bluuebunny/crossref_metadata_2025 huggingface dataset:
Studies of Robust Two Stage Preconditioners for the Solution of Fully Implicit Multiphase Flow Problems
Authors: Al-Shaalan Tareq M. , Klie Hector , Dogru Ali H. , Wheeler Mary F.
Published: February 2009

The solution of the linear system of equations for a large scale reservoir simulation has several challenges. Preconditioners are used to speed up the convergence rate of the solution of such systems. In theory, a preconditioner defines a matrix M that can be inexpensively inverted and represents a good approximation of a given matrix A. In this work, two-stage preconditioners consisting of the approximated inverses M1 and M2 are investigated for multiphase flow in porous media. The first-stage preconditioner, M1, is approximated from Ausing four different solution methods: (1) constrained pressure residuals (CPR), (2) lower block Gauss-Seidel, (3) upper block Gauss-Seidel, and (4) one iteration of block Gauss-Seidel. The pressure block solution in each of these different schemes is calculated using the Algebraic Multi Grid (AMG) method. The inverse of the saturation (or more generally, the nonpressure) blocks are approximated using Line Successive Over Relaxation (LSOR). The second stage preconditioner, M2, is a global preconditioner based on LSOR iterations for the matrix A that captures part of the original interaction of different coefficient blocks. Several techniques are also employed to weaken the coupling between the pressure block and the nonpressure blocks. Effective decoupling is achievedby: (1) an IMPES-like approach designed to preserve the integrity of pressure coefficients, (2) Householder transformations, (3) the alternate block factorization (ABF), and (4) the balanced decoupling strategy (BDS) based on least squares. The fourth method is a new technique developed in this work. The aforementioned preconditioning techniques were implemented in a parallel reservoir simulation environment, and tested for large-scale two-phase and three-phase black oil simulation models. This study demonstrates that a two-stage preconditioner based on balanced decoupling strategy (BDS) or ABF combined with Gauss-Seidel sweeps, that also incorporate nonpressure solutions for M,delivers both the fastest convergence rate and the most robust option overall without compromising parallel scalability.
Well Placement Optimization Using a Genetic Algorithm With Nonlinear Constraints
Authors: Emerick Alexandre A. , Silva Eugênio , Messer Bruno , Almeida Luciana F. , Szwarcman Dilza , Pacheco Marco Aurélio C. , Vellasco Marley M. B. R.
Published: February 2009

Well placement optimization is a very challenging problem due to the large number of decision variables involved and the nonlinearity of the reservoir response as well as of the well placement constraints. Over the years, a lot of research has been done on this problem, most of which using optimization routines coupled to reservoir simulation models. Despite all this research, there is still a lack of robust computer-aided optimization tools ready to be applied by asset teams in real field development projects.

This paper describes the implementation of a tool, based on a Genetic Algorithm, for the simultaneous optimization of number, location and trajectory of producer and injector wells. The developed software is the result of a two-year project focused on a robust implementation of a computer-aided optimization tool to deal with realistic well placement problems with arbitrary well trajectories, complex model grids and linear and nonlinear constraints.

The developed optimization tool uses a commercial reservoir simulator as the evaluation function without using proxies to substitute the full numerical model. Due to the large size of the problem, in some cases involving more than 100 decision variables, the optimization process may require thousands of reservoir simulations. Such a task has become feasible through a distributed computing environment running multiple simulations at the same time.

The implementation uses a technique called Genocop III – Genetic Algorithm for Numerical Optimization of Constrained Problems – to deal with well placement constraints. Such constraints include grid size, maximum length of wells, minimum distance between wells, inactive grid cells and user-defined regions of the model, with non-uniform shape, where the optimization routine is not supposed to place wells.

The optimization process was applied to three full-field reservoir models based on real cases. It increased the net present values and the oil recovery factors obtained by well placement scenarios previously proposed by reservoir engineers. The process was also applied to a synthetic case, based on outcrop data, to analyze the impact of using reservoir quality maps to generate an initial well placement scenario for the optimization routine without using an engineer-defined configuration.
Efficient Simulation for Low-Salinity Waterflooding in Porous and Fractured Reservoirs
Authors: Wu Yu-Shu , Bai Baojun
Published: February 2009

Low-salinity brine injection has emerged as a promising, cost-effective improved oil recovery (IOR) method for waterflooding reservoirs. Laboratory tests and field applications show that low-salinity waterflooding could lead to significant reduction of residual oil saturation. There has been a growing interest with an increasing number of low-salinity waterflooding studies. However, there are few quantitative studies on flow and transport behavior of low-salinity IOR processes. This paper presents a general mathematic model (1) to incorporate known IOR mechanisms and (2) to quantify low-salinity waterflooding processes. In our mathematical conceptual model, salt is treated as an additional "component" to the aqueous phase, based on the following physical considerations: salt is transported only within the aqueous phase by advection and diffusion, and also subject to adsorption onto rock solids; relative permeability, capillary pressure, and residual oil saturation depend on salinity. Interaction of salt between mobile and immobile water zones is handled rigorously using a multi-domain approach. Fractured rock is handled using the multiple-continuum model or a discrete-fracture modeling approach. The conceptual model is implemented into a general-purpose reservoir simulator for modeling low-salinity IOR processes, using unstructured, regular, and irregular grids, applicable to 1-D, 2-D, and 3-D simulation of low-salinity water injection into porous media and fractured reservoirs. As demonstrated, the model provides a general capability for quantitative evaluation of low-salinity waterflooding in site-specific investigations.
Integrated Reservoir Simulation and Basin Models: Reservoir Charging and Fluid Mixing
Authors: Chen Zhangxin , Chen Hongsen , Carruthers Dan , Zhou Guoqiang
Published: February 2009

Perhaps the most important unconstrained aspect of petroleum systems analysis concerns the charging and emplacement of petroleum to a structure or prospect. Petroleum charge rates, leakage, and spill control petroleum residence time in a reservoir, which is fundamental for prediction of biodegration rates, seal integrity (failure), and oil quality, all of which are affected by fluid mixing processes. While forward models can estimate plausible charge rates based on thermal histories, there are no field data proxies for the charge rates that are necessary to constrain migration and charge models. To solve this problem, we are coupling high resolution, full physics reservoir simulation protocols to full 4D basin models such that gradients in petroleum compositions from models and from chemical analysis can be used to constrain charges rates. This new generation of hybrid reservoir simulator/basin models necessitates rapid high resolution fluid mixing solvers and multicomponent fluids.

This paper deals with the development of compositional fluid mixing simulators that can be coupled with basin modeling. These simulators will enable the forward simulation of detailed reservoir charging and fluid property evolution, coupling the effects of advection, diffusion, gravity segregation, and biodegration to predict the development of compositional gradients in petroleum columns that can be used to constrain reservoir charging and alteration processes. In this paper the effects of advection, diffusion, and gravity segregation are particularly studied. The traditional simulator for solving the isothermal gravity/chemical equilibrium problem is deduced as a special example of the simulators presented here. Numerical experiments to show these effects are given.
Field Development Optimization Applied to Giant Oil Fields
Authors: Litvak Michael L , Angert Patrick F
Published: February 2009

A new optimization technology has been demonstrated for giant oil and gas-condensate fields. Because of the very large number of wells involved, optimization is carried out on well patterns, well spacing in patterns, order of drilling different zones, etc. Earlier developed technology for the optimization of well placement, drilling schedule, well trajectories, and injection strategy has been extended for the optimization of field development schemes involving a very large numbers of wells.

The powerful optimization procedure is based on a global optimization technique such as the Genetic Algorithm and other mixed integer optimizers. Potential field development schemes that match field development constraints are identified. A global optimizer is then applied to determine the optimum field development scheme relative to pre-defined economic criteria and analysis. A statistical proxy procedure is utilized to reduce the number of optimization iterations and computing time required to solve this difficult optimization problem.

Economic indicators (e.g. net present value, incremental rate of return, capital efficiency, discounted payback, etc.) or oil/gas recovery are maximized subject to field development constraints. The multiple reservoir models representing uncertainties in reservoir geology are handled within the workflow and are represented in predicted results.

The applications of this optimization technology is clearly demonstrated to be a powerful and sufficiently general tool for analysis of most real world field development planning issues. Significant improvements (3-13 %) in oil/gas recovery and net present value are demonstrated in the optimum cases when compared with the best manually achieved reference field development case.
Equivalent Well Block Radius for Three Dimensional Flow
Authors: Dogru Ali H.
Published: February 2009

A new analytical expression has been developed for the equivalent well block radius for three dimensional (3D) flow. The new equation has the same structure as Peaceman's equation with two new parameters added. Therefore, implementation in a reservoir simulator is straight forward. Numerical experiments have shown that Peaceman's equation for two dimensional (2D) flow can cause high rate errors for the partially penetrating wells. The new formula reduces these errors to a few percent.

In this paper, derivation was presented for a vertical well, steady-state single phase flow with uniform and nonuniform grids. Multiphase, transient flow, horizontal wells and partial completion within a grid block is under development and will be presented in a new paper.
Black Oil Delumping: Running Black Oil Reservoir Simulations and Getting Compositional Wellstreams in the North Kuwait Jurassic Complex
Authors: Ghorayeb Kassem , Limsukhon Manoch , Dashti Qasem , Aziz Rafi Mohammad
Published: February 2009

The North Kuwait Jurassic Complex (NKJC) consists of five fields, each with three identified reservoirs within the naturally fractured Jurassic carbonate formation. These reservoirs contain multiple fluid types (gas-condensate and volatile oil) at near-critical conditions.

Multiple scenario production forecasts are required to prepare an optimal development plan for the complex. Current compartmentalization understanding based on geological and engineering data led to 24 isolated segments for which up to 24 separate simulation models can be potentially built. Because of global production targets and constraints, these models cannot be run in isolation. A multiple reservoir simulations coupling controller that dynamically apportions global production targets among different reservoirs is used for the purpose.

Compositions from different reservoirs are needed for surface facility design and operation. Compositional simulation is prohibitively computationally expensive for a multi-scenario production performance study for the NKJC. Black oil reservoir simulation is computationally far less demanding than compositional simulation. It does not, though, provide the detailed compositional information necessary for surface process modeling.

We demonstrate that using a black oil delumping method based primarily on the compositional information generated when simulating the laboratory depletion process (CVD, CCE, DL) overcomes the main limitation of black oil reservoir simulation in the NKJC. The method enables the composition and component molar rates of a producing well from a black oil reservoir simulation to be accurately reconstituted. Full computational advantages of black oil modeling are obtained while preserving the reservoir details required for an accurate prediction of well and reservoir behavior. Comparison of results obtained from a compositional model to those obtained from a black oil model using black oil delumping shows excellent agreement.

This study shows that black oil simulation with black oil delumping is a viable alternative to compositional simulation and fulfills the requirements for multi-scenario production forecasts in the NKJC.
History Matching Using a Hierarchical Stochastic Model with the Ensemble Kalman Filter: A Field Case Study
Authors: Zhang Yanfen , Oliver Dean S.
Published: February 2009

The growth in the application of optimization in reservoir management has placed greater demands on the application of history matching to produce models that not only reproduce the historical production behavior, but also preserve geological realism and quantify forecast uncertainty. Geological complexity and limited access to the subsurface typically result in a large uncertainty in reservoir properties and forecasts. There is, however, a systematic tendency to underestimate such uncertainty, especially when rock properties are modeled using Gaussian random fields. In this paper, we address two sources of uncertainty: uncertainty in regional trends by introducing stochastic trend coefficients and uncertainty in variogram model by treating correlation length or range as a stochastic variable instead of a well-determined variogram parameter. The hierarchical parameters including trend coefficients and heterogeneities can be estimated using ensemble Kalman filter (EnKF) for history matching.

Hierarchical or multi-scale heterogeneities are generally poorly represented, especially in deepwater reservoirs. We developed a hierarchical description of heterogeneities that introduced new variables into the reservoir description. We tested our method for updating these variables using production data from a deepwater field whose reservoir model has over 200,000 unknown parameters. The match of reservoir simulator forecasts to real field data using a standard application of EnKF had not been entirely satisfactory, as it was difficult to match water cut in one of the wells. None of the realizations of the reservoir exhibited water breakthrough using the standard method. By adding uncertainty in trends of reservoir properties, the ability to match the water cut and other production data was improved substantially.

The results indicate that an improvement in the generation of the initial ensemble and in the variables describing the property fields give an improved history match with plausible geology. It reduces the tendency to underestimate uncertainty while still providing reservoir models that match data.
History Matching of Hydrate Formation and Dissociation Experiments in Porous Media
Authors: Phirani J. , Pitchumani R. , Mohanty K. K.
Published: February 2009

Gas hydrates are crystalline, ice-like compounds of gas (e.g., methane) and water molecules that are formed under high pressure and low temperature. Many of the transport properties of porous media containing hydrates are unknown and difficult to measure experimentally. The goal of this work is to match laboratory experiments of hydrate formation and dissociation in cores to estimate some of these transport properties. An implicit, thermal, compositional simulator is used which accounts for four components (hydrate, water, methane and salt) and five phases (hydrate, aqueous, gas, ice, and salt precipitate). The transformation of methane and water to hydrate is modeled by a reaction with the kinetics controlled by the hydrate surface area. The key unknown is the variation of permeability within the core. Permeability and its spatial variation are used as parameters to match the experimental results.
Advanced Reservoir Management Workflow Using an EnKF Based Assisted History Matching Method
Authors: Seiler A. , Evensen G. , Skjervheim J. -A. , Hove J. , Vabø J. G.
Published: February 2009

This paper demonstrates the potential and advantages of the Ensemble Kalman filter (EnKF) as a tool for assisted history matching, based on its sequential processing of measurements, its capability of handling large parameter sets, and on the fact that it solves the combined state and parameter estimation problem.

A method and a thorough workflow for updating reservoir simulation models using the EnKF is developed. In addition, we present a method for updating relative permeability curves, as well as an improved approach for updating fault transmissibility multipliers.

The proposed workflow has been applied on a complex North Sea oil field. The EnKF successfully provides an ensemble of history matched reservoir models. A significant improvement in the history match is obtained by updating the relative permeability properties in addition to porosity and permeability fields and initial fluid contacts. Fault multipliers are estimated, and it is shown how the use of transformations, which handles non-Gaussian model variables, makes it possible to determine if a fault is open, closed, or partially closed with respect to flow.

The presented method is an innovative contribution to reservoir management workflows, which show growing interest in real time applications and fast model updating. Sequential data assimilation provides an updated reservoir model conditioned on the most recent production data. The updated ensemble is used to predict the uncertainty in future production and it is demonstrated that the EnKF leads to improved predictions with reduced uncertainty.
Modeling Well Inflow Control with Flow in Both Annulus and Tubing
Authors: Neylon K. , Reiso E. , Holmes J. A. , Nesse O. B.
Published: February 2009

We present a model for well inflow control devices (ICDs) that includes the effects of an annulus in which the flow between the ICDs is open or partially obstructed by the presence of packers, and we describe the application of this model in a full-field simulator. Flow in an open or partially obstructed annulus requires looped flowpaths to be modeled within the well. We describe the extension to the formulation of the well model together with considerations to ensure that the resulting equations have a Jacobian matrix that is invertible and explain the necessary modifications to the techniques used to solve the resulting linear system.

The effect of simulating flow in both the annulus and the tubing was investigated in two case studies involving ICDs: a synthetic case and a sector of a North Sea field model. Results showing significant differences between the inflow profiles of horizontal wells with and without packers in the annulus are presented.
Scale Up Methodology for Wettability Modification in Fractured Carbonates
Authors: Delshad Mojdeh , Najafabadi Nariman Fathi , Sepehrnoori Kamy
Published: February 2009

Recent research findings suggest that wettability modification holds a great potential for increased oil production from mixed-wet and fractured carbonates. Our current knowledge of the field-scale performance of these processes is very limited despite very favorable results obtained in the laboratory-scale experiments. Reservoir simulation is required to properly scale up the process from laboratory to field conditions and to understand and interpret reservoir data. Without a mechanistic simulation tool and adequate scale up, it is unlikely that a cost-effective process can be developed and applied economically. The predictive simulation and methodology to scale up such a complex process will reduce the risk of failure of field projects.

A chemical compositional reservoir simulator with the capability to model oil recovery from mixed-wet carbonate rocks in both static imbibition and dynamic fractured block experiments using chemicals to alter wettability is used for this scale up study. The simulator captured the key recovery processes of capillary and natural imbibition, wettability alteration, buoyancy, oil mobilization, and viscous pressure gradient in imbibition experiments.

Proper scaling from laboratory to field indicates that the synergy of wettability alteration, ultra low interfacial tension, and emulsification under small viscous pressure gradient provides an attractive and profitable opportunity in fractured carbonate reservoirs. Dimensionless scaling groups and numerical simulations are presented for each experimental condition to aid in understanding the time dependence and up-scaling of the laboratory results to field scale applications.

The oil recovery results of the static imbibition experiment were successfully scaled using a reference time based on gravity emphasizing that the buoyancy was a dominant mechanism in this case. The scale up simulations for the dynamic fractured block experiment indicated favorable conditions for field scale applications with more dominance of viscous forces.
Ensemble-Based Closed-Loop Optimization Applied to Brugge Field
Authors: Chen Yan , Oliver Dean S.
Published: February 2009

In closed-loop reservoir management, geologic properties are updated sequentially using available data, and model-based optimization is used to search for the optimal operating strategy. Ensemble-based methods can be used to solve both data assimilation and production optimization with the gradient approximated from an ensemble. This ensemble-based closed-loop optimization method is flexible and has been illustrated using a small scale problem in Chen et al. (2008). The dimensionality of the model parameter and control parameter space are high in large scale problems. Approximating the gradient using small ensembles might result in unsatisfactory solution of the ensemble-based closed-loop optimization. In this paper the ensemble-based closed-loop optimization is applied to a large scale SPE Benchmark study. Brugge field, a synthetic reservoir, is designed as a common platform to test different methods for closed-loop reservoir management. The problem was designed to mimic real field scenarios, and as a result is by far the largest and most complex test case on closed-loop optimization. The Brugge field model consists of nine layers and the number of active cells is 44550. It has one internal fault and seven rock regions with different relative permeability and capillary pressure functions. There are 20 producers and 10 injectors in the field. Noise corrupted production data are provided monthly. Additionally, time-lapse seismic data are available at year ten. Each well has three different completions that can be controlled independently. The producing life of the reservoir is 30 years and the objective of optimization is to maximize the net present value at the end of 30 years.

Due to the complexity of this test case, several advanced techniques are used in order to improve the solution of the ensemble-based closed-loop optimization. Saturation normalization is used to account for the presence of difference rock regions. Localization is used in the assimilation of production and seismic data to increase the effective size of the ensemble and to alleviate the effect of spurious correlations resulted from the small ensemble. Relative permeability curves and initial oil water contact are estimated together with the gridblock properties. Covariance inflation is used to maintain the desired variability in the ensemble. We expect that these techniques will also be critical in real field application of the ensemble-based closed-loop optimization.
Field Applications of Waterflood Optimization via Optimal Rate Control With Smart Wells
Authors: Alhuthali Ahmed H. , Datta-Gupta Akhil , Yuen Bevan , Fontanilla Jerry P.
Published: February 2009

Waterflood optimization via rate control is receiving considerable attention because of increasing deployments of smart well completions and I-Field technology. The use of inflow control valves (ICV) allows us to optimize the production/injection rates of various segments along the wellbore, thereby maximizing sweep efficiency and delaying water breakthrough. Field scale rate optimization problems, however, involve highly complex reservoir models, production and facility constraints, and a large number of unknowns. In this paper we propose an approach that is computationally efficient and suitable for large field cases. It is based on our previous work that relies on equalizing arrival time of the waterfront at all producers for maximizing the sweep efficiency. We use streamlines to efficiently and analytically compute the sensitivity of the arrival times with respect to well rates. We also account for geologic uncertainty via a stochastic optimization framework using multiple realizations. Analytical forms for gradients and Hessian of the objective functions are derived, making our optimization computationally efficient for large-scale applications. Finally, optimization is performed under operational and facility constraints using a sequential quadratic programming approach.

We demonstrate our approach using two field-scale examples. The first one is a synthetic example called "Brugge" field, a benchmark case based on a North Sea Brent-type field. The production optimization of this field is carried out as part of a closed loop process where the production history is matched prior to the production optimization. The production optimization is performed over multiple realizations for 20 years and involves 30 wells equipped with three ICVs per well. The second example is a super-giant Middle Eastern field which has over 50 years of historical oil production. The optimization is performed for 20 years on a portion of this field which contains nearly 300 wells consisting of conventional vertical and horizontal wells and smart horizontal wells. In both examples, multiple field-related constraints are imposed, such as the maximum well injection and production rates, the maximum allowable drawdown, restriction on high water cut wells and voidage replacement for pressure maintenance. The results clearly demonstrate the viability of our approach, and the benefits of optimal rate control with a considerable increase in cumulative oil production and a substantial decrease in the associated water production.
A Dual Scale Approach to Production Data Integration into High Resolution Geologic Models
Authors: Kim Jong Uk , Datta-Gupta Akhil
Published: February 2009

Inverse problems associated with reservoir characterization are typically under-determined and often have difficulties associated with stability and convergence of the solution. A common approach to address this issue is through the introduction of prior constraints, regularization or reparameterization to reduce the number of estimated parameters.

We propose a dual scale approach to production data integration that relies on a combination of coarse-scale and fine-scale inversions while preserving the essential features of the geologic model. To begin with, we sequentially coarsen the fine-scale geological model by grouping layers in such a way that the heterogeneity measure of an appropriately defined ‘static’ property is minimized within the layers and maximized between the layers. Our coarsening algorithm results in a non-uniform coarsening of the geologic model with minimal loss of heterogeneity and the ‘optimal’ number of layers is determined based on a bias-variance trade-off criterion. The coarse-scale model is then updated using production data via a generalized travel time inversion. The coarse-scale inversion proceeds much faster compared to a direct fine-scale inversion because of the significantly reduced parameter space. Furthermore, the iterative minimization is much more effective because at the larger scales there are fewer local minima and those tend to be farther apart. At the end of the coarse-scale inversion, a fine-scale inversion may be carried out, if needed. This constitutes the outer iteration in the overall algorithm. The fine-scale inversion is carried out only if the data misfit is deemed to be unsatisfactory.

We demonstrate our approach using both synthetic and field examples. The field example involves waterflood history matching of a structurally complex and faulted offshore turbiditic oil reservoir. Permeability and fault transmissibilities are the main uncertainties. The geologic model consists of more than 800,000 cells and 10 years of production data from 8 producing wells. Using our dual scale approach, we are able to obtain a satisfactory history match with a finite-difference model in less than a day in a PC. Compared to a manual history matching, the dual scale approach is shown to better preserve the geological features and the pay/non-pay juxtapositions in the original geologic model.
History Matching With Parametrization Based on the SVD of a Dimensionless Sensitivity Matrix
Authors: Tavakoli Reza , Reynolds Albert C.
Published: February 2009

In gradient based automatic history matching, calculation of the derivatives of all production data with respect to gridblock rock properties (sensitivities) and other model parameters is not feasible for large-scale problems. Thus, the Gauss-Newton method and Levenberg-Marquardt algorithm, which require calculation of all sensitivities to form the Hessian, are seldom viable. For such problems, the quasi-Newton and nonlinear conjugate gradient algorithms present reasonable alternatives as these two methods do not require explicit calculation of the complete sensitivity matrix or the Hessian. Another possibility, the one explored here, is to define a new parameterization to radically reduced the number of model parameters.

We provide a theoretical argument which indicates that reparametrization based on the principal right singular vectors of the dimensionless sensitivity matrix provides an optimal basis for re-parametrization of the vector of model parameters. We present and apply to example problems two algorithms for using this parametrization. Like LBFGS, these algorithms avoid explicit computation of individual sensitivity coefficients. Explicit computation of the sensitivities is avoided by using a partial singular value decomposition based on a form of the Lanczos algorithm. At least for all synthetic problems that we have considered, the reliability, computational efficiency and robustness of the methods presented here are as good as those obtained with quasi-Newton methods.
Numerical Simulation of the In-situ Upgrading of Oil Shale
Authors: Fan Y. , Durlofsky L. J. , Tchelepi H.
Published: February 2009

Oil shale is a highly abundant energy resource, though commercial production has yet to be realized. Thermal in-situ upgrading processes for producing hydrocarbons from oil shale have recently gained attention, however, in part because of promising results reported by Shell using their In-situ Conversion Process. This and similar processes entail heating the oil shale to about 325°C, when the kerogens in the shale decompose through a series of chemical reactions into liquid and gas products. In this paper we present a detailed numerical formulation of the in-situ upgrading process. Our model, which can be characterized as a thermal-compositional, chemical reaction and flow formulation, is implemented into Stanford's General Purpose Research Simulator (GPRS). The formulation includes strongly temperature-dependent kinetic reactions, fully-compositional flow and transport, and a model for the introduction of heat into the formation through downhole heaters. We present detailed simulation results for representative systems. The model and heating patterns are based somewhat on information in Shell patents; chemical reaction and thermodynamic data are from previously reported pyrolysis experiments. After a relatively modest degree of parameter adjustment (with parameters restricted to physically realistic ranges), our results for oil and gas production are in semi-quantitative agreement with available field data. We also investigate various sensitivities and show how the produced hydrocarbon components are impacted by heater temperature and location. The ability to model these effects will be essential for the eventual design and optimization of in-situ upgrading operations.
Data Assimilation of Coupled Fluid Flow and Geomechanics via Ensemble Kalman Filter
Authors: Chang Haibin , Chen Yan , Zhang Dongxiao
Published: February 2009

In reservoir history matching or data assimilation, dynamic data such as production rates and pressures are used to constrain reservoir models and to update model parameters. As such, even if under certain conceptualization the model parameters do not vary with time, the estimate of such parameters may change with the available observations and thus with time. In reality, the production process may lead to changes in both the flow and geomechanics fields, which are dynamically coupled. For example, the variations in the stress/strain field lead to changes in porosity and permeability of the reservoir and hence in the flow field. In weak formations such as the Lost Hills oilfield, fluid extraction may cause a large compaction to the reservoir rock and a significant subsidence at the land surface, resulting in huge economic losses and detrimental environmental consequences. The strong nonlinear coupling between reservoir flow and geomechanics possesses a challenge to construct a reliable model for predicting oil recovery in such reservoirs. On the other hand, the subsidence and other geomechanics observations can provide additional insight into the nature of the reservoir rock and help constrain the reservoir model if used wisely. In this study, the Ensemble Kalman filter (EnKF) approach is used to estimate reservoir flow and material properties by jointly assimilating dynamic flow and geomechanics observations. The resulting model can be used for managing and optimizing production operations and for mitigating the land subsidence. The use of surface displacement observations improves the match to both production and displacement data. Localization is used to facilitate the assimilation of a large amount of data and to mitigate the effect of spurious correlations resulting from small ensembles. Since the stress, strain, and displacement fields are updated together with the material properties in The EnKF, the issue of consistency at the analysis step of the EnKF is investigated. A 3D problem with reservoir fluid-flow and mechanical parameters close to those of the Lost Hills oilfield is used to test the applicability.
An Object Oriented Approach to Goal Based Well Management
Authors: Davidson J. E. , Yang Y. , Netemeyer S. , Banki A. , Do L.
Published: February 2009

A reservoir simulator may be considered a collection of objects: reservoir nodes, producers, injectors, tubing, surface facilities, and drilling rigs. Each of these objects has attributes (variables that describe their state) and can perform actions (manipulation of attributes) on themselves or upon other objects. Engineers assemble these objects together to form a model of reservoir and surface facilities. Equations that describe the physical processes occurring in the reservoir model define some of the interactions between the objects. Engineers can further refine the interactions between the objects by imposing constraints and objectives on the facilities by well management. The interactions between the objects, goals, constraints, policies, physics and numerics can become quite complex. This paper will describe two approaches to controlling the facilities in a reservoir simulation model.

The first approach allows the engineer to define a set of instructions that tests for conditions and modifies the facilities based on those results. These instructions are translated into computer code, compiled and linked at run-time thereby giving engineers almost complete control over the facility network model. But with this flexibility comes the burden of writing and maintaining the instructions. Three different user interfaces for the well management instructions are described and compared.

The second approach allows the engineer to make use of the facility network objects to specify goals, constraints and strategies for production, injection, and well scheduling without having to develop solution algorithms. This paper will discuss the flexibility of these two object-oriented approaches to well management in reservoir simulation.
Local Parameterization of Geostatistical Realizations for History Matching
Authors: Ding D-Y. , Roggero F.
Published: February 2009

Reservoir characterization needs the integration of various data, and especially dynamic information such as production or 4D seismic data through history matching. This paper presents a local domain parameterization technique to update geostatistical realizations for assisted history matching. This technique allows us to change locally geostatistical realizations through the variation of geometrical domains whose geometry and size can be easily controlled and parameterized.
Randomized Maximum Likelihood with Permeability Samples Generated by a Predictor Corrector Technique
Authors: Feng T. , Mannseth T. , Aanonsen S. I.
Published: February 2009

To assess the uncertainty in reservoir descriptions and performance predictions, the a posteriori probability density function (pdf) for the unknown model parameters is needed. The only practical way to evaluate the posterior pdf is by sampling. Permeability samples for performance forecasting should be consistent with all available information. Markov chain Monte Carlo (McMC) samples correctly from the posterior distribution, but is computationally extremely intensive. Randomized maximum likelihood (RML) is a good approximation to McMC that involves history matching of each permeability sample. Although RML is computationally less intensive than McMC, the computational effort to generate a sufficiently large number of samples is therefore huge for all but very small reservoir models.

In this work, we have investigated if the sampling procedure can be made more efficient by using a predictor-corrector approach in the history matching step of RML. The predictor applies sequential history matching to obtain an estimate with few degrees of freedom, utilizing only part of the available information. The corrector downscales the predictor estimate in a two-step procedure involving all available information, including the estimate obtained with the predictor. The first corrector step is a variant of Kriging. The second corrector step is a history match, again involving few degrees of freedom, with basis functions derived from the results of the predictor. The method is demonstrated and compared to regular RML through numerical examples, indicating that predictor-corrector RML is computationally more efficient than regular RML.
Multipoint Flux Approximations via Upscaling
Authors: Potsepaev R. , Farmer C. L. , Fitzpatrick A. J.
Published: February 2009

This paper investigates the control volume method with multipoint flux approximation (MPFA) applied to the discetization of –div(K(x)grad u) = f(x), the equation describing fluid flow through anisotropic porous media. The permeability tensor K(x) is allowed to have discontinuities. Transmissibility coefficients are obtained from local numerical flow experiments (transmissibility upscaling) for each cell face. Monotonicity of the solution matrix is discussed and a version of the method that provides an M-matrix is described. Convergence and numerical flux consistency of the scheme for uniform permeability tensor are studied. This discretization scheme is applied to reservoir simulation on 3D structured grids with distorted geometry, highly anisotropic media and discontinuities in the permeability tensor. Simulation results are presented and compared with results from other two-point and multipoint flux approximations.
Multiphase, 3-D Flow Simulation With Integrated Upscaling, MPFA Discretization, and Adaptivity
Authors: Lambers J. V. , Gerritsen M. G. , Fragola D.
Published: February 2009

We present a multi-point flux approximation (MPFA) scheme for simulation of 3-D multi-phase flow on adapted grids. It is an extension of the VCMP (Variable Compact Multi-Point) scheme, which constructs stencils that are locally adapted to flow through transmissibility upscaling. The proposed integration of upscaling, MPFA stencil selection and gridding leads to an optimized flow discretization that can accurately resolve full-tensor effects, is compact, and leads to low upscaling errors.

The grid adaptivity is driven by both upscaling, in a pre-processing stage, and by solution gradients during run-time. During transmissibility upscaling, the grid is refined to resolve important flow features such as high permeability flow paths. During run-time, we refine the grid locally, as needed, to accurately resolve saturation fronts, and coarsen once the front passes. We do not employ downscaling techniques, but compute transmissibilities for the newly refined regions using the upscaling methodology that can be effectively applied to localized regions.

The numerical tests presented in this paper show that the method leads to higher upscaling accuracy as compared to commonly used upscaling methods. On average, error in total flow is reduced by a factor of two, and the fine-scale velocity field is resolved with greater accuracy as well. They also illustrate that saturation fronts can be resolved accurately using single-phase upscaling only by employing VCMP on adapted grids.

The combined strategy promises to significantly improve the workflow of coarse-scale modeling for flow simulations such as those routinely performed in the industry.
Modeling Polymer Flood in an Unstructured Grid Simulator
Authors: Verma Santosh , Adibhatla Bhargaw , Kaminsky Robert , Wattenbarger Chick , Davidson Jeffrey
Published: February 2009

This paper describes the development of a comprehensive polymer flood modeling capability within a reservoir simulator that uses an unstructured grid framework. The polymer modeling capability includes a number of specialized capabilities. Polymer solution viscosity is modeled as a function of polymer concentration, shear rate, multiple salt components, and reservoir temperature. The polymer solution viscosity model handles both shear thinning and shear thickening. High near-wellbore shear rates are accounted for when determining well flow rates through a mobility correction. Thermal degradation of the polymer is modeled as a function of polymer concentration, ion concentrations, and reservoir temperature. Polymer retention and its impact on flow are also modeled. In addition to describing these capabilities, the numerical schemes used to solve the flow problems are discussed and example applications are presented.
Adaptive Local-Global VCMP Methods for Coarse-Scale Reservoir Modeling
Authors: Chen T. , Gerritsen M. G. , Durlofsky L. J. , Lambers J. V.
Published: February 2009

Upscaling is often applied to generate practical simulation models from highly detailed geocellular descriptions. In this paper we develop and evaluate a new upscaling procedure – a variable compact multipoint adaptive local-global technique (VCMP-ALG) – that is able to capture, accurately and efficiently, both full-tensor and global flow effects in the coarse model. The method successfully combines the positive attributes of its two underlying component procedures: the variable compact multipoint (VCMP) flux scheme, which provides coarse-scale transmissibilities that are appropriate for use in problems characterized by strong full-tensor permeabilities, and adaptive local-global (ALG) upscaling, which accounts for the effects of large-scale flow in the upscaling computations without solving any global fine-scale flow problems. The performance of the local-global VCMP upscaling technique is evaluated for multiple realizations of oriented variogram-based models and synthetic deltaic systems. Extensive numerical results for 2D cases demonstrate that the VCMP-ALG approach provides better overall accuracy than either of the underlying methods – an extended local VCMP technique and an adaptive local-global procedure based on two-point flux approximations – applied individually. The extension of the VCMP-ALG method to irregular quadrilateral grids is also accomplished. Finally, we present results for two-phase oil-water flows, for which the models based on the VCMP-ALG method again provide the best overall accuracy.
General Nonlinear Solution Strategies for Multiphase Multicomponent EoS Based Simulation
Authors: Voskov D. V. , Younis R. M. , Tchelepi H. A.
Published: February 2009

We present a novel reservoir flow simulation framework built on top of an Automatic Differentiation with Expression Templates Library (ADETL). Given discrete algebraic expressions of the governing conservation equations, associated constraint relations, and equations of state, the ADETL library generates efficient computer code for the corresponding Jacobian matrix. The framework allows for complete flexibility in the specification of the independent variables, which leads to unified simulator for different formulations and solution strategies. We study the behavior of several widely used nonlinear formulations and solution strategies for general-purpose compositional simulation. The numerical behaviors using different variable sets, including the so called natural- and mass-type variables, are investigated. We also report on tie-line based parameterization strategies for compositional modeling. The focus is on the fully implicit method (FIM), where the full Jacobian (primary and secondary algebraic equations in terms of both the primary and secondary variables) is constructed. Schur-complement reduction of the full Jacobian is used to assemble the (reduced) Jacobian for the primary equations as a function of the primary unknowns only. The numerical challenges associated with the nonlinear hydrodynamic and thermo-dynamic interactions associated with compositional displacement processes are the focus of this investigation. These include phase appearance and disappearance, crossing into and out of the critical region, wide pressure variations in space and time. The behavior of the Newton iterations as a function of timestep size is analyzed for different variable sets, alignment of equations (including linear and nonlinear constraints), and nonlinear updating strategies. Comparisons are performed for several challenging multi-phase multi-component problems of practical interest.