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ECMOR XII - 12th European Conference on the Mathematics of Oil Recovery
- Conference date: 06 Sep 2010 - 09 Sep 2010
- Location: Oxford, UK
- ISBN: 978-90-73781-89-4
- Published: 06 September 2010
101 - 117 of 117 results
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Simulation of Flow Effects during Acidizing in Carbonate Oil Reservoirs
Authors R.D. Kanevskaya, I.A. Volnov and A.U. MarkovaThe acidizing and the acid fracturing are the most common and effective methods of well stimulation for carbonate reservoirs. These technologies permit cleaning and extending pore channels and creating new channels and fractures. The new mathematical model of acidizing in carbonate reservoir is presented. It accounts for two-phase flow of oil and acid water solution, kinetics of rock dissolution and porosity increasing. It is suggested that the salt generated by the reaction dissolves in water and the carbon dioxide is oil and water soluble. The permeability is assumed to be porosity dependent. Both acidizing and acid fracturing are considered. Numerical solution of the problem is obtained. Some analytical results are derived using the characteristic method for quasilinear equations. The model allows investigating dimensions of the acid penetration zone, the duration of the dissolution reaction and the needed length of the shut-in period. It makes possible to optimize the acid treatment design. On the basis of the obtained solution the efficiency of acid treatment and acid fracturing is estimated by calculation of the achieved skin-factor. Some real cases are analyzed, field and calculated data are in good agreement.
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Coupled Geomechanics and Reservoir Modelling in SAGD Recovery
Authors S.Z. Zandi, G.R. Renard, N.J. Nauroy and N.G. GuyThe Steam Assisted Gravity Drainage (SAGD) process is a thermal enhanced oil recovery (EOR) method which appears tremendously successful, especially for bitumen. SAGD process results in a complex interaction of geomechanics and multiphase flow in cohesionless porous media. In this process, continuous steam injection changes reservoir pore pressure and temperature, which can increase or decrease the effective stress in the reservoir. Quantification of the state of deformation and stress in the reservoir is essential for the correct prediction of reservoir productivity, seal integrity, hydro fracturing and well failure. In SAGD process, reservoir geomechanics analysis is concerned with the simultaneous study of fluid flow and the mechanical response of the reservoir. The objective of this paper is to show the importance of taking into account the role of geomechanics in SAGD numerical modelling and to provide a better description of the rock contribution to fluid flows in the SAGD process. Therefore, we introduce a geomechanics-reservoir partially coupled approach, which allows a better prediction of the SAGD process to be performed. The results of numerical simulations show that the classical treatment of deformation of reservoir through the rock compressibility in the conventional reservoir theory is not a rigorous framework to represent the evolution of high porous rock strains that play a significant role in the performance of SAGD.
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Simulation of Interface Dynamics Across Pore Discontinuities
Authors R. Maniero and I. LunatiWe study the dynamics of a water-oil meniscus moving from a smaller to a larger pore. The process is characterised by an abrupt change in the configuration, yielding a sudden energy release. A theoretic study for static conditions provides analytical solutions of the surface energy content of the system. Although the configuration after the sudden energy release is energetically more convenient, an energy barrier must be overcome before the process can happen spontaneously. The energy barrier depends on the system geometry and on the flow parameters. The analytical results are compared to numerical simulations that solve the full Navier-Stokes equation in the pore space and employ the Volume Of Fluid (VOF) method to track the evolution of the interface. First, the numerical simulations of a quasi-static process are validated by comparison with the analytical solutions for a static meniscus, then numerical simulations with varying injection velocity are used to investigate dynamic effects on the configuration change. During the sudden energy jump the system exhibits an oscillatory behaviour. Extension to more complex geometries might elucidate the mechanisms leading to a dynamic capillary pressure and to bifurcations in final distributions of fluid phases in porous media.
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Modeling of Shut-in Well Fluid Redistribution
More LessThis paper presents a mathematical model devised to simulate the hydrocarbon fluid redistribution in a well, from steady-state flow until the fluid columns are fully segregated upon equilibrium over the shut-in period. The modeling of shut-in well depends greatly on grasping the underlying physics to mathematically describe and model the transient flow process. A pre-calculation to obtain the steady-state flowing gradient is performed to acquire input for the shut-in model. The salient features of this shut-in modeling process are described, including simulation of (1) gas-liquid interface movement, (2) reservoir fluid influx, (3) wellhead pressure build-up, and (4) bottom-hole pressure build-up over the transient fluid redistribution period. Three producing oil wells in Malay Basin were selected to assess the shut-in well modeling capability. The evaluation showed that the model predicted wellhead and bottom-hole build-up pressure are in good agreement with the pressure build-up test results obtained from the field. This methodology provides an alternative mean to obtain bottom-hole data without well intervention, which provides insight into well performance, improves reservoir management and decision making.
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Modeling of Pressure and Solution Gas on Microemulsion Phase Behavior
Authors M. Roshanfekr and R.T. JohnsThe effect of pressure and solution gas in crude can significantly change the optimal salinity of a surfactant flood (SP). The shift in the optimal salinity must currently be measured using high pressure experimental equipment, which is difficult to perform. This paper presents a novel approach to predict optimum salinity for live crudes at high pressure based solely on optimal salinity and solubilization ratio measurements made at atmospheric pressure. We use the well established relationship that the logarithm of the optimum salinity is a linear function of the equivalent alkane carbon number (EACN) at atmospheric pressure. The procedure corrects that data for the effect of pressure and methane content in the oil. We compare our predicted results to all high-pressure data available in the literature. We show that the linear trend of the logarithm of optimum salinity with EACN can be accurately corrected to higher pressures based solely on alkane density changes at atmospheric pressure. A similar correction can also be made for the optimum solubilization ratio. The optimal salinity for live crude is determined from the calculated EACN for the live oil, and the calculated optimum salinity versus EACN relationship at the pressure of interest. The results very accurately predict and explain all measured data in the literature, including that of Puerto and Reed (1983). We further incorporate the method in UTCHEM, where the optimum can vary spatially based on calculated methane content (using a cubic EOS) and pressure.
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Dynamic Foam Behavior in the Entrance Region of a Porous Medium
Authors E. Ashoori, D. Marchesin and W.R. RossenIn foam EOR, complex dynamics of bubble creation and destruction controls foam properties. Here we focus on the entrance region, where injected gas and liquid are transformed into foam. We solve for water saturation and foam texture in the entrance region using the population-balance foam model of Kam (2008), which features three steady states (no foam, strong foam, and an unstable intermediate state) at some injection rates, as seen in experiments. If foam is not pre-generated, and capillary-pressure gradients are neglected, as in many published simulation studies, the final steady state downstream is the one with highest water saturation - the weakest foam. In some cases, in the presence of capillary pressure, analysis of the asymptotic dynamic behavior in the vicinity of possible downstream steady states may rule out some possible steady states. We show that the apparent length of entrance region can be quit different if one measures water saturation or pressure gradient. Finally, we fit foam kinetic parameters to the length of the entrance region seen in some experiments; a companion paper (Ashoori et al., 2010b) investigates the effect of these parameters on the traveling wave at the shock front downstream.
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Multi-dimensional Multi-variant and Multi-scale Modeling of Reservoir Heterogeneities
Authors J.W. Huang, G. Bellefleur and B. MilkereitReservoir heterogeneity in this study is the term describing the spatial distribution of dissimilar rock properties in the earth medium. Reservoirs contain multiple petrophysical properties, each having different degrees of statistical correlations with others. For example, compressional wave velocity is usually positively and strongly correlated with shear wave velocity, whereas the correlation of density to resistivity or porosity to permeability is often not straightforward. In this paper, we describe a new method to model three dimensional heterogeneous rock properties at different correlation lengths. This algorithm is able to honor different degrees of correlation among multiple reservoir petrophysical properties, match borehole logs and simultaneously mimic the statistical features observed in the data. It provides a heterogeneous environment in which a variety of geophysical experiments can be performed. This includes the estimation of petrophysical properties and the study of geophysical response to the heterogeneities. In addition, our approach can be easily implemented on current parallel architectures to construct large three dimensional reservoir models without loss of accuracy. We apply the modeling approach to the gas hydrate reservoir located in Northwest Territory of Canada, where in situ gas hydrate volume is estimated. We show that by using rock physics theory, statistical parameters estimated from well logs, and the horizontal correlation length estimated from acoustic impedance inversion, the amount of gas hydrate is nearly an order of magnitude lower than earlier estimates which did not include effect of small-scale heterogeneities. Monte Carlo simulations show that the estimated amount and uncertainty of gas hydrate will decrease if the stochastic models are conditioned by well logs. The synthetic cross borehole seismic data illustrate that strong scattering due to the multi-scale heterogeneities can have a severe impact on seismic imaging of the reservoir.
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Magnesium from Solution Mining of Bischofite Layers and Carnallite Layers
Authors R. Velema, J. Bullen, J. Visser and J. BruiningThe MgCl2 raw material is recovered using solution mining at a depth of a 1500 to 2000 meters. These caverns are formed in stacks bischofite, carnallite and halite (NaCl). The bischofite (carnallite) layers consist mainly of NaCl and but contains at least 35% MgCl2. The recovery is implemented by the injection of fresh water in the potassium/ magnesium salt layer which becomes saturated with MgCl2. The carnallite and bischofite layers largely consist of the less soluble NaCl, with interdispersed magnesium salts. In this case, the main transport mechanism would be natural convection through a porous salt layer. It is interesting to know whether a sponge like structure will remain after carnallite and bischofite are eaten out of the NaCl matrix or whether this structure collapses by the omnipresent stress fields. Comparison of field data with the presented model can in principle be used to answer this question
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Developing and Analysis of a Mathematical Model to Predict Temperature and Inflow Profile in Multi-lateral Wells
Authors M. Mostofinia, J. Mohseni, P. Pourafshary and Z. LavafianIn wells with multiple pay zones, portion of each layer in total flow rate is a long standing challenge. Aim of this paper is to find one of temperature log avail namely inflow rate estimation. However current methods can give the inflow rate only for single phase flow. In this paper a novel temperature distribution model is developed in wells with multiple pay zones.It accounts for all the real conditions such as non-homogeneous multiphase flow and phase changes which have been ignored by previous authors. A temperature model in reservoir accounting for oil degassing, convection and conduction heat transfer is coupled with wellbore model. Then the model was used as a tool to find inflow rate from each pay zone. We found produced water and gas from reservoir is cooler than produced oil while water coning cause warming effect. Also, it has been shown that how ignoring oil degassing in reservoir cause overestimation of sandface temperature. The predicted inflow rate from temperature model was compared with spinner flowmeter results. The error was between 10-15 percent which is reasonable. This work is helpful to identify zones producing excessive water or gas entries and realize necessity of reservoir stimulation.
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The Flows Features of Viscous-plastic Fluids in Anisotropic Porous Media
Authors V.V. Kadet, N.M. Dmitriev and M.T. MamedovModern state of the oil extraction is characterized by increase of hard recoverable reserves of hydrocarbon raw material including quasiviscous oils occurring in anisotropic reservoirs. As a rule such oils are the viscous-plastic fluids which flow in porous medium appears after the excess of some limiting gradient of pressure. In the last century the flow law of viscous-plastic fluids in isotropic layers has been offered. This law requires generalization on a case of flow in anisotropic porous media, so long as real reservoirs of hydrocarbons show the anisotropy of reservoir properties. In the present paper are received the flow laws of viscous-plastic fluids in all types of anisotropic porous media. The laboratory method of combined determination of the absolute permeability tensor and the tensor of limiting gradient of pressure for anisotropic reservoirs is suggested. The results of experiments spent by the given method which confirm tensor nature of the limiting gradient of pressure are presented. Presented expressions for flow laws with limiting gradient of pressure can be used in hydrodynamic simulators under the modeling fields of quasiviscous oils.
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Bottomhole Formation Zone Modeling Using Analytical and Numerical Approach
Authors S. Stepanov and V. VasilyevAt present, most of the companies that work in oil and gas industry are facing the situation which urges them to improve the efficiency of field development and, particularly, residual resources development. The solution of this problem requires comprehensive approach which should account for all significant factors attributable to field development including the consistency of hydrodynamic simulation modeling. This is especially concerned with the genuine understanding of correct modeling of processes occurring in bottomhole formation zone, both from the point of displacement processes physics, and from the point of mathematical algorithms applied to solving respective differential equations. From the above standpoints this paper furnishes the findings of bottomhole formation zone modeling problem study. Calculations were made for individual wells. It is shown that the complex nonmonotonic actual watercut history of the well can be represented by solving respective inverse problems with proper account taken for capillary and deformation processes. The relative phase permeabilities vs. pressure gradient relationship and capillary-gravity transition zone allow explaining of nonmonotonic watercut well history even at the constant well flow rate. The degree of inaccuracy in reservoir performance calculations made on numeric filtration models using coarser grids is supported by well-watercut analytical solution. In this context the concept of correction function that allows smoothening of coarse cells impact is introduced. It is also shown that use of stream line method in the well-vicinity area allows essential improvement of flow structure description and enhancement of reservoir performance calculation adequacy. Thus, when solving the problems of practical importance it appears that though the existing software simulators are capable of generating history-matched numerical filtration models, in most of the cases such models are not adequate to the reality, especially in terms of describing bottomhole formation zone processes.
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Formation of Set of Injectors on Oilfields
Authors A.I. Ermolaev, A.M. Kuvichko and V.V. SolovyevThis paper describes optimization of non-great oilfields work with complex geology. If oilfield has complex geology and great heterogeneity of its properties then non-regular grids is effective. There are two different strategies. First is to find rational placement of new injectors with the given placement of producers. Second is to find some producers rationally to convert them to injectors. In the first task the term ‘rational placement’ is a placement of injectors which provides possible minimum of total distance from injector to each connected producer and the average equality of connected producers to each injector. In the second task the term ‘rational conversion’ is a conversion when producers with maximum water cut and water production are converted to injectors, but the possible minimum of total distance from each injector to connected producers is provided. Included heuristic criteria and their levels of factor may vary depending on expert evaluation. It allows including not only geological and technical information and makes these algorithms very flexible. All tasks are formed in terms of integer programming, so they can be solved using special algorithms. Described models and algorithms are rational to use for making good initial reservoir work design.
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Effective Permeability Calculation a Numerical Artifact or Genuine Problem
Authors M. Pal and J. JenningsABSTRACT Subsurface reservoirs generally have a complex description in terms of both geometry and geology. This poses a continuing challenge in modelling and simulation of reservoirs due to variations at different length scales. Consequently, averaging and/or homogenization techniques are needed to scale up the fine scale grid information to resolve the flow on coarse grid. The representation of fine grid properties on a coarse grid scale is obtained via the principle of upscaling. Upscaling has been standard procedure in reservoir simulation for many decades. Upscaling approaches used in industry ranges from analytical to numerical upscaling. In recent years with the increase in complexity of geological models there has been a greater push in the industry towards used of numerical upscaling techniques. In this paper we will present some numerical experiment using standard finite-difference simulators to address the challenges, which still exists in application of numerical upscaling techniques. We will try to address the question that the standard finite-difference simulators may underestimate effective permeability when applied to heterogeneous systems and anisotropic grids. Keywords: Upscaling, Permeability, Geology, Finite-difference Simulators, Anisotropic Grids.
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Exponential Time Integrators for 3D Reservoir Simulation
More LessWe investigate exponential time integrators which we use, in conjunction with an upwind weighted finite volume discretization in space, for the efficient and accurate simulation of advection-diffusion processes including non-linear chemical reactions in highly heterogeneous 3D oil reservoirs with more than 528k unknowns. The exponential integrators are based on the variation of constants solution and solve the linear system exactly. While this is at the expense of computing the exponential of the stiff matrix representing the finite volume discretization, the use of real Leja points or the Krylov subspace technique to approximate the exponential makes these methods competitive compared to standard finite difference-based time integrators. We investigate two exponential time integrators, the second-order accurate Exponential Euler Midpoint (EEM) scheme and Exponential Time Differencing of order one (ETD1). All our numerical examples, which include advection-diffusion-reaction simulations performed on the classical SPE10 test case, demonstrate that our methods are highly competitive compared to standard semi-implicit time integrators. This competitiveness comprises two components: efficiency and accuracy. Our results suggest that exponential time integrators such as the ETD1 and EEM schemes can readily be applied to large-scale 3D reservoir simulations with several million of unknowns.
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Validation of Dynamic Coefficient Correlation Related to Dynamic Fluid Flow in Porous Media Using Experimental Results
Authors M. Mirzaei, G.C. Sills and D.B. DasMost traditional descriptions of macroscopic multiphase flow processes are based on an empirical extension of Darcy’s law supplemented with non-linear functional relationships between capillary pressure (Pc), saturation (S) and relative permeability (Kr). New multiphase flow theories have been proposed which indicate that Pc should be given a more general thermodynamic definition and its functional relationships with saturation should be generalized to include a capillary damping coefficient, called dynamic coefficient. Some correlations have been suggested based on numerical studies to relate dynamic coefficient to fluid and porous media characteristic. These correlations should be examined to evaluate whether they can be utilized at various flow conditions and whether the dynamic coefficient has any practical significance on a larger scale. One approach in this regard is to carry out experiments in laboratory accompanied by numerical modeling to simulate the experiments, calculate dynamic coefficient from both experimental and numerical results to validate such correlation. In this paper, the results of laboratory scale experiments on a homogeneous porous media accompanied by modeling two-phase flow at laboratory scale are presented. Simulation results are compared with experimental results to testify the accuracy of proposed enhanced flow equations and dynamic coefficient correlations. It is shown that flow equations need to be extended to account for dynamic effects. The result indicates that another term needs to be included in conventional flow equations to predict flow behavior and displacement efficiencies in heterogeneous media precisely. The results confirm that dynamic effect is a function of different parameters which depend on both porous media and fluids properties. Also proposed correlation is valid in homogeneous porous media and can be applied in heterogeneous porous media with extra parameters considered in the correlation to reflect degree of heterogeneity of porous media. This will be extremely beneficial to studies involved in designing EOR processes and techniques, predicting efficiency when engineers are dealing with geologically complex formations, and updating existing reservoir modeling and simulation tools.
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Non-iterative Phase Behavior Computation for General Compositional Problem
Authors R. Zaydullin, D.V. Voskov and H.A. TchelepiThis paper presents an efficient methodology for the computation of the thermodynamic phase behavior associated with a multi-component multiphase flow in the porous media. The method is based on the interpolation of supporting points for both pressure and composition, adaptively computed in the tie-line space. For the parameterization of displacement curve, associated with the compositional process, only a limited number of supporting points in compositional space are needed, depending on predefined precision. Special techniques are used for the adaptive construction of supporting points, because of the complicated behavior of the solution route in the compositional space. The parameterized compositional space is triangulated using Delaunay tessellation and natural-neighbor interpolation technique is used inside the simplex. The following computation of phase behavior for the composition simulation is an iteration-free procedure and doesn’t require any EoS calculations. Based on this method, we developed a new nonlinear formulation for general purpose compositional simulation for both immiscible and miscible displacement. Our numerical experience shows that the nonlinear behavior of the new formulation has some advantages in comparison with the standard approach. The one important advantage of the approach is the possibility for the direct analysis of the system of conservation law in the hyperbolic limit, since we can directly decouple characteristics, driven by thermodynamic behavior, with pressure and directly compute eigenvalues for each supporting simplex. The efficiency and accuracy of the method are demonstrated for several multi-dimensional compositional problems of a practical interest.
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Constrained Nonlinear Optimization for Extreme Scenarii Evaluation in Reservoir Characterization
Authors N. Metla, F. Delbos, S. Da Veiga and D. SinoquetThe goal of reservoir characterization is the estimation of unknown reservoir parameters by integrating available data in order to take decisions for production scheme and to anticipate risks development in the future. In this inverse problem, the associated forward model consist of a fluid flow simulator and a petro-elastic model based on rock physic Gassmann equations. A set of admissible models comprises models that fit up the observed data to a prescribed tolerance. Hence, the probable set of reservoir data forecasts is the response of the forward simulator, up to a future time, to the set of admissible models. Among them, extreme scenarios forecasts are of great interest for reservoir engineers because they outline risks associated with reservoir development. By evaluating the posterior distribution of the reservoir parameters, a standard Bayesian approach can assess future data forecasts and their associated uncertainty. However, this approach is not well suited to explore extreme scenarios which usually correspond to the tails of the posterior distribution. In this work we propose a practical approach to evaluate such extreme scenarios without relying on the Bayesian framework. This approach consists in solving a nonlinear optimization problem subject to nonlinear constraints. The cost function to be minimized or maximised is a nonlinear function depending on reservoir data forecasts. The standard problem is to explore scenarios which give a maximum total oil production up to a future time. Nonlinear inequality constraints further impose an acceptable history match on a given period of time. This optimization problem is solved with the IFP solver SQPAL developed to solve general nonlinear programming problems dealing with nonlinear constraints. The potential of the approach is illustrated on a synthetic reservoir problem. The results are then compared to the ones obtained using SQA : an IFP free derivative optimization solver.
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