A multilevel preconditioner and its shared memory implementation for a new generation reservoir simulator

As a result of the interplay between advances in computer hardware, software, and algorithm, we are now in a new era of large-scale reservoir simulation, which focuses on accurate flow description, fine reservoir characterization, efficient nonlinear/linear solvers, and parallel implementation. In this paper, we discuss a multilevel preconditioner in a new-generation simulator and its implementation on multicore computers. This preconditioner relies on the method of subspace corrections to solve large-scale linear systems arising from fully implicit methods in reservoir simulations. We investigate the parallel efficiency and robustness of the proposed method by applying it to million-cell benchmark problems.

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.

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.

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.

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.

Layer regrouping for water-flooded commingled reservoirs at a high water-cut stage

Layer regrouping is to divide all the layers into several sets of production series according to the physical properties and recovery percent of layers at high water-cut stage, which is an important technique to improve oil recovery for high water-cut multilayered reservoirs. Dif- ferent regroup scenarios may lead to different production performances. Based on unstable oil-water flow theory, a multilayer commingled reservoir simulator is established by modifying the production split method. Taking into account the differences of layer properties, including per- meability, oil viscosity, and remaining oil saturation, the pseudo flow resistance contrast is proposed to serve as a characteristic index of layer regrouping for high water-cut multilayered reservoirs. The production indices of multi- layered reservoirs with different pseudo flow resistances are predicted with the established model in which the data are taken from the Shengtuo Oilfield. Simulation results show that the pseudo flow resistance contrast should be less than 4 when the layer regrouping is implemented. The K-means clustering method, which is based on the objec- tive function, is used to automatically carry out the layer regrouping process according to pseudo flow resistances. The research result is applied to the IV-VI sand groups of the second member of the Shahejie Formation in the Shengtuo Oilfield, a favorable development performance is obtained, and the oil recovery is enhanced by 6.08 %.

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.

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.

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.

A new methodology for grouping and averaging capillary pressure curves for reservoir models

Primary drainage capillary pressure data are usually correlatable with a 3D predictable property of grid cells.Accordingly,rock typing is normally performed based on an established correlation.Primary drainage as well as corresponding imbibition and/or secondary drainage capillary pressure curves are averaged to establish a saturation table for each rock type region in reservoir modeling.This study in-vestigates the reliability of this industry-accepted methodology,and has two main contributions.First,we show that if different types of capillary pressures are plotted against water saturation,comparing them might be highly misleading.We demonstrate that although primary drainage capillary pressure data may be plotted against water saturation,the imbibition and secondary drainage capillary pressure data should be plotted against imbibed water saturation.This would enable reservoir engineers to check whether rocks with similar primary drainage capillary pressures do or do not have similar imbibition/secondary drainage counterparts.Using this technique,rock quality can be also deduced from imbibition and secondary drainage capillary pressure curves.We use capillary pressure data measured on limestone and sandstone samples from the Asmari Formation in three Iranian oilfields to evaluate our technique.The second contribution of this study is the proposal of a new methodology for preparing capillary pressure curves for reservoir models.In our methodology,a grid cell can represent more than one rock type region,each specific to a saturation function.As a part of this methodology,we present new physically meaningful equations for averaging primary drainage,imbibition,and secondary drainage capillary pressure curves.

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.

Machine learning inspired workflow to revise field development plan under uncertainty

We present an efficient and risk-informed closed-loop field development (CLFD) workflow for recurrently revising the field development plan (FDP) using the accrued information. To make the process practical, we integrated multiple concepts of machine learning, an intelligent selection process to discard the worst FDP options and a growing set of representative reservoir models. These concepts were combined and used with a cluster-based learning and evolution optimizer to efficiently explore the search space of decision variables. Unlike previous studies, we also added the execution time of the CLFD workflow and worked with more realistic timelines to confirm the utility of a CLFD workflow. To appreciate the importance of data assimilation and new well-logs in a CLFD workflow, we carried out researches at rigorous conditions without a reduction in uncertainty attributes. The proposed CLFD workflow was implemented on a benchmark analogous to a giant field with extensively time-consuming simulation models. The results underscore that an ensemble with as few as 100 scenarios was sufficient to gauge the geological uncertainty, despite working with a giant field with highly heterogeneous characteristics. It is demonstrated that the CLFD workflow can improve the efficiency by over 85% compared to the previously validated workflow. Finally, we present some acute insights and problems related to data assimilation for the practical application of a CLFD workflow.

Numerical Approach of a Coupled Pressure-Saturation Model Describing Oil-Water Flow in Porous Media

Two-phase flow in porous media is a very active field of research,due to its important applications in groundwater pollution,CO_(2)sequestration,or oil and gas production from petroleum reservoirs,just to name a few of them.Fractional flow equations,which make use of Darcy's law,for describing the movement of two immiscible fluids in a porous medium,are among the most relevant mathematical models in reservoir simulation.This work aims to solve a fractional flow model formed by an elliptic equation,representing the spatial distribution of the pressure,and a hyperbolic equation describing the space-time evolution of water saturation.The numerical solution of the elliptic part is obtained using a finite-element(FE)scheme,while the hyperbolic equation is solved by means of two dif-ferent numerical approaches,both in the finite-volume(FV)framework.One is based on a monotonic upstream-centered scheme for conservation laws(MUSCL)-Hancock scheme,whereas the other makes use of a weighted essentially non-oscillatory(ENO)reconstruc-tion.In both cases,a first-order centered(FORCE)-αnumerical scheme is applied for inter-cell flux reconstruction,which constitutes a new contribution in the field of fractional flow models describing oil-water movement.A relevant feature of this work is the study of the effect of the parameterαon the numerical solution of the models considered.We also show that,in the FORCE-αmethod,when the parameterαincreases,the errors diminish and the order of accuracy is more properly attained,as verified using a manufactured solution technique.

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.

The effect of interbeds on distribution of i ncremental oil displaced by a polymer flood

This paper discusses the effect of influencing factors on the distribution of incremental oil displaced by a polymer flood （extra-displaced oil） using numerical reservoir simulation. These factors include the location, area and permeability of a thin low-permeability interbed, and the perforation location relative to the interbed. Simulation results show the locations from where the incremental oil was displaced by the polymer solution. The interbed position from the oil formation top affects the location of extra-displaced oil. The interbed area has a slight influence on the whole shape of extra-displaced oil. Larger interbed area leads to higher partition extent of extra-displaced oil. Higher vertical permeability of interbeds contributes to worse partition extent of extra-displaced oil and the partition effect disappears if the ratio of vertical to horizontal permeability is more than 0.05. The perforation location relative to the interbed affects polymer displacement efficiency, and also has a significant effect on the distribution of extra-displaced oil in polymer flooding.

Terahertz time-domain spectroscopy of a simulated pore structure to probe particle size and porosity of porous rock

The particle sizes and porosities of simulated pore structures are probed by terahertz time-domain spectroscopy.A double-peak time-domain spectrum phenomenon is observed when the terahertz（THz） pulses illuminated a pore and a particle. The amplitudes of the two peaks depend strongly and monotonically on the particle size and porosity. A model is used to study the phenomenon, and the computational results agreed with the experimental measurements. These measurements indicate the terahertz spectroscopic behaviors of pores and particles, suggesting that terahertz spectroscopy can be used as a noncontact probe of porosity.