021 TOWARD RESERVOIR SIMULATION ON GEOLOGICAL GRID MODELS Abstract 1 We present a reservoir simulation scheme that gives accurate resolution of both large-scale and fine-scale flow patterns. The method uses a mixed multiscale finite-element method (MMsFEM) to solve the pressure equation on a coarse grid and a streamline-based technique to solve the fluid transport on a fine-scale subgrid. Through this combination we aim towards a numerical scheme that facilitates reservoir simulation of large heterogeneous geomodels without upscaling. We validate the method by applying it to a 3D upscaling benchmark case taken from the 10th SPE Comparative Solution Project. The numerical
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Parallel Anisotropic Cartesian Grid Adaptation for In-Situ Combustion Simulations
Authors J. Nilsson, M. Gerritsen and R. YounisB022 PARALLEL ANISOTROPIC CARTESIAN GRID ADAPTATION FOR IN-SITU COMBUSTION SIMULATIONS Abstract 1 A parallel anisotropic adaptive Cartesian grid method for simulating in-situ combustion processes is presented. It is based on local cell-based grid refinement that allow fast transition from coarse to fine grids with very few extra cells. The anisotropic refinements allow for an improved alignment of the grid with important features in both the flow and the geology. The pressure equation is discretized on these anisotropic cells with a novel higher order compact finite volume method. The fluxes are computed with a second order accurate finite difference approximation combined
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A Parallel, Multiscale Approach to Reservoir Modeling
Authors O.I. Tureyen, O. Karacali and J. CaersB023 A PARALLEL MULTISCALE APPROACH TO RESERVOIR MODELING Abstract 1 Fine scale heterogeneities may have a significant effect on flow performances in subsurface formations. A large number of grid cells are required to capture the effect of such heterogeneities on flow responses. However flow simulation is rarely feasible without prior upscaling. This presents a problem for the joint integration of fine (well-log) and coarse (seismic production) data. Most approaches proceed in a hierarchical fashion where small scale data is integrated on the fine scale and after upscaling large scale data is integrated on a separate coarse scale. The correspondence between
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Reservoir Streamline Simulations Accounting for Effects of Capillarity and Wettability
Authors R.A. Berenblyum, A.A. Shapiro and E.H. StenbyB024 RESERVOIR STREAMLINE SIMULATION ACCOUNTING FOR EFFECTS OF CAPILLARITY AND WETTABILITY Abstract 1 In this work we present the mathematical grounds and the numerical developments necessary for introduction of the capillary forces and the wettability into a streamline-based simulator. The corresponding simulation tool (the CapSL simulator) has been developed on the basis of the 3DSL0.25 streamline simulator by R.Batycky SUPRI-C group Department of Petroleum Engineering Stanford. Our simulator is capable of predicting the two phase displacement with full account for capillary effects varying between different zones of a heterogeneous reservoir. Introduction In this paper we briefly describe the mathematical grounds
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A Front-Tracking Method for Hyperbolic Three-Phase Models
More LessB025 A FRONT-TRACKING METHOD FOR HYPERBOLIC THREE-PHASE MODELS Abstract 1 We develop and apply a front-tracking method for the numerical simulation of three-phase flow in porous media. The proposed framework combines analytical solutions to the corresponding Riemann problem with an efficient front-tracking method to study Cauchy and initial-boundary value problems. The method has the ability to track individual waves and give very accurate (or even exact) resolution of discontinuities. This numerical procedure is then used in combination with a streamline method for the simulation of three-dimensional three-phase flow problems. We demonstrate the applicability of the method through several numerical examples
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