Iterative coupling reservoir simulation on high performance computers

In this paper, the iterative coupling approach is proposed for applications to solving multiphase flow equation systems in reservoir simulation, as it provides a more flexible time-stepping strategy than existing approaches. The iterative method decouples the whole equation systems into pressure and saturation/concentration equations, and then solves them in sequence, implicitly and semi-implicitly. At each time step, a series of iterations are computed, which involve solving linearized equations using specific tolerances that are iteration dependent. Following convergence of subproblems, material balance is checked. Convergence of time steps is based on material balance errors. Key components of the iterative method include phase scaling for deriving a pressure equation and use of several advanced numerical techniques. The iterative model is implemented for parallel computing platforms and shows high parallel efficiency and scalability.

CHARACTERISTIC FINITE DIFFERENCE ALTERNATING-DIRECTION METHOD ANDANALYSIS FOR NUMERICAL RESERVOIR SIMULATION

Petroleum science has made remarkable progress in organic geochemistry and in the research into the theories of petroleum origin, its transport and accumulation. In estimating the oil-gas resources of a basin, the knowledge of its evolutionary history and especially the numerical computation of fluid flow and the history of its changes under heat is vital. The mathematical model call be described as a coupled system of nonlinear partial differentical equations with initial-boundary value problems. This thesis, from actual conditions such as the effect of fluid compressibility and the characteristic of large-scal science-engineering computalion. puts forward a kind of characteristic finite difference alternating-direction scheme. Optimal order estimates in L-2 norm are derived for the error in the approximate solutions.

THE MULTIGRID METHOD FOR RESERVOIR SIMULATION

This paper describes a way of solving the reservoir simulation pressure equation using mulligrid technique. The subroutine MG of four-grid method is presented. The result for 2-D two-phase problem is exactly the same as that of the SOR method and the CPU time is much less than that of the latter one.

Investigation of the influences of asphaltene deposition on oilfield development using reservoir simulation

This paper investigates the deposition of asphaltenes in the porous medium of the studied field in Russia and predicts production profiles based on uncertainty evaluation. This problem can be solved by dynamic modeling, during which production profiles are estimated in two scenarios: with and without the activation of the asphaltene option. Calculations are carried out for two development scenarios: field operation under natural depletion and water injection into the aquifer as a reservoir pressure maintenance system. A full-scale compositional reservoir simulation model of the Russian oilfield was created. Within a dynamic simulation, the asphaltene option was activated and the asphaltene behavior in oil and porous medium was tuned according to our own special laboratory experiments. The model was also matched to production historical data, and a pattern model was prepared using the full-scale simulation model. Technological and the asphaltene option parameters were used in sensitivity and an uncertainty evaluation. Furthermore, probable production profiles within a forecast period were estimated. The sensitivity analysis of the pattern model to input parameters of the asphaltene option allowed determining the following heavy-hitters on the objective function: the molar weight of dissolved asphaltenes as a function of pressure, the asphaltene dissociation rate, the asphaltene adsorption coefficient and the critical velocity of oil movement in the reservoir. Under the natural depletion scenario, our simulations show a significant decrease in reservoir pressure and the formation of drawdown cones leading to asphaltene deposition in the bottom-hole area of production wells, decreasing their productivity. Water injection generally allows us to significantly reduce the volume of asphaltene phase transitions and has a positive effect on cumulative oil production. Injecting water into aquifer can keep the formation pressure long above the pressure for asphaltene precipitation, preventing the asphaltene deposition resulted from interaction of oil and water, so this way has higher oil production.

Development Plan of East Unity Oil Field, Sudan, Using Reservoir Simulation Study

Simulation study was applied in the development planning of East Unity oilfield, Sudan. A grid consisting of 2 000 cells was constructed. A major challenge of the study wasto evolve a full field development and future reservoir management strategy that would ensuremaximum recovery of oil based on well Un51. Simulation shows that Un51 as injection well inAradiebaC would yield better oil recovery than to be production well.

KRYLOV SUBSPACE PROJECTION METHOD AND ITS APPLICATION ON OIL RESERVOIR SIMULATION

Krylov subspace projection methods are known to be highly efficient for solving large linear systems. Many different versions arise from different choices to the left and right subspaces. These methods were classified into two groups in terms of the different forms of matrix H-m, the main properties in applications and the new versions of these two types of methods were briefly reviewed, then one of the most efficient versions, GMRES method was applied to oil reservoir simulation. The block Pseudo-Elimination method was used to generate the preconditioned matrix. Numerical results show much better performance of this preconditioned techniques and the GMRES method than that of preconditioned ORTHMIN method, which is now in use in oil reservoir simulation. Finally, some limitations of Krylov subspace methods and some potential improvements to this type of methods are further presented.

Methods in Oil Recovery Processes and Reservoir Simulation

The exploitation of an oil field is a complex and multidisciplinary task, which demands a lot of prior knowledge, time, and money. A good reservoir characterization is deemed essential in the accomplishment of Enhanced Oil Recovery (EOR) processes in order to estimate accurately the properties of the porous medium affecting the flow properties. Several techniques at a field scale are currently being used to determine these properties, which are time and money consuming. But these alone do not guarantee the success of the project. Reservoir simulation and numerical techniques were then included in the pre-development and follow-up studies as an effective tool to determine the productivity and future behavior of the oil field. As the computational power increased, more advanced and detailed models were developed, including different chemical and physical phenomena. But alongside this process, there was an active research in the area of reservoir simulation, improving the accuracy and efficiency of the numerical schemes used for the flow, transport, and energy equations. The aim of this review is to address the topics described. Firstly, the origin of an oil recovery process, the economic factors and field tests involved are introduced. Secondly, the oil and porous medium origin and characterization as well as an introduction to the fundamental concepts and equations are associated to reservoir simulation. Finally, a brief description and analysis of the techniques are used in reservoir simulation employing finite difference methods, their downsides and possible ways to overcome these problems.

Numerical Simulation of Oil-Water Two-Phase Flow in Low Permeability Tight Reservoirs Based on Weighted Least Squares Meshless Method

In response to the complex characteristics of actual low-permeability tight reservoirs,this study develops a meshless-based numerical simulation method for oil-water two-phase flow in these reservoirs,considering complex boundary shapes.Utilizing radial basis function point interpolation,the method approximates shape functions for unknown functions within the nodal influence domain.The shape functions constructed by the aforementioned meshless interpolation method haveδ-function properties,which facilitate the handling of essential aspects like the controlled bottom-hole flow pressure in horizontal wells.Moreover,the meshless method offers greater flexibility and freedom compared to grid cell discretization,making it simpler to discretize complex geometries.A variational principle for the flow control equation group is introduced using a weighted least squares meshless method,and the pressure distribution is solved implicitly.Example results demonstrate that the computational outcomes of the meshless point cloud model,which has a relatively small degree of freedom,are in close agreement with those of the Discrete Fracture Model(DFM)employing refined grid partitioning,with pressure calculation accuracy exceeding 98.2%.Compared to high-resolution grid-based computational methods,the meshless method can achieve a better balance between computational efficiency and accuracy.Additionally,the impact of fracture half-length on the productivity of horizontal wells is discussed.The results indicate that increasing the fracture half-length is an effective strategy for enhancing production from the perspective of cumulative oil production.

Multilevel Constrained Pressure-Temperature Residual Preconditioners for Large-Scale Non-Isothermal Reservoir Simulation via Restricted Additive Schwarz Algorithms

The industry-standard constrained pressure residual(CPR)algorithm is often able to effectively improve the robustness behavior and the convergence speed of linear iterations for isothermal reservoir simulation.In this paper,we present and study an improved extension of CPR to the constrained pressure-temperature residual(CPTR)version for non-isothermal reservoir problems in heterogeneous porous media.In the proposed preconditioner,the corresponding approximations for the inverse of matrices are computed under a domain decomposition framework by using the restricted additive Schwarz(RAS)algorithm,to equally deal with the coupled thermalpressure-saturation reservoir system and highly exploit the parallelism of supercomputer platforms.Moreover,we introduce and develop a family of multilevel CPTR preconditioners with suitable coarse grid corrections,to further improve the applicability of this two-stage preconditioner for large-scale computation.Numerical results for strong heterogeneous flow problems show that the new approach can dramatically improve the convergence of linear iterations,and demonstrate the superiority of CPTR over the commonly used RAS preconditioners.The parallel scalability of the non-isothermal reservoir simulator is also studied versus a supercomputer with tens of thousands of processors.

Numerical Simulation of Asphaltene Precipitation and Deposition during Natural Gas and CO_(2) Injection

Asphaltene deposition is a significant problem during gas injection processes,as it can block the porous medium,the wellbore,and the involved facilities,significantly impacting reservoir productivity and ultimate oil recovery.Only a few studies have investigated the numerical modeling of this potential effect in porous media.This study focuses on asphaltene deposition due to natural gas and CO_(2) injection.Predictions of the effect of gas injection on asphaltene deposition behavior have been made using a 3D numerical simulation model.The results indicate that the injection of natural gas exacerbates asphaltene deposition,leading to a significant reduction in permeability near the injection well and throughout the reservoir.This reduction in permeability strongly affects the ability of gas toflow through the reservoir,resulting in an improvement of the displacement front.The displacement effi-ciency of the injection gas process increases by up to 1.40%when gas is injected at 5500 psi,compared to the scenario where the asphaltene model is not considered.CO_(2) injection leads to a miscible process with crude oil,extracting light and intermediate components,which intensifies asphaltene precipitation and increases the viscosity of the remaining crude oil,ultimately reducing the recovery rate.

Numerical Simulation of Two-Phase Flow in Glutenite Reservoirs for Optimized Deployment in Horizontal Wells

It is known that the pore media characteristics of glutenite reservoirs are different from those of conventional sandstone reservoirs.Low reservoir permeability and naturally developed microfractures make water injection in this kind of reservoir very difficult.In this study,new exploitation methods are explored.Using a real glutenite reservoir as a basis,a three-dimensional fine geological model is elaborated.Then,combining the model with reservoir performance information,and through a historical fitting analysis,the saturation abundance distribution of remaining oil in the reservoir is determined.It is shown that,using this information,predictions can be made about whether the considered reservoir is suitable for horizontal well fracturing or not.The direction,well length,well spacing and productivity of horizontal well are also obtained.

Application of auxiliary space preconditioning in field-scale reservoir simulation

We study a class of preconditioners to solve large-scale linear systems arising from fully implicit reservoir simulation. These methods are discussed in the framework of the auxiliary space preconditioning method for generality. Unlike in the case of classical algebraic preconditioning methods, we take several analytical and physical considerations into account. In addition, we choose appropriate auxiliary problems to design the robust solvers herein. More importantly, our methods are user-friendly and general enough to be easily ported to existing petroleum reservoir simulators. We test the efficiency and robustness of the proposed method by applying them to a couple of benchmark problems and real-world reservoir problems. The numerical results show that our methods are both efficient and robust for large reservoir models.

Toward Cost-EffectiveReservoir Simulation Solvers on GPUs

In this paper,we focus on graphical processing unit(GPU)and discuss how its architecture affects the choice of algorithm and implementation of fully-implicit petroleum reservoir simulation.In order to obtain satisfactory performance on new many-core architectures such as GPUs,the simulator developers must know a great deal on the specific hardware and spend a lot of time on fine tuning the code.Porting a large petroleum reservoir simulator to emerging hardware architectures is expensive and risky.We analyze major components of an in-house reservoir simulator and investigate how to port them to GPUs in a cost-effective way.Preliminary numerical experiments show that our GPU-based simulator is robust and effective.More importantly,these numerical results clearly identify the main bottlenecks to obtain ideal speedup on GPUs and possibly other many-core architectures.

Optimized polymer flooding projects via combination of experimental design and reservoir simulation

The conventional approach for an EOR process is to compare the reservoir properties with those of successful worldwide projects.However,some proper cases may be neglected due to the lack of reliable data.A combination of experimental design and reservoir simulation is an alternative approach.In this work,the fractional factorial design suggests some numerical experiments which their results are analyzed by statistical inference.After determination of the main effects and interactions,the most important parameters of polymer flooding are studied by ANOVA method and Pareto and Tornado charts.Analysis of main effects shows that the oil viscosity,connate water saturation and the horizontal permeability are the 3 deciding factors in oil production.The proposed methodology can help to select the good candidate reservoirs for polymer flooding.

THE OPTIMAL VARIABLE SUCCESSIVE OVER RELAXATION (OVSOR) METHOD FOR THREE-DIMENSIONAL RESERVOIR SIMULATIONS

This present paper has proved the theorem of the Point Optimal Variable Successive Over Relaxation (OVSOR) method of the three-dimensional unsteady flow in the reservoir, and has put forward a formu- la for calculating optimal parameters for OVSOR which vary with space points and time points. Using this method, internal memory of computer is the smallest, calculating work is the smallest, and calculating funds are the smallest. It is very easy to operate on microcomputers for three-dimensional res- ervoir simulation. The method is stable and convergent even if the time steps are taken to be large (for example, one year). The same applies for space steps. It is applicable both for homogeneous, isotropic porous mediums and for heterogeneous, anisotropic porous medium. On IBM microcomputers with internal memory of 512 thousand bytes, 8000 grid points may be cal- culated for three-dimensional simulation. It takes only two minutes to get convergence for one time step. It may be extended to three-dimensional heat conduction equation and three-dimensional simulation of the ground water flow. It looks much more advantageous for two-dimensional simulation.

Controlling the uncertainty in reservoir stochastic simulation

Unexpected noise in reservoir stochastic simulation realization may be too high to make the realization useful, especially when there is a lack of hard data. Through discussing the uncertainties, we present two ways to control the uncertainty ratio that is brought by the algorithm of stochastic simulation. By reasonably reducing the random value of the stochastic simulation result, the unexpected values introduced by the residual that associates with random series can be controlled. Another way when the data disperse unevenly is to control the stochastic simulation order by grouping the points that need to be simulated to make those points which can be simulated by more neighborhood hard data calculated first. Both methods do not go against the core stochastic simulation algorithm.

Fully coupled fluid-solid productivity numerical simulation of multistage fractured horizontal well in tight oil reservoirs

A mathematical model, fully coupling multiple porous media deformation and fluid flow, was established based on the elastic theory of porous media and fluid-solid coupling mechanism in tight oil reservoirs. The finite element method was used to determine the numerical solution and the accuracy of the model was verified. On this basis, the model was used to simulate productivity of multistage fractured horizontal wells in tight oil reservoirs. The results show that during the production of tight oil wells, the reservoir region close to artificial fractures deteriorated in physical properties significantly, e.g. the aperture and conductivity of artificial fractures dropped by 52.12% and 89.02% respectively. The simulations of 3000-day production of a horizontal well in tight oil reservoir showed that the predicted productivity by the uncoupled model had an error of 38.30% from that by the fully-coupled model. Apparently, ignoring the influence of fluid-solid interaction effect led to serious deviations of the productivity prediction results. The productivity of horizontal well in tight oil reservoir was most sensitive to the start-up pressure gradient, and second most sensitive to the opening of artificial fractures. Enhancing the initial conductivity of artificial fractures was helpful to improve the productivity of tight oil wells. The influence of conductivity, spacing, number and length of artificial fractures should be considered comprehensively in fracturing design. Increasing the number of artificial fractures unilaterally could not achieve the expected increase in production.

Numerical simulation of groundwater under complex karst conditions and the prediction of roadway gushing in a coal mine:a case study in the Guang'an Longtan Reservoir in Sichuan Province, China

Numerical simulation of groundwater in karst areas has long been restricted by the difficulty of generalizing the hydrogeological conditions of reservoirs and of determining the relevant parameters due to the anisotropy and discontinuity of the karst water-bearing media in these areas. In this study, we used the Guang'an Longtan Coal mine in Sichuan as an example, and generalized the complex hydrogeological conditions in the reservoir area. A finite element numerical flow model was used to simulate current and future scenarios of roadway gushing at the bottom of the coal mine at pile number 1 + 700 m. The results show that the roadway section corresponding to valleys has a gushing quantity of 4323.8–4551.25 m^3/d before impoundment. Modeled water inflow after impoundment increased to 1.6 times the water inflow before impoundment, which threatens the impoundment as well as the roadway's normal operation. Therefore, roadway processing measures are needed to guarantee the safety of the impoundment and of the mining operation.

Simulation of Oil-Water Flow in a Shale Reservoir Using a Radial Basis Function

Due to the difficulties associated with preprocessing activities and poor grid convergence when simulating shale reservoirs in the context of traditional grid methods,in this study an innovative two-phase oil-water seepage model is elaborated.The modes is based on the radial basis meshless approach and is used to determine the pressure and water saturation in a sample reservoir.Two-dimensional examples demonstrate that,when compared to the finite difference method,the radial basis function method produces less errors and is more accurate in predicting daily oil production.The radial basis function and finite difference methods provide errors of 5.78 percent and 7.5 percent,respectively,when estimating the daily oil production data for a sample well.A sensitivity analysis of the key parameters that affect the radial basis function’s computation outcomes is also presented.

3D seismic forward modeling from the multiphysical inversion at the Ketzin CO_(2) storage site

From June 2008 to August 2013,approximately 67 kt of CO_(2) was injected into a deep saline formation at the Ketzin pilot CO_(2) storage site.During injection,3D seismic surveys have been performed to monitor the migration of sequestered CO_(2).Seismic monitoring results are limited by the acquisition and signal-to-noise ratio of the acquired data.The multiphysical reservoir simulation provides information regarding the CO_(2) fluid behavior,and the approximated model should be calibrated with the monitoring results.In this work,property models are delivered from the multiphysical model during 3D repeated seismic surveys.The simulated seismic data based on the models are compared with the real data,and the results validate the effectiveness of the multiphysical inversion method.Time-lapse analysis shows the trend of CO_(2) migration during and after injection.