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ECMOR XI  11th European Conference on the Mathematics of Oil Recovery
 Conference date: 08 Sep 2008  11 Sep 2008
 Location: Bergen, Norway
 ISBN: 9789073781559
 Published: 08 September 2008
81  100 of 105 results


Tiesimplex Based Framework for General Multiphase Thermodynamic Equilibrium Computations
Authors D.V. Voskov and H.A. TchelepiWe present a general framework for thermodynamic equilibrium calculations of multiphase, multicomponent mixtures. We use the fact that the compositional space can be represented as a highdimensional simplex. For given values of pressure and temperature, the phase behavior of a particular system can be described using a lowdimensional tiesimplex, for example, tielines and tietriangles for two and three phase systems, respectively. In general, a highdimensional compositional space can be parameterized using a lower dimensional tiesimplex subspace. Tiesimplex computation and interpolation procedures complement the parameterization to complete the mathematical framework. The robustness and efficiency of the method is demonstrated using several multiphase equilibrium problems of practical interest. One type of problem is the equilibrium flash calculation of systems with a large number of phases. The complexity and strong nonlinear behaviors associated with such systems pose serious difficulties for standard techniques. The tiesimplex representation of the equilibrium data, which may be obtained using a particular equationofstate for example, can be preprocessed. The parameterized space can be used to obtain the phase compositions (i.e., flash results) or used as an initial guess to accelerate convergence of standard Equation of State (EoS) based procedures. The second type of application is multiphase multicomponent displacement problems. In the standard compositional simulation approach, an EoS is used to describe the phase behavior. For each gridblock, given the temperature, pressure and overall compositions, the EoS is used to detect the phase state (e.g., one, two, or more phases), and to calculate the phase compositions, if multiple phases are present. These EoS computations can dominate the overall simulation cost. Adaptive computation of the tiesimplex space can be used to speed up the EoS computations of largescale problems of practical interest by an order of magnitude, or more.



Use of a Reduced Method in Compositional Simulation
Authors R. Okuno, R.T. Johns and K. SepehrnooriSimulating gas injection processes requires a compositional model to predict the fluid properties resulting from mass transfer between reservoir fluid and injection gas. A drawback of compositional simulation is the efficiency and robustness of phase equilibrium calculations. Reduced methods for phase equilibrium calculations have been studied as a potential solution to improve the efficiency of compositional simulation. However, most of those studies have been performed only in standalone calculations, and the robustness and efficiency of a reduced method has not been confirmed in compositional simulation. In this research we develop a robust and efficient algorithm for a reduced method and validate it in compositional simulation. We examine the efficiency and convergence property of the conventional algorithm for a reduced method, and solve several implementation problems in a compositional simulator. The reduced method is implemented in UTCOMP, a compositional IMPEC simulator, to demonstrate the performance for various numbers of components and degrees of miscibility. The results show that the reduced method enables significant saving in execution time of compositional simulation without loss of accuracy, compared to standard methods. Also, we observe that the reduced method exhibits improved robustness especially for miscible processes where composition paths go near critical regions.



Adapted Nonlinear Optimization Method for Production Data and 4D Seismic Inversion
Authors D. Sinoquet and F. DelbosIntegrated inversion of production history data and 4D seismic data for reservoir model characterization leads to a nonlinear inverse problem that is usually cumbersome to solve : the associated forward problem based, on one hand, on fluid flow simulation in the reservoir for production data modeling, and on the other hand, on a petroelastic model for 4D time lapse seismic data modeling, is usually computationally time consuming, the number of measurements to be inverted is large (up to 500 000), the number of model parameters to be determined is up to 100. Moreover, all the derivatives of the modeled data with respect to those parameters are usually not available. We propose an optimization method based on a Sequential Quadratic Programming algorithm which uses gradient approximation coupled with a BFGS approximation of the Hessian. In addition, the proposed method allows to handle equality and inequality nonlinear constraints. Some realistic applications are presented to illustrate the efficiency of the method.



The Hamiltonian Monte Carlo Algorithm in Parameter Estimation and Uncertainty Quantification
Authors S. Subbey, M. Alfaki and D. HauglandThe Hamiltonian Monte Carlo (HMC) algorithm is a Markov Chain Monte Carlo (MCMC) technique, which combines the advantages of Hamiltonian dynamics methods and Metropolis Monte Carlo approach, to sample from complex distributions. The HMC algorithm incorporates gradient information in the dynamic trajectories and thus suppresses the random walk nature in traditional Markov chain simulation methods. This ensures rapid mixing, faster convergence, and improved efficiency of the Markov chain. The leapfrog method is generally used in discrete simulation of the dynamic transitions. In this paper, we refer to this as the leapfrog–HMC. The primary goal of this paper is to present the HMC algorithm as a tool for rapid sampling of high dimensional and complex distributions, and demonstrate its advantages over the classical Metropolis Monte Carlo technique. We demonstrate that the use of an adaptive–step discretization scheme in simulating the dynamic transitions results in an algorithm which significantly outperforms the leapfrog–HMC algorithm. Relevance to reservoir parameter estimation and uncertainty quantification will be discussed.



Stochastic Optimization Using EA and EnKF – A Comparison
Authors O. Pajonk, M. Krosche, R. SchulzeRiegert, R. Niekamp and H.G. Matthiesulation are increasingly included in bestpractice workflows in the Oil & Gas industry. Most optimization methods applied to model validation in reservoir simulation, including socalled Evolutionary Algorithms like Genetic Algorithms (GA) and Evolution Strategies (ES), use an objective function definition based on the overall simulation period. The integration of a sequential data assimilation process is conceptually not embedded in those optimization methods. The Ensemble Kalman Filter (EnKF) has entered this field for its appealing features. Sequential data assimilation allows the implementation of realtime model updates where classical optimization techniques require simulating the complete history period. This may have negative effects on efficiency and use of computing time. In contrast, EnKF sequentially assimilates information streams into a set of numerical models. While being a special case of a fully fledged particle filter the EnKF method with application to reservoir simulation has proven to generate results with a reasonable amount of ensemble members. The similarities between a particle filter (Monte Carlo Filter) and an Evolutionary Algorithm (Generic Algorithm) have been previously pointed out from a rather theoretical point of view (1,2). In this work we present a concise overview of Evolutionary Algorithms and the Ensemble Kalman Filter in such a way that the crossrelations become apparent. Similarities are highlighted and the potential for hybrid couplings is discussed. Practical implications for the implementation of these methods are derived. 1. Higuchi, Tomoyuki. Monte carlo filter using the genetic algorithm operators. Journal of Statistical Computation and Simulation. 1997, Vol. 1, 59, pp. 123. 2. —. Selforganizing Time Series Model. [book auth.] A. Doucet, J.F.G. de Freitas and N.J. Gordon. Sequential Monte Carlo Methods in Practice. s.l. : Springer, 2001, pp. 429444.



Waterflooding Efficiency of the Oil Rim Development
More LessWe consider an oil rim development with waterflooding using. We offer to discuss a system where recovery and injection horizontal wells have parallel orientation and are drilled in the oil rim. These researches are based on mathematical modeling that allows us to describe and simulate reservoir behavior. The model is quite simplified and takes into account only the most important factors. The problem is represented as a threephase 2D model. Considering area is a vertical section of the element of development system and consists of a space between the recovery and injection wells. A system of differential equations describing filtration process consists of one parabolic and two hyperbolic equations which are solved for certain initial and boundary conditions by using finitedifference methods. Here are used implicit schemes for both parabolic and hyperbolic equations. Let’s consider a simplified optimization problem and study the following objective function determining profit on the oil rim development. The objective function depends on both natural and technological factors: rock and fluid properties, an oil rim thickness, waterpressure system activity, a distance between wells, their positions and operating regimes, etc. In this work the author explores some technological factors which influence an oil recovery factor and the objective function, and analysis waterflooding efficiency for the oil rim development. One significant effect has been found out. The effect is in an oil recovery increasing since time moment, when injected water has covered the oil rim and displaces a gas cone. This is a characteristic feature of thin oil rims development. The applied method based on mathematical modeling permits to solve projection and control problems.



Applicability of Newtonbased Optimization Method Merged with the Monte Carlo Approach to Log Interpretation
Authors D. Viberti, E. Salina Borello and V. RoccaThe determination of the main petrophysical parameters is normally based on the log data. During the log interpretation process suitable mathematical algorithms taking into account all the available data and information are applied in the attempt to reliably relate log measurements to mineralogy, porosity and water saturation. Uncertainty is always associated to the results of the interpretation due to possible errors in the measurements, in the selected petrophysical models, and/or in the input parameters required by the models. The possibility to estimate the reliability of the petrophysical characterization of the reservoir rocks has a strong impact on the evaluation of the hydrocarbon originally in place (HOIP) and, thus, on the technical and economical exploitation strategies. The evaluation of the uncertainties associated to the results of the well log interpretation process can be performed only by applying a methodology that couples a robust optimization process to a representative statistical approach. On the basis of previous studies and applications to real cases, a methodology for log inversion and uncertainty estimation was formulated. According to this methodology, log interpretation was performed using the iterative solution of the Lagrangian relaxed problem with the GaussNewton algorithm, in which the constrains were managed with the active set method; the Monte Carlo statistical approach was applied to the log interpretation routine in order to assess the associated uncertainty. The use of a fast iterative inversion method proved fully compatible with the use of the Monte Carlo approach to estimate the range of uncertainty associated to the reservoir characterization. The rigorous formulation of the methodology and a discussion of the applicability limits and convergence requirements of the inversion method are presented in this paper. Results of the analyses that were carried out in the study showed that the validity limits were perfectly consistent with the domain of the petrophysical interpretation. The results obtained by the application of the methodology to a real case, a deepwater exploration well data complicated by a poor characterization of the reservoir fluids, is also presented the paper.



Reservoir Simulation Quality Assessment Based on History Matching in Well Bore Zone
Authors S. Stepanov and V. VasilyevNumerical reservoir simulation is often accompanied by difficulties with history matching, especially as regards history matching of individual wells. On the one hand, the problems are explained by amount and quality of initial information on a reservoir. On the other hand, these problems pertain to numerical realization of a simulator applied, in particular, to well bore zone modeling. The expertise gained in reservoir simulation often demonstrates the excess of calculated watercut values over the actual ones. Similar situation occurs while performing an analytical solution of the well bore zone displacement problem. Therefore, it appears to be necessary to assess quality of reservoir simulation in terminology of wellcell fluid distribution. In order to solve the given problem, a special inverse well bore zone modeling problem has been formulated, which accounts for actual development data and numerical results of reservoir simulation obtained using the developmenttarget model created. The uncertainty analysis is based on Monte Carlo method, the objective function is minimized using NelderMead method. The key adjusted parameters are porosity, absolute & relative permeability, capillary pressure. At solving inverse problems, the filtration features become apparent, which relate to combined action of capillary, gravity and elastic forces. It is noted how important is to get a proper description of a well bore zone filtration process. Variance in results obtained with/without capillary pressures is shown. Also, it is demonstrated that the reservoir simulation models with relatively simple filtration pattern but with account for capillary, gravity and elastic forces can reproduce the complex watercut dynamics of the wells under study. The suggested method has been tested on one of Orenburg oilfields. Application of the given approach allows to analyze and adjust the numerical models on a new level, and avoid multiple reservoir simulation runs that distort a physical essence of actual displacement.



Comprehensive Model of Heat Transfer between ESP Motor and Multiphase Fluid Included Solid Phase
By A.V. YazkovThis work is devoted to developing of comprehensive mechanistic model of heat transfer between an ESP motor and multiphase fluid. The model takes into account not only such parameters as flow pattern, gas/oil ratio, flow regime, etc. but also solid phase. Solid phase was included based on modern experimental investigations in the area of heat transfer in multiphase systems containing solid phase and flowing in annuli. The developed model was verified by means of temperature data taken using telemetry system during steadystate production from the wells with ESPs. Based on the model sensitivity analysis for the change of such parameters as solid size, solid phase concentration, and motor shroud size was performed. Impact of each parameter on motor cooling is discussed. It is shown that optimization of motor shroud size can lead to significant heat transfer enhancement between the ESP motor and solidliquid mixture as compared to heat transfer between the ESP motor and liquid. This effect is achieved due to solid particles which have sufficient freedom in bombarding motor wall so that they thin viscous boundary layer. However, if the motor shroud size selection is inconsistent to the given solid phase concentration and solid particle size, this can cause deterioration of thermodynamic conditions for motor cooling.



Effect of Kinetics of Permeability Alteration on Development of Clayey Oil Formation
By M. ChirkovFormation damage, a common problem associated with field operations, is often a major factor in reducing the productivity and injectivity of a well in a petroleum reservoir. Numerous laboratory and field studies indicate that formation damage occurs during many phases of reservoir development – drilling, completion, workover, production, stimulation, waterflooding, or improved oil recovery. Formation damage is a process of initial permeability reduction. At present many mathematic formation damage models are developed. В настоящее время разработано множество математических моделей изменения проницаемости. This models contain a number of parameters: the rate constant for reentrainment, the rate constant for liquid absorption, the phenomenological constants for swelling potential and the release constant for swellable fines, the rate constant for release rate, the rate constant for change in pore size with depositional morphology, the critical pressure force required to mobilize fines, plugging efficiency, the critical total pore volume flux for the onset of swelling, and the coefficient of volumetric thermal expansion. In order to describe formation damage, the parameters must be known. That is very problematic. We analyzed a number of laboratory experiments and formation damage studies. Comparing the results we defined that permeability has similar kinetics of alteration for different damaging mechanism. Next we determined the principal damaging mechanisms of real oil formation and associated them with laboratory relations of permeability alteration. As a result the integrated relations of permeability reduction were obtained. This method can be used as a predictive tool for quantitative predictions of field development showings for different rock types and operation strategies. Equations of permeability kinetics were entered into computer hydrodynamic model of oil formation. The effect of permeability kinetics on formation development process was shown concerning clay oil formation. Based on laboratory and field observations the methods of enhanced oil recovery and formation damage prevention were proposed.



Modeling of Borehole Zone Influence on Stimulation Efficiency of Gas Production
Authors L. Gaidukov and N.N. MikhailovDuring development of gas field one of the most serious problem is a well production decline due to borehole zone properties deterioration. For well production recovery there are a lot of various methods. And hydrochloric acid treatment received a large area of implementation. However it is a common practice that actual well production increase is lower then expected. This fact has a negative influence on the economic indexes and may bring to loss of profit. Estimation of treatment efficiency demand knowledge of such impotent value as relative increase of gas production. Previously believed that after borehole zone treatment the borehole zone permeability can change only trough cleaning and seam dissolution. But special research showed that after borehole zone treatment the compressibility of the seam may change too. In connection with above we build a mathematical model of gas filtration toward the well with complex borehole zone witch take into account both blockage and compressibility. In case when we consider borehole zone blockage only the filtration equation has analytical solution in terms of integral function. But when we account compressibility of the seam a numerical methods are needed. We considered relative permeability of gas as product of two functions k(r,p)=A(r)*f(p), where function A(r) simulate a borehole zone blockage and f(p) simulate compressibility of the seam. Previously function A(r) was considered as fully modeling. There are various formulation of its view such as linear function, quadratic function, root function and constant function. But all of these formulations haven’t a physical validation. We suggest using probable convolutions method with Gaussian kernel for welllogging data interpretation and definition redial borehole zone filtration properties. In our previous papers showed that a view of A(r) function greatly influence on well production. That is why an adequate definition of this function is very impotent. Using this model we researched dependence of hydrochloric acid treatment efficiency from such parameters as radius of acid penetration, permeability on the well, coefficient of compressibility. And we offered technological scheme of treatment efficiency prediction.



Geomechanical Constrains for Assisted Wellbore Trajectory Design – Stability Navigation Algorithm
More LessIn wellbore stability studies, traditional methods to predict optimum drilling directions on an established stress regime involve punctual contour plots tied to a corresponding depth, which are treated as a discontinuous set of solutions for one continuous problem: the trajectory definition. In other words, desired well positions are isolated estimations that take time to refine into one integrated stability proposal. Due to this obstacle, these studies focus primarily on delivering optimum mud plans that only quote on reference drilling directions, instead of integrated mudtrajectory optimized solutions. A Stability Navigation Algorithm (SNA), developed in this study, represents a new philosophy on addressing drilling direction effects in wellbore stability. Managed stress redistributions around a borehole constitutes the basis on the algorithm’s navigation (search) criteria, resulting in interesting exposures of path volumes where complete “stable” trajectories are viable, based on geomechanical constraints for breakout widths and fracture potentials, trajectory delimitations, DLS and mud weights. The main idea is to upgrade unbound well positions into complete trajectories with automated recursive wellbore stability analysis performed by a SNA. The algorithm runs on a 3D geomechanical model, thus rock mechanical properties distribution is a mayor factor affecting possible solutions. This study analyses the development of the algorithm, its computation strategy and a proposed workflow or application method, based on the interpretation of the resulting behaviors of the outputs. Application scenarios are discussed, as well as the input parameters, and 3D visualization (interpretation) techniques.



Mathematical Modeling of Multiphase Flow in Fracture Media
Authors A.K. Pergament, P.Y. Tomin and V.A. SemiletovThe multiphase flow in fractural media with different fractal structures is considered. The homogenized model of processes depends on the structure pattern. One of them leads to the known double porosity model, the other may be described by tensor total and pseudo phase permeability. The influence of the capillary effects is taken into consideration. The algorithms of the tensor permeability calculation are developed by using the selfsimilar properties of the fractal structure. We have used the support operator method for difference scheme construction. This method allows approximating both the dissipative energy and phase flux. The results of modeling some problems are represented.



Optimisation of Scale Squeeze Treatment Designed for Heterogeneous Reservoir
By R. PaswanScale deposition in the near wellbore region is an extensive problem in hydrocarbon production. When sea water breakthrough occurs, scale formed by mixing of sea water with formation water flows into the wellbore to the surface. It deposited through out its path and reduces the path for hydrocarbon flow. Sever deposition of scale inside the tube or near wellbore region, highly diminishes the productivity of the well. Scale inhibitor squeeze treatment is one of the remediation processes to avoid scale deposition in the near wellbore region. High water producing zones brings more scale into the tube and therefore these zones are targeted to treat primarily. In heterogeneous reservoirs, squeezed chemicals placed into the fluid flow favourable zones rather than zones targeted to treat. To maximise the affectivity of the treatment, optimisation of the treatment is necessary. To aid in the process of optimisation of squeeze treatment, near wellbore simulation approach is applied. Using near wellbore simulation approach, sensitivity of the different parameters involved in squeeze design (e.g., main slug volume, main slug concentration, overflush volume etc) is determined to find an optimum concentration and optimum slug volume which can enhance the placement of scale inhibitor in unfavourable zones. It is found that the main slug concentration and overflush volume are significant factor which affect the chemical placement. This presentation describes the severity of scale problem and following up the process of optimisation of squeeze treatment using near wellbore simulation.



Reducing Well Test Duration at the Design Stage by Means of Successive Deconvolution Application on the D. Field Example
By A.V. YazkovThe issue of systematic approach to well test design does not leave any doubts. It is particularly relevant for test design in an explored area with the complex geology where we usually possess the minimum of data about the reservoir and are required to derive the latter with sufficient confidence for the shortest time. Deconvolution technique allows us to decrease duration of well testing to the minimum albeit demands of linearity of the system investigated. In this work the thorough particular well test design is performed in the attempt to take into account all the issues concerning application of deconvolution technique and conventional test data interpretation. For design purposes the integration of simulations in Eclipse and Saphir was done in order to built unsophisticated but representative model in Saphir. Also the influence of aquifer and well interference were regarded. The interference was taken into account to linearize the system for deconvolution technique application. The method for time distribution between drawdown and buildup in the test sequence was suggested. Sensitivity analysis is implemented to reservoir and well parameters. Also the conventional test and test for deconvsolution are compared and economics issue are adduced.



Reservoir Characterization Using the Continuous Wavelet Transform (CWT) Combined with the Self Organizing Map (SOM)
By S. OuadfeulThe main goal of this paper is to identify lithologies from welllogs data using the continuous wavelet transform CWT combined with the self organizing map (SOM), we based at the fractional Brownian motion character of welllogs data we estimate the Holder exponent at each depth. The set of Holder exponents calculated for all welllogs data represents the input of the neural machine. Our system gives at each entry a specified lithology. We applied this technique at synthetics and real welllogs data, obtained results showed that the proposed technique is a powerful tool for reservoir characterization, witch is a crucial problem in geophysics. Because it attribute at each set of roughness coefficients (witch are directly related to the rocks types ) a particular lithology. Keywords: Lithologies , welllogs data , the CWT , the Self Organizing Map SOM , Holder exponent , roughness coefficients.



Structure and Mobility of Irreducible Oil in Anthropogenic Changed Formations
More LessIrreducible oil (IO) is researched as hydrodynamic system, consisting of separate types. IO of micro and macrolevel, connate and conventionally mobile IO were defined. We identified that such technological factors as pressure gradient, wettability, surface tension, etc. effect IO significantly. Irreducible oil saturation (IOS) is one of the most important parameter characterizing development efficiency. Traditionally IOS was associated with formation microconstruction and considered through displacement efficiency using its relationship with filtration capacity properties of formation. IOS was considered as one of producing formation properties. Technology influence on final oil recovery used to be determined through volumetric efficiency. It was determined that conventionally mobile irreducible oil becomes movable under the critical pressure gradient to capillary pressure ratio. When the mobility threshold is reached the values of IOS depend on technological displacement condition. After achieving the second threshold value almost all conventionally mobile oil is withdrawn and only connate oil remains in formation. Present geotechnological models do not take the IOS influence of these factors into consideration. Therefore the dynamic models of IOS were developed with the attention paid on threshold mobility character, operating practices and mechanisms of IOS formations. Distribution research of IOS in croswell area was based on special hydrodynamic models. Results of investigation technology effect on IOS (e.g. well spacing system, pattern arrangement, disturbances and modernization of designed system) are presented. As shown, the compound anthropogenic heterogeneity of IOS is formed in crosswell area even for homogeneous formations. Depending on well spacing system IOS can be heterogeneous regarding displacement efficiency and phase permeability. We consider the possibility of additional IO recovery using intensive technologies (flow control, sidetracks, horizontal wells). Taking different well spacing systems, analysis of relative influence of formation microconstruction and of technological factors on IOS was given.



Asymptotic DykstraParsons Estimates and Confidence Intervals
Authors S. Pintos, C. Bohorquez and N.V. QueipoThe DykstraParson (DP), the most popular heterogeneity static measure among petroleum engineers, may be at a significant error, in particular when assumptions are made about the permeability distribution (parametric approaches) that may lead to unrealistic reservoir performance predictions and unsuccessful development plans. This paper presents the development of an asymptotic distribution of the DykstraParsons coefficient that is independent of the probability distribution of the permeability variable. The effectiveness (bias and confidence intervals) of the proposed approach is demonstrated by comparing the results those obtained using the classical method, and wellknown parametric methods, under different scenarios of reservoir maturity levels (i.e., number of wells), and degree violations of the logNormal probability density function assumption. The results show that in the vast majority of the case studies the proposed approach outperformed previously reported methods, in particular, resulted in a significant reduction of the bias and, with confidence intervals always including the estimated DP coefficient. In addition, an excellent agreement was observed between the asymptotic cumulative distribution of the DP coefficient and the corresponding empirical distribution for sample sizes as low as 100, which allows classifying reservoirs according to their DP coefficient with high success rates.



Pressure Transient Analysis and Simulation of Nonconventional Wells
Authors V.A. Iktissanov and R.R. IbatullinNowadays nonconventional wells (horizontal, multilateral, Rad Tech and others) are being extensively drilled throughout the world for the development of lowprofit fields. Construction of these wells enables to reduce filtration resistivity resulting in productivity index increase and costs reduction. To select the optimal well design with regard to reservoir characteristics, effective well operation and determination of filtration characteristics one should possess calculation methods for steady and unsteady liquid flow in reservoir. Few related papers have been published so far. However analytical methods for steady flowing are suitable for homogeneous beds with simple geometry and equal length laterals. Available approaches for description of pressure build up allow to account for various lateral trajectories but FEA or semianalytical decisions methods are too laborintensive for practical application. Commercial program for interpretation of pressure build up is lacking. Therefore simple methods of productivity index determination and pressure transient test interpretation are suggested for nonconventional wells. These methods are suitable for low thickness beds. The basis of these methods is the superposition of filtration resistivity for two plane problems. Trajectory of laterals is simulated as a number of closely spaced vertical wells or nodes. The suggested method allows determining the field of application and regularities for nonconventional wells. Dimensionless fluidmovement profile calculated from steady fluid flow and a superposition method for pressure builds up in the nodes are used for determination of pressure build up. For description of build up in a node we recommend a diffusion equation in Laplace space and Stephest numerical algorithm. The problem is solved for porous and porousfractured reservoirs. Numerical calculations show that crossflows occur after the horizontal or multilateral well shutdown. Pressure derivative maximum testifies to low effective length of the borehole or positive skineffect. Knowledge of effective intervals length is critical to pressure curve interpretation.



Simulation of Hydrocarbon Filtration Processes in Porous Media Using the Decomposition of the Simulation Zone
Authors A.V. Akhmetzyanov and A.I. ErmolaevSetting and solving of the discussed problem is caused by the next circumstances: 1. The possibilities of the software for hydrodynamic simulation aimed on finding optimal project and management of field development are extremely limited. 2. Filtration parameters in porous media can’t be obtained by interpolation. It causes the necessity to define them for every block separately. 3. The filtration equations are nonlinear. Therefore the parameters of these equations are changed while the field is being developed. That’s why it is permanently necessary to carry out history matching. A new approach is suggested to solve the listed problems. It is based on hierarchical simulation and the decomposition of the simulation zone. In this case the field is institutionally divided into homogeneous blocks (geological objects). In its turn every block is divided into elements. An element may contain only one well or no one. The number of hierarchy levels and the character of links between them is defined by the number and the superposition of homogeneous blocks in the field, by the method of blocks decomposition into elements, by methods the initial multiphase filtration equations were approximated. Special attention is paid to the calculation of the filtration flows distribution and the values of pressure inside every element. Thanks to the usage of perturbation method the solving of the equations system with quasilinear and nonlinear operators adds up to the solving of linear systems chain. The suggested approach how to solve the problem of the filtration processes simulation may be used for all the types of hydrocarbon fields excluding gas hydrate deposits.
