The particle-in-cell method (PIC), especially the latest version of it, the material point method (MPM), has shown significant advantage over the pure Lagrangian method or the pure Eulerian method in numerical simulations of problems involving large deformations. It avoids the mesh distortion and tangling issues associated with Lagrangian methods and the advection errors associated with Eulerian methods. Its application to multiphase flows or multi-material deformations, however, encounters a numerical difficulty of satisfying continuity requirement due to the inconsistence of the interpolation schemes used for different phases. It is shown in Section 3 that current methods of enforcing this requirement either leads to erroneous results or can cause significant accumulation of errors. In the present paper, a different numerical method is introduced to ensure that the continuity requirement is satisfied with an error consistent with the discretization error and will not grow beyond that during the time advancement in the calculation. This method is independent of physical models. Its numerical implementation is quite similar to the common method used in Eulerian calculations of multiphase flows. Examples calculated using this method are presented.

Summary General, ensemble phase-averaged equations for multiphase flows were specialized for the simulation of the steam-assisted-gravity-drainage (SAGD) process. In the average momentum equation, fluid/solid and fluid/fluid viscous interactions are represented by separate force terms. This equation has a form similar to that of Darcy's law for multiphase flow but augmented by the fluid/fluid viscous forces. Models for these fluid/fluid interactions are suggested and implemented into the numerical code CartaBlanca. Numerical results indicate that the model captures the main features of the multiphase flow in the SAGD process, but the detailed features, such as plumes, are missed. We find that viscous coupling among the fluid phases is important. Advection time scales for the different fluids differ by several orders of magnitude because of vast viscosity differences. Numerically resolving all these time scales is time consuming. To address this problem, we introduce a steam-surrogate approximation to increase the steam-advection time scale, while keeping the mass and energy fluxes well-approximated. This approximation leads to approximately a 40-fold speedup in execution speed of the numerical calculations at the cost of a few percentage errors in the relevant quantities.

Abstract A tightly integrated high performance parallel simulator for the management and optimization of multiple reservoirs, wells, and surface facilities is presented with subsea and giant field example applications cases. These cases have helped to develop and improve subsequent simulator releases. Specialized production management algorithms are implemented by flexible user-developed procedures written in a specialized object-based Fortran-like language. Tight coupling enables accurate prediction of all phase production rates and multiple gas and water injection rates. The new reservoir simulation tool was applied to the multireservoir Greater Plutonio (GtP) field in offshore Angola and to the giant Prudhoe Bay Unit (PBU) field in Alaska. These cases have provided the greatest challenges to the simulator in the BP system and have driven development. In both cases, the simulations were developed coupling the reservoir to the surface facilities, and user-developed procedures were included to manage and optimize production. Numerous algorithmic improvements were made to the base code to accommodate additional required functionality for the user management procedures and to achieve sufficient performance for the extensive PBU network model. For GtP, four fields were included in the full network model with multiple wells, risers, manifolds, and seabed pipeline connections. Procedures were used to model the gas injection, export, riser gas lift optimization, and facility and production constraints. Another procedure replicated the yearly production engineering optimization by shutting in wells by water-cut class for week-long tests each January. From these tests, the procedure selected the best combination of wells to accelerate oil production for the remainder of the year. Results have shown good agreement with actual production. For the PBU, a development campaign is underway to enable predictive simulation, including algorithms for predictive well management (PWM), seam tuning, and automatic drilling. The PWM algorithm for the optimal allocation of wells to low- and high-pressure systems in each of the six PBU flow stations will be implemented by user procedures. New functionality is also being developed to improve parallel operation of the network and to enable intelligent selective use of the network over time. The effort is expected to lead to substantially improved simulator performance in terms of flexibility and practicality. Many of the new features have benefited other assets. The updated simulator represents a step change in reservoir engineering management capability for the operator, resulting from increased accuracy, performance, and user flexibility. Tight coupling with scalable high performance enables accurate and stable prediction and operation. The inclusion of an extensive user procedure facility for customizable production management algorithms enables both mirroring of existing management practices and the testing of a variety of proposed alternatives. User procedures can be reused and shared among assets.

Abstract A tractable, predictive modeling approach for Cold Heavy Oil Production with Sand (CHOPS) remains a significant practical challenge. In CHOPS, instabilities of oil-sand interactions lead to formation of meso-scale structures, such as wormholes or other defects. The sand stress concentration around these structures often leads to sand failure, and production of sand in the process. The failure and motion of sand alter the permeability, and hence affect the oil production. Because these structures result from the instability of the oil-sand interactions, sizes, shapes and locations of these structures are unpredictable. One can only describe them using the statistical methods. Furthermore, in typical well-drainage scale or multi-well-scale numerical simulations these mesoscale structures are typically below the level of resolution and must be modeled as sub-grid-scale effects. Rigorous well-drainage-scale averaged governing equations can be easily derived, but closure models for the sand stress and sand production cannot be adequately developed without proper description of the sub-grid effects. The sub-grid momentum balance equation for sand demands that the divergence of the sand stress balances the gravity, pressure gradient and oil drag. Since gravity is a constant, and for a given mesoscale structure, the oil flow rate and hence the drag is determined by the imposed macroscopic pressure gradient, without information from sub-grid-scale pressure variation, we assert that the pressure gradient is the only independent variable affecting the stress and failure in sand. This leads to the proposition of closing the well-drainage-scale averaged governing equations in terms of the pressure gradient without explicitly involving the sand stress. Based on this proposition we derive a well-drainage-scale pressure diffusion equation without explicit representation of the sand stress. To develop the closure models, we can extract information from both explicit full-physics simulations of the sub-grid-scale effects with resolved sand stress and from pilot scale production data. Full physics simulations using the multiphase material point method are shown to adequately model lab-scale wormhole experiments. History matched simulations at the well-drainage scale are shown to track transients in pilot data and are a measure of the success of the modeling approach.

Abstract Cold Heavy Oil Production with Sand (CHOPS) is a well-known primary heavy oil recovery method. In CHOPS, a key mechanism of production is the formation of wormholes. Wormholes are believed to be nearly cylindrical zones of high permeability that originate from production wells when sand is produced along with the oil. A multi-scale modelling approach based on the multiphase material point method (MMPM) has been applied to the problem of developing a general predictive capability for CHOPS and wormhole growth. The MMPM is a Lagrangian-Eulerian methodology which permits simulation of multiphase flow problems with fluid-structure interaction in which there is substantial material deformation, damage and failure. MMPM is applied to the problem of simulating the growth of a wormhole in unconsolidated sand with live oil including the effect of foamy oil and sand failure. The simulation results show general features such as asymmetry and slugging. Comparison with experimental data for wormhole length with time was favourable. Up-scaling of the method is required to make predictions on the well to field scale. For this purpose, an up-scaled pressure-field-driven scheme has been developed to predict wormhole network structure. It is hypothesized that a pressure-field-based approached is adequate for a macroscopic simulation with resolution above the length scale of the wormhole tips at which the tensor nature of the failure mechanics are more important. The model includes a generalized sand failure criterion that couples with a non-linear pressure equation and foamy oil and sand flow equations. The model resolves separate wormhole regions emerging from the CHOPS pilot well. Robust history matching of commercial pilot production data is provided as partial model validation.

Numerical calculation of interactions of different materials, such as fluid-structure interactions, has been a significant challenge for many numerical methods especially when the problem involves large deformation of solids that interact with fluids. For a fluid the stress can often be calculated from the strain rate, which can be calculated directly from the velocity fields. For a solid material, the stress is related to the strain of the material, which cannot be calculated directly from the velocity field. To calculate strain in a solid material one either uses Lagrangian meshes to track the history of the material deformation, or advects the strain or stress in the solid material through Eulerian meshes. The first approach often suffers from issues related to mesh tangling in cases of large deformation, while the second approach suffers from numerical diffusion that renders numerically inaccurate results and causes difficulties in locating material interfaces. Difficulties related to modeling interactions of materials undergoing large deformations are not only limited to the numerical aspects, but also involve theoretical models when material interactions result in mixing of the material, or involve mesoscale structures smaller than the resolution of computational meshes, such as porous structures of the material or fragmentation of solids under impact. The pore size and the debris size can be smaller than the resolution of the meshes. To practically model these interactions, one has to rely on macroscopic models that consider interactions of the materials at both the macroscopic and the microscopic scales. Numerical schemes used need to have the capability of tracking material deformation history with little or no numerical diffusion and without issues related to mesh tangling under a large deformation. In this paper we introduce such a theoretical framework and a numerical method that can be used to model such interactions. The theoretical framework is based on a recently formulated continuous multiphase flow theory. The numerical method is based on the material point method extended to calculate multiphase flows. Several numerical examples are presented.

in many models for disperse two-phase flows, the pressure of the disperse phase is often assumed to be the same as that of the continuous phase, or differ only by an amount caused by the surface tension. This type of model is referred to as an equilibrium pressure model. Recent research indicates that the stress difference between the phases caused by dynamics of the motion can be significantly important in the modeling of disperse two-phase flows. Although this difference is still ignored in most calculations of disperse multiphase flows for various reasons, when an equilibrium pressure model is applied to continuous multiphase flows, a conceptual difficulty arises. For instance, the equilibrium pressure model cannot be used to study the tensile break of a sponge with interconnected pores, because the air in the pores can never go into tension while the sponge material does not break without tension.To avoid this conceptual difficulty, a multipressure model is introduced for continuous multiphase flows by analyzing and then modifying the implicit assumption about the volumetric strain rates involved in the equilibrium pressure model. Numerical implementations of the multipressure model are discussed. An example using the multipressure model is presented. Published by Elsevier Ltd.

CartaBlanca is a flexible software environment for prototyping physical models and simulation of a wide range of physical systems. It employs modern discretization schemes and solution methods for nonlinear physics problems on unstructured grids. CartaBlanca adopts an object-oriented, component-like design using the Java programming language. CartaBlanca is implemented with the finite-volume method and material point method (MPM). For the finite-volume method, the Arbitrary Lagrangian-Eulerian (ALE) method is used to provide flexibility with regard to physical models. Optionally, MPM can be used to effectively trace large deformation of materials while avoiding mesh tangling issues in Lagrangian methods and numerical diffusion issues in Eulerian methods. The Jacobian-Free Newton Krylov (JFNK) method is used for the solution of the nonlinear algebraic systems arising from the discretization of the governing partial differential equations. CartaBlanca has been used to simulate multiphase flows, fluid-structure interactions, heat transfer and solidification, and free surface flows. The basic equations solved in CartaBlanca are based on multiphase flow theory. Single phase flow is treated as a special case of multiphase flow. Considerable work has been devoted to the study of disperse and continuous multiphase flows. In disperse multiphase flows, there is only one continuous phase and all other phases are in the form of particles, droplets or bubbles with sizes small compared to the macroscopic length scale of the flow. A continuous multiphase flow, in contrast, contains more than one continuous phase occupying regions or forming interconnected networks with length scales comparable to the macroscopic length i

A multi-phase flow code is used to simulate the separation of an aqueous and an organic stream in the rotor zone of an annular centrifugal contactor. Different values for the mixture viscosity and for the initial volume fractions of the components are considered. A simple model for mass transfer of a species between phases is used. Geometrical effects are found to have significant influence on the separation of the two-phase mixture.

During the past two decades, Los Alamos National Laboratory (LANL) has developed computational algorithms and software for analysis of multiphase flow suitable for high-speed projectile penetration of metallic and nonmetallic materials, using a material point method (MPM)-multiphase flow method (MFM). Recently, ACTA has teamed with LANL to advance a computational algorithm for simulating complex weapon-target interaction for penetrating and exploding munitions, such as tank rounds and artillery shells, as well as non-exploding kinetic energy penetrators. This paper will outline the mathematical basis for the MPM-MFM method as implemented in LANL's CartaBlanca code. CartaBlanca, written entirely in Java using object-oriented design, is used to solve complex problems involving (a) failure and penetration of solids, (b) heat transfer, (c) phase change, (d) chemical reactions, and (e) multiphase flow. We will present its application to the penetration of a steel target by a tungsten cylinder and compare results with time-resolved experimental data published by Anderson, et. al., Int. J. Impact Engng., Vol. 16, No. 1, pp. 1-18, 1995.

Plasma simulation is an important example of a high‐performance computing application where computer science issues are of great relevance. In a plasma, each particle, electron or ion, interacts with the external fields and with other particles in ways that can be readily and effectively emulated using object‐oriented programming. However, the great cost of plasma simulations has traditionally discouraged object‐oriented implementations due to their perceived inferior performance compared with classic procedural FORTRAN or C. In the present paper, we revisit this issue. We have developed a Java particle‐in‐cell code for plasma simulation, called Parsek. The paper considers different choices for the object orientation and tests their performance. We find that coarse‐grained object orientation is faster and practically immune from any degradation compared with a standard procedural implementation (with static classes). The loss in performance for a fine‐grained object orientation is a factor of about 50%, which can be almost completely eliminated using advanced Java compilation techniques. The Java code Parsek also provides an interesting realistic application of high‐performance computing to compare the performance of Java with FORTRAN. We have conducted a series of tests considering various Java implementations and various FORTRAN implementations. We have also considered different computer architectures and different Java Virtual Machines and FORTRAN compilers. The conclusion is that with Parsek, object‐oriented Java can reach CPU speed performances more or less comparable with procedural FORTRAN. This conclusion is remarkable and it is in agreement with the most recent benchmarks, but is at variance with widely held misconceptions about the alleged slowness of Java. Copyright © 2005 John Wiley & Sons, Ltd.