Multigrid Pressure Solver for Proppant Transport Modelling in Hydraulic Fracturing Simulators

A 6M digital twin for modeling and simulation in subsurface reservoirs

The dynactin complex is required for activation of the dynein motor complex, which plays a critical role in various cell functions including mitosis. During metaphase, the dynein-dynactin complex removes spindle checkpoint proteins from kinetochores to facilitate the transition to anaphase. Three components (p150(Glued), dynamitin, and p24) compose a key portion of the dynactin complex, termed the projecting arm. To investigate the roles of the dynactin complex in mitosis, we used RNA interference to down-regulate p24 and p150(Glued) in human cells. In response to p24 down-regulation, we observed cells with delayed metaphase in which chromosomes frequently align abnormally to resemble a "figure eight," resulting in cell death. We attribute the figure eight chromosome alignment to impaired metaphasic centrosomes that lack spindle tension. Like p24, RNA interference of p150(Glued) also induces prometaphase and metaphase delays; however, most of these cells eventually enter anaphase and complete mitosis. Our findings suggest that although both p24 and p150(Glued) components of the dynactin complex contribute to mitotic progression, p24 also appears to play a role in metaphase centrosome integrity, helping to ensure the transition to anaphase.

Atmospheric conditions in which cellular-roll cloud patterns are apparent, and dependence of the aspect ratios of the cells on depths of the convective layer and the stability ratio are investigated by examining satellite pictures and aerological data over eastern Asia during cold air outbreaks in the months January to March for 1975–82. Vertical profiles of temperature and relative humidity in the convective layer along the cloud bands over the ocean show an increase of static stability, relative humidity, and layer depth in the downwind direction. Longitudinal convective rolls are realized when vertical wind shear is between 10−3 and 10−2 sec−1, and three-dimensional open cells are realized below these values. The cloud top height is proportional to l3/5 of the cloud-band spacing for l≲20 km and to l2/5 for l≳20 km. The obtained aspect ratio for longitudinal rolls ranges from 5 to 18, increasing in the downwind direction at a rate of 1/110 km, while open cells are obtained in the range from 8 t...

We describe a novel approach for up-scaling of geological models of heterogeneous reservoirs. The method, which is based on the use of wavelet transformations, incorporates all the relevant data on the permeability, porosity, and other important properties of a reservoir at all the important scales. It generates a nonuniform computational grid which preserves its resolved structure in the regions around the wells and in the high-permeability zones, but is scaled up in the rest of the geological model. To demonstrate the accuracy and efficiency of the method, we apply it to the study of three important problems, namely, the pressure transient analysis, unstable miscible displacements, and two-phase flows. In the study of multiphase flows, we apply a new and robust front detection method. The numerical dispersion is eliminated by a high-order total variation diminishing (TVD) method which yields results that are as accurate as those obtained by the dual-mesh methods, but with a greatly-reduced computational cost. The speed-up in the computations is up to three orders of magnitude. 1. Introduction Computer simulation of unstable miscible displacements and multiphase flows in petroleum reservoirs involves intensive computations1. Advances in measurement and estimation techniques, together with considerable progress in the development of methods for characterization of petroleum reservoirs, can provide significant amounts of data on various properties of the reservoirs. Using such data, modern geostatistical techniques generate highly resolved geological models of heterogeneous petroleum reservoirs. To carry out reservoir simulations, the governing flow and transport equations are discretized, and the flow domain is divided into grid blocks which are characterized by the associated rock properties. Due to computational limitations (mainly computation time) it is not feasible to carry out multiphase flow simulations with a computational grid that corresponds to the highly resolved geological model. It is, therefore, necessary to up-scale the properties of the grid blocks of the geological model in order to develop a coarsened grid that can be used in reservoir simulation with a reasonable amount of computation time. Up-scaling also plays a critical role in reservoir planning and management. In the past, it was common to forecast production based on reservoir simulations that used deterministic models of reservoirs - those that did not take into account the effect of the uncertainties in the distributions of the reservoirs' properties. However, deterministic models yield predictions that may be more harmful to reservoir planning and management than not having a model at all, since the appraisal of the potential production of a petroleum field must take into account the effect of the uncertainties in the properties of the field. Under such conditions, production forecast obtained by a stochastic model of a reservoir allows the quantification of the effect of the uncertainties on the reservoir performance by simulation of fluid flow in many possible realizations of the same reservoir, which are necessarily very time consuming. To reduce the simulation time, up scaling of the geological model is a natural and, perhaps, the only feasible way. For simulation of single-phase flows, the most important parameter is the absolute permeability, for which up-scaling methods are well-established. However, simulation of multiphase flows involves, in addition to computing the equivalent absolute permeabilities of the coarsened blocks, adjustments to the phase flow through the connected blocks of the coarsened grid. To accomplish this many methods have been proposed, including up-scaling techniques that employ pseudo-functions, the so-called dual-mesh approaches, and simpler non-uniform coarsening methods.

While direct numerical simulation (DNS) of multiphase flows has been the focus of many research investigations in recent years, large eddy simulation (LES) of multiphase flows remains a challenge. There is no standardized set of governing equations for multiphase LES. Different approaches and formulations have been discussed in the literature, each with its own advantages and disadvantages. In this paper, the conventional (non-weighted) filtering approach is compared with the density-weighted Favre filtering method by evaluating the subgrid scale (SGS) energy transfer for a simple test case of a shear-thinning droplet in air. The findings reveal that, unlike the Favre filtering approach, the conventional filtering method results in a notable amount of nonphysical backward scatter in the flow. Based on these results, the Favre filtering method appears preferable and is applied to the a priori analysis of shear-thinning liquid jets, where the viscosity has been modeled using the Carreau–Yasuda model. First, by explicitly filtering existing DNS data of shear-thinning jet breakup into stagnant air, the order of magnitude of different SGS terms is evaluated using the Favre filtering method. Consistent with earlier studies on Newtonian jets, the present study indicates that the diffusive term remains negligible, while the convective term plays a dominant role. Functional and structural models for the closure of the convective SGS term are assessed by means of a correlation analysis and an order of magnitude study. Existing structural models provide good results for both Newtonian and shear-thinning cases. Promising a posteriori model candidates are discussed.

This article considered the numerical simulation of multicomponent multiphase flow in porous media. The resulting system of nonlinear equations linearized by the Newton-Raphson method and solved wi...

Multiphase flow simulations are essential methods for providing information such as the evolution of phase fraction (gas, liquid and solid), velocities, pressure, temperature and flow regimes at every time during a process. Dynamic flow simulations also help reservoir, drilling, and production engineers to develop a proper well design. DamBreak problem is one of the most well-known problems in computational fluid dynamics (CFD); it is a dynamic hydraulic phenomena and the numerical simulation requires sophisticated mathematical modeling. OpenFOAM, is used to run CFD simulations in this thesis.;One of the main issues in CFD is that the simulations are time-consuming. In this work, will use artificial intelligence (AI) to predict the behavior of the system at each time-step of the process at a lower run time. DamBreak problem is defined base on a two-dimensional rectangular tank with a barrier at the bottom, the liquid column (water in this study) at the left side of the tank behind the wall. As soon as the wall collapse, the water will pour down, resulting in complicated fluid dynamics. The main data-set, generated by OpenFOAM flow simulations, is used for building the smart proxy model (SPM), using the network toolbox in MATLAB. Neural network (NN) is applied with feed-forward back propagation method and the training algorithm is Levenberg Marquardt.;Results indicate that the smart proxy can run 3 seconds of the DamBreak process, which takes 8 hours of computational time with 4 processors when is done by using OpenFOAM, takes less than 2 minutes using the developed SPM on one processor. SPM is also capable of predicting the CFD results in non-cascading condition and up to around 40 time-steps in cascading condition with acceptable error (less than %10).

A two-step finite volume method for the simulation of multiphase fluid flow in heterogeneous and anisotropic reservoirs

Based on the principle of virtual works, a multiphase smoothed particle hydrodynamics (SPH) model is further developed from the foundation of Hu X Y et al. (2006) and Grenier N et al. (2009). In the present model, the surface tension force implementation suitable for the multiphase flows with a large density ratio is applied, and this allows a good continuity at the multiphase interface. Artificial displacement correction is applied to keep the particles distributing uniformly in the whole flow field, and therefore any artificial viscous term is never needed; this is very important in the numerical simulation of viscous flows since the introduction of artificial viscosity changes the Reynolds number. Background pressure and interface sharpness force are added in the equation of state and the equation of momentum respectively to ensure the multiphase interface stability and smoothness; this is essential in the simulation of multiphase flows with large density difference at the multiphase interface. Two types of viscosity expressions suitable for multiphase flows are introduced and analyzed; the conclusion is that the formula proposed by Morris et al. (1997) and its similarly derived forms can give more accurate results. In the numerical validations, an oscillating droplet test is applied first to confirm the accuracy of the surface tension model and good results are achieved. This demonstrates that the artificial displacement and the interface sharp force will make negligible effects to the surface tension implementation. After that, two classic quantitative benchmarks of rising bubbles are simulated and the results of SPH agree well with the reference data. Moreover, in the two numerical benchmarks, the effect of the artificial displacement, the choice of the viscosity expression, and the type of the kernel function are compared and finally an optimal combination of these numerical aspects is recommended. Based on the above numerical investigations, the splitting process of an initially circular bubble is simulated and the numerical results agree well with the experimental data. In the last numerical case, the process of chasing and merging between two rising bubbles in vertical direction is simulated, based on which the mechanisms of these interesting interactions between two rising bubbles are analyzed. It is demonstrated in the present work that further improved multiphase SPH model may provide a potential method for the research of bubble dynamics.

An energy preserving formulation for the simulation of multiphase turbulent flows

This paper presents a numerical model that intends to simulate efficiently the surface instability that arise in multiphase flows, typically liquid-gas, both for laminar or turbulent regimes. The model is developed on the in-house computing platform TermoFluids, and operates the finite-volume, direct numerical simulation (DNS) of multiphase flows by means of a conservative level-set method for the interface-capturing. The mesh size is optimized by means of an adaptive mesh refinement (AMR) strategy, that allows the dynamic re-concentration of the mesh in the vicinity of the interfaces between fluids, in order to correctly represent the diverse structures (as ligaments and droplets) that may rise from unstable phenomena. In addition, special attention is given to the discretization of the various terms of the momentum equations, to ensure stability of the flow and correct representation of turbulent vortices. As shown, the method is capable of truthfully simulate the interface phenomena as the Kelvin-Helmholtz instability and the Plateau-Rayleigh instability, both in the case of 2-D and 3-D configurations. Therefore it is suitable for the simulation of complex phenomena such as simulation of air-blast atomization, with several important application in the field of automotive and aerospace engines. A prove is given by our preliminary study of the 3-D coaxial liquid-gas jet.

Development of singular value decomposition based solution scheme for a numerical simulation of multiphase flow

Liquid surge refers to an excessive liquid inflow to a slug catcher or a separator and is one of the main issues in flow assurance. The wellhead choke valves of gas wells must be adjusted to maintain the target flow rate as the reservoir pressure drops. The wellhead choke opening can be determined by conducting multiphase pipeline transient flow simulations to achieve the target flow rate and avoid liquid surges. However, it is not financially and computationally practical to conduct many multiphase transient pipeline flow simulations simultaneously for hundreds of wells. We found that flow rates and maximum liquid surge volumes for gas wells can be predicted accurately using simple machine learning models when the wellhead choke valve is adjusted. The machine learning models provided accurate predictions (R2 > 0.99) regarding flow rates and maximum liquid surge volumes for different wellhead pressure drop plans, vertical and horizontal well lengths, and current operating conditions in cases involving two real fields, the Horn River Basin (HRB) and Rakhine Basin field. The wellhead operating conditions that are appropriate for achieving the target flow rate and avoiding liquid surges can be efficiently determined using the machine learning models instead of multiphase transient pipeline flow simulators. The proposed approach also accurately estimated downhole pressures that are necessary to evaluate reservoir performances given wellhead pressures and flow rates. Lastly, we presented what features are dominant in predicting liquid surge volumes, flow rates, and downhole pressures in feature importance analyses.

Simulation of multiphase flows in porous media

The study and development of high-order discretization techniques for the modeling and simulation of multiphase flows in petroleum reservoirs are still a challenge from the computational viewpoint due to the difficulty posed by some physical features such as heterogeneity and anisotropy of the medium, that are of paramount importance in this class of applications. In this paper, we present a preliminary investigation of the very high order Spectral Finite Volume Method (SFVM) for the discretization of the saturation equation that describes the 1-D Oil-Water displacement through porous media. In this equation, the hyperbolic term is discretized using a high order SFVM, the capillary term is approximated using a second order CVFD (Control Volume Finite Difference) method and the integration in time is carried out using a third-order Runge–Kutta method. On the other hand, to prevent numerical oscillations near shocks, that are typical from higher order schemes, a slope limiter procedure is used in the reconstruction stage. To evaluate the performance of the SFVM some simple model problems, including capillarity and gravity, are solved, yielding accurate and efficient results. The use of very high order formulations can be of utmost importance, particularly for multidimensional and real large-scale applications with complex wave structures.