ECMOR XI - 11th European Conference on the Mathematics of Oil Recovery

Simulating 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 stand-alone 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.

The 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.

We consider an oil rim development with waterflooding using. We offer to discuss a system where recovery and injection horizontal wells have parallel orien-tation 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 prob-lem is represented as a three-phase 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 finite-difference 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 prop-erties, an oil rim thickness, water-pressure 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 effi-ciency 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 pro-jection and control problems.

Numerical 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 well-cell 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 development-target model created. The uncertainty analysis is based on Monte Carlo method, the objective function is minimized using Nelder-Mead 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.

Formation 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 re-entrainment, 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.

In 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 mud-trajectory 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.

Scale 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.

The main goal of this paper is to identify lithologies from well-logs data using the continuous wavelet transform CWT combined with the self organizing map (SOM), we based at the fractional Brownian motion character of well-logs data we estimate the Holder exponent at each depth. The set of Holder exponents calculated for all well-logs 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 well-logs 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 , well-logs data , the CWT , the Self Organizing Map SOM , Holder exponent , roughness coefficients.

The Dykstra-Parson (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 Dykstra-Parsons 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 well-known parametric methods, under different scenarios of reservoir maturity levels (i.e., number of wells), and degree violations of the log-Normal 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.

Setting 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.