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ECMOR VII - 7th European Conference on the Mathematics of Oil Recovery
- Conference date: 05 Sep 2000 - 08 Sep 2000
- Location: Baveno, Italy
- ISBN: 978-90-73781-13-9
- Published: 05 September 2000
48 results
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Inverse viscous fingering to predict proppant back-production
Authors D. van Batenburg and E. BiezenProppant back-production from hydraulically fractured wells is a great operational problem to the oil and gas industry. Apart from safety problems related to erosion of tubing and valves extra equipment and operators are required to handle wells that produce proppant.
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Analytic modelling of production into complex wells
Authors P. J. P. Egberts and P. A. FokkerThe vast amount of completion options for hydrocarbon reservoirs calls for fast productivity evaluation tools. We present a calculation method that can perform this task. It is a semi-analytical method that fully acounts for the 3D flow near the well. A superposition of analytical functions is tuned to approximate the boundary conditions by adjusting a finite number of free parameters. The method can be applied to multi-layer, multi-well reservoir completions with, optionally, finite conductive fractures. Gas reservoirs are approached with a linearization of the pressure equation.
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A multi-point flux approximation scheme for the well modelling in reservoir simulations
Authors Y. Ding and L. JeanninThe control-volume schemes are discussed for the modelling of vertical wells. The key problem of the well modelling is the accurate fluid flow calculation in the well vicinity. In this paper, the flux truncation errors are analyzed on the gridblocks in the near well region. It is shown that truncation errors of the standard approach might be large in the near well region due to the well singularity, and new numerical scheme is needed to be developed to reduce these errors. In this paper, a multi-point flux approximation scheme is presented for the flow modelling in the well vicinity. This scheme can take into account the particular well flow pattern, grid distortion and heterogeneity. It is suitable for any kinds of grids and heterogeneous media
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Use of experimental design in resolving inverse problems - application to history matching
Authors I. Zabalza-Mezghani, G. Blanc, D. Collombier and M. MezghaniHistory matching constitutes a crucial phase in a reservoir study. The aim is to build a model integrating all available data to reduce uncertainties on reliable production forecasts and in particular a model that reproduces the dynamic data.
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Using the gradual deformation method for optimization
Authors M. Le Ravalec-Dupin and B. NoetingerIn this paper, we focus on iterative optimization processes based upon the gradual deformation method. It is shown that such processen converge exponentiatly to the global minimum, at least for linear problems. Additionally, we evidence that the gradual deformation method does not preserve the spatial variability for great numbers of iterations. However, this bias is negligible for practical reservoir engineering problems.
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MPFA for faults and local refinements with application to field simulations
Authors I. Aavatsmark, Ø. Bøe, E. Reiso and R. TeiglandThis paper extends the multipoint fluxapproximation (MPFA) control-volume method to quadrilateral grids for which the adjacent cells do not necessarily share corners. Examples are grids with faults and locally refined grids. This paper gives a derivation of the method for such grids.
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The mathematical modelling of multi-phase flow in inhomogenous media
Authors A. K. Pergament, A. V. Koldoba, Y. A. Poveschenko and N. A. SimousWe have considered the mathematical properties of the filtration equations and demonstrated that there are finite velocities of the shock waves and contact discontinuities of the saturations and phase concentrations. These features are the same ones as tor hyperbolic equations.
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Discretization on non-matching quadrilaterals in anisotropic and heterogeneous porous media
Authors T. Mannseth, J. Mykkeltveit, H. A. Friis and M. HaveraaenUse of non-matching quadrilateral grid cells within reservoir simulation occurs in connection witti local grid refinement and may also occur when modelmg faults. Accurate simulation of multi-phase porous-media flow also requires discretization techniques able to handle non-orthogonal grid cells, strong heterogeneities, and anisotropy witti arbitrary principal directions, in combination.
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Efficient finite volume schemes adapted to a new hybrid mesh model in reservoir simulation
Authors L. Jeannin, S. Sarda, Y. Ding and P. LemonnierThis paper presents finite volume schemes adapted to a new hybrid mesh model. The hybrid mesh is composed of: 1/ a global structured CPG grid describing the reservoir field, 2/ a structured radial grid around each well, 3/ an unstructured polyhedral grid connecting the two previous ones.
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The numerical analysis of convection and diffusion-dispersion effects in multiphase compositional modelling
Authors F. Häfner, A. Behr, A. Nekrassov and D. PolonskiThis paper describes a three-dimensional (3D), three-phase reservoir simulation model for compositional applications.
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Compositional simulation using a new streamline method
Authors F. Bratvedt, K. Bratvedt, P. Childs, M. Crane and R. OlufsenStreamline methods have been used for numerical approximation of the mathematical model for fluid flow since the 1800's and have been applied in petroleum engineering since the late 1950's. For reservoir simulation, however, finite differente simulators have always been the norm. Recently, streamline methods have emerged as an alternative to finite differente simulation for large, heterogeneous modeas that are difficult for traditional simulators to model adequately. 1,2,3,4,5
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The pseude function approach to discretisation
Authors S. Ekrann and T. LitlehamarIn the pseudo function approach, transmissibilities for reservoir simulation are constructed by inverting some (local) model solution of the equations in question.
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Hydrocarbon production forecasting with limited data - how to fill the gaps
By M. NepveuIn the proces of quantifying hydrocarbon production forecast of reservoirs the pertinent questions are: • How do we parameterize reservoirs both meaningfully and efficiently ? • Which criterion should be used in determining how good a history match really is? • How do we search/characterize the parameter space of a reservoir efficiently and in an unbiased manner? • How do we perform forward modeling of the hydrocarbon recovery efficiently, yet with good accuracy?
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E&P Decision support system for asset management
Authors F. J. T. Floris and M. R. H. E. PeersmannIn recent years the emphasis in the development of new methodologies and tools has been on integration. The major software vendors are taking great effort in integrating their software tools to focus on the business proceses. The new challenge lies in using the data generated by these packages to support the decision making proces.
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A gradient-based approach of history-matching of both production and 4 D seismic data
Authors O. Gosselin, A. Cominelli, S. v/d Berg and S. D. ChowdhuryThe reservoir characterisation methods are still improving the integration of all available data for more accurate predictions, but the litmus test remains the history-matching confrontation, after a period of production, between observed data and simulated data as predicted by the numerical model of the reservoir.
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Optimal location of pilot points in history matching
Authors M. Mezghani, F. Roggero and J-P. RaymondThe objective of the pilot point method is to constrain geostatistical realizations to dynamic data. The basic principle of the method is to introduce control points to makelocal modifications in the reservoir model using conditional geostatistical techniques. The pilot point values are inversion parameters that are updated in an optimization process. The main drawback of the method is the lack of criteria for choosing the location of the pilot points.
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Chaotic optimization for reservoir history matching
Authors S. Mantica and G. ManticaComputer-aided history matching of oil production data requires the solution of a challenging minimization problem. Usually, gradient based techniques have been applied to this aim: starting from an initial guess of the solution, these methods converge to the closest local minimum, along specified descend directions. Typically, however, the parameter space is populated by many, local minima, each giving a different response in terms of forecasted production profiles. Theoretically, it is thus important to identify the lowest possible minimum among all candidates.
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Honouring the reservoir characterisation in a 3D simulation model through suitable grid block properties
By C. MonicoThe issue of honouring reservoir characterisation in a 3D simulation model is a critical aspect of reservoir modeping. Hence, a computer calculation procedure has been devised to suitably determine grid block properties.
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A probalistic model for three-phase relative permeabilities in simple pore systems of heterogeneous wettability
Authors M. I. J. van Dijke and K. S. SorbieA method has been developed to determine the saturation-dependencies of three-phase relative permeabilities, based on classification of the underlying pore occupancies in a completely accessible porous medium.
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Coupled inversion of permeability and acoustical impedance - an outstanding data integration
Authors L. Pianelo, D. Guérillot and T. GallouëtThe description of a reservoir internal architecture in Reservoir Engineering needs seismic acquisitions and well tests. They provide us with information about the petrophysical parameters of the underground, such as permeability and the acoustical impedance.
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The benefit of coupling geophysical inversion problems with fluid flow simulation
Authors M. Chacara, I. Magniant, Y. Manin, J-P. Delhomme and N. ÉberléThis paper describes a reservoir monitoring interpretation method that combines time-lapse downhole DC electrical measurements and multiphase fluid flow simulation to infer both the electrical (resistivity) and fluid flow (relative permeability) properties of the medium. The two types of earth properties are linked through petrophysical laws. We use a Bayesian inference approach, where the knowledge of the parameters of interest is quantified through probability density functions. The solution is given by the posterior probability density of parameters related to the relative permeability of each fluid phase
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Modelling chemical displacement in corefloods and the near-well formation to optimise treatments and minimise environmental damage
By E. J. MackayAs waterflooded reservoirs mature, hydrocarbon production will probably be accompanied by high watercuts. However, there are various environmental and formation damage problems associated with water production, additional to the obvious economic disadvantages.
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Flow of water through channels filled with elastically-deformable polymer gels
Authors C. Yang, C. A. Grattoni, A. H. Muggeridge and R. W. ZimmermanA mathematical model is developed for the flow of water through a channel impregnated with a polymer gel.
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Time scaling of the rates of produced fluids in laboratory displacements in porous media
Authors C. Laroche, Y. C. Yortsos and J. KamathIn a recent study¹ it was shown that the ratio of the flow rates of the produced fluids in an immiscible displacement can be used to identify geometrical and petrophysical characteristics of a reservoir. In this paper we consider its application to displacements in 1-D laboratory cores.
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Flow based modules for grid generation in two and three dimensions
Authors A. Castellini, M. G. Edwards and L. J. DurlofskyA novel method for grid generation in reservoir simulation is presented. Grid generation can be simplified by decomposing the domain into a set of subdomains such that modular grid generation can be performed within each subdomain. Local modular grids can be generated according to the local geometry, geology and/or mean flow conditions. The focus here is on the development of three dimensional flow based modules that can be generated locally and independently. A single local flow response can be used to define mean flow streamlines that naturally cluster in high velocity regions of the module. Results computed with the new flow based grids demonstrate a significant improvement in accuracy when compared with conventional Cartesian grids of similar resolution.
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A fast Markov chain Monte Carlo method for conditioning reservoir models to dynamic data
Authors J. Caers and S. SrinivasanThe integration of dynamic data, such as well-test or production data, has become an increasingly important task for accurate reservoir characterization. Integration of dynámic data is mathematically treated as an ili-posed inverse problem.
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Constraining random field models to seismic data - getting the scale and the physics right
By J. CunningA new algorithm for constraining geostatistical models to high density 3D seismic data is described. The algorithm is based on a physically reasonable convolutional forward model to relate high resolution data at the log or simulation scale to the low resolution data available from seismic.
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Simulation of hydraulically fractured horizontal and vertical wells to well testing accuracy using unstructured grids
Authors R. Banerjee, D. Gunasekera and K. FletcherThis paper introduces grids that model vertical and horizontal wells with single or multiple fractures and the flow around them so that even early time effects can be modelled accurately. Algorithms that generate these grids are discussed.
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Modelling of fluid flow around and within highly deviated horizontal wells
Authors G. Heinemann, A. Abdelmawla and S. BrockhauserThis paper presents the implementation of irregularly shaped horizontal and slanted Wells in a fieldscale reservoir simulation model.
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connection transmissibility factors in reservoir simulation for slanted wells in 3D grids
Authors R. A. Klausen and I. AavatsmarkA new simple method for computing the connection transmissibility factor, CF, for a well oriented in an arbitrary direction in a 3D grid is presented.
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Mathematical modelling of sand production by plastic dilatant flow of fragmented matrix under filter forces
More LessSand production from a poorly consolidated formation during gas, oil or water, recovery is an old, but yet unsolved problem of petroleum and geomechanical engineering. To onderstand this phenomenon, it is necessary to find the reasons why sand grafins (that is, fragments of the destroyed matrix) begin to move towards a well.
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Topological shape optimisation in reservoir engineering
Authors D. Rahon, P. F. Edoa and M. MasmoudiThe shape optimisation method is frequently used in solid mechanics. It consists in modifying, in an iterative way, the geometry of the object or the body to be identified in order to minimise a criterion also called the objective function. These optimisation techniques do not allow topology change. The final and the initial body have the same number of components and the connections are not modified.
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Modelling fluid flow in reservoirs crossed by multiscale fractures - a new approach
Authors N. Henn, B. Boubiaux, M. Quintard and S. SakthikumarSome of the most productive oil and gas reservoirs are found in formations crossed by multiscale fractures/faults. Among them, conductive faults may closely control reservoir performance. However, their modelling encounters numerical and physical difficulties linked with (a) the necessity to keep an explicit representation of faults through small-size gridblocks, (b) the modelling of multiphase flow exchanges between the fault and the neighbouring medium, especially if the latter is fractured and modelled as a dual medium.
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Permeability of fractured porous media
Authors I. Bogdanov, V. V. Mourzenko, J. -F. Thovert and P. M. AdlerFlow in fractured porous media was first investigated by Barenblatt and Zheltov (1960) and Barenblatt et al. (1960) by means of the double porosity model. A direct and complete solution of the flow in such media is given in this paper. Some preliminary results are presented and discussed; they show the importance of the percolation threshold of the fracture network and possibly of the porous matrix.
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Application of a truncation error estimate to time step selection in a reservoir simulator
By T. BarkveTime step selection in a reservoir simulator is a balance between minimizing work load and maximizing accuracy. The paper presents derivation of an estimate for the time truncation error for a discretized nonlinear system of differential equations and use of this estimate as basis for time step selection. The relationship between the truncation error and the solution error is discussed.
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Efficient multilevel method for local grid refinement for massively parallel reservoir simulation
Authors L. S. K. Fung and A. H. DogruThe objective of this work is to develop a robust and efficient multilevel parallel algorithm to solve regelar composite grids resulting from local sub-gridding of a multi-million-cell base grid. The strategy is to formulate an iterative scheme on a grid-by-grid basis such that the regelar structure of the matrix at each stage is preserved. The multilevel method applied here utilizes an algebraic fill-in method similar to the one proposed in BEPS but has been generalized to the multi-component multi-phase flow context.
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Implicit scheme and domain decomposition method for multiphase fluid flow in porous medium
Authors E. Flauraud, I. Faille, F. Willien, F. Nataf and F. SchneiderWe are concerned with incompressible three-phase fluid flow in sedimentary basins cut by faults along which block displacements can occur (CERES project). In order to handle these complex geometries, we use Domain Decomposition (DD) techniques. Indeed, faults divide the basin into blocks that naturally define computational subdomains. The mathematical model that describes the physical phenomena leads to a strongly coupled nonlinear system of a hyperbolic equation for saturation and a parabolic equation for pressure.
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Dispersive properties of porous cracked media
Authors E. M. Chesnokov, J. H. Queen, Y. A. Kukharenko, I. O. Bayuk and J. M. HooperThe method of averaging has been very effective in modeling the elastic constants of inhomogeneous anisotropic multiphase media. There are however, many, cases of interest where difficulties arise applying this approach.
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Influence of the fine-scale heterogeneity patterns on large-scale behaviour of miscible transport in porous media
Authors A. M. M. Elfeki, F. M. Dekking, J. Bruining and C. KraaikampAn extensive series of numerical simulations on two-dimensional flow and miscible transport are carried out. The purpose of performing these simulations is to study the influence of fine-scale heterogeneitypatterns (i.e., horizontal laminations, cross-bedding at 45 degrees and 135 degrees) with short range and long range correlation structure on large-scale behavior of miscible transport in porous media.
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Boundary effects in the upscaling of absolute permeability - a new approach
Authors P. Terpolilli and T. HontansIn reservoir engineering, the upscaling of the absolute permeability is now a well established technique.
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Micro-scale diffusion controlled dissolution - a physical analysis of instability based on numerical modelling of dissolution patterns
Authors F. Golfier, D. Lasseux, B. Bazin and M. QuintardAcid injection in porous medium is a process widely used for stimulation of petroleum wells. Acid solution flows into the formation and reacts with the porous solid so that rock permeability increases.
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A fully-implicit upscaling method for accurate representation of the balance of viscous and capillary forces
Authors K. D. Stephen and G. E. PickupIn many cases, small-scale laboratory measurements of relative permeability and capillary pressure must be upscaled carefully to obtain large-scale rock/fluid properties for accurate reservoir simulation.
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On oil displacement by gas injection
Authors V. M. Entov and D. V. VoskovA two-step procedure is developed for solving 1D problems of multicomponent two-phase flow generic for EOR processes based on gas injection. First, general mathematical framework underlying this approach is presented briefly. Then its realization is illustrated by examples for 4- and 5-component systems with constant partition coefficienis and for oil displacement by CO2. Directions of future research are also discussed.
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Nonlinear waves on fluid-fluid interface in porous media as the model of gas-oil fields
Authors M. Panfilov, J-M. Crolet and C. CalugaruThe new mathematical model is proposed to describe the gravity-elasastic deformations of the interface between two fluids in weakly deformable porous media. Instead of a cumbersome system of flow equations linked by the kinetica and dynamica conditions at the interface, the new model represents a system of PDE written explicitly with respect to the vertical coordinate of the interface and the interface pressure.
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