Model For Flow In Porous Media Research Articles

Parameter sampling capabilities of sequential and simultaneous data assimilation: II. Statistical analysis of numerical results

We assess and compare parameter sampling capabilities of one sequential and one simultaneous Bayesian, ensemble-based, joint state-parameter (JS) estimation method. In the companion paper, part I (Fossum and Mannseth 2014 Inverse Problems 30 114002), analytical investigations lead us to propose three claims, essentially stating that the sequential method can be expected to outperform the simultaneous method for weakly nonlinear forward models. Here, we assess the reliability and robustness of these claims through statistical analysis of results from a range of numerical experiments. Samples generated by the two approximate JS methods are compared to samples from the posterior distribution generated by a Markov chain Monte Carlo method, using four approximate measures of distance between probability distributions. Forward-model nonlinearity is assessed from a stochastic nonlinearity measure allowing for sufficiently large model dimensions. Both toy models (with low computational complexity, and where the nonlinearity is fairly easy to control) and two-phase porous-media flow models (corresponding to down-scaled versions of problems to which the JS methods have been frequently applied recently) are considered in the numerical experiments. Results from the statistical analysis show strong support of all three claims stated in part I.

Modeling and analysis of evaporation processes from porous media on the REV scale

The dynamics of drying processes from porous media are critically influenced by the intensity of an adjacent free flow and by processes at the interface between free flow and the porous medium. In this paper, the influence of hydraulic properties of a porous medium and of the interaction between fluids and porous medium on the drying dynamics during the capillary-flow dominated stage-1 and transition to the diffusion-dominated stage-2 are studied using a coupled free-flow—porous-medium flow model on the REV scale. We present a detailed model concept that considers mass balance equations, an energy balance equation, and the coupling to the adjacent free flow. Key microscale processes are identified and incorporated in the macroscale description of the evaporation process. Own experimental results are used to illustrate main features of the modeling framework. We demonstrate that the use of a homogeneous distribution of soil parameters without consideration of pore-scale induced nonlinearities in the numerical simulations results in a rather constant drying rate in stage-1, which was not observed for the high evaporative demand in the experiments. To account for the dependency of the drying rate on the surface moisture content, special conditions based on the work of Haghighi et al. (2013) and Schlunder (1988) are analyzed for their applicability on the REV scale. Typical features of a drying process, such as different stages of the drying rate, could be reproduced.

Parallel numerical simulation of two-phase flow model in porous media using distributed and shared memory architectures

A two-phase (water and oil) flow model in a homogeneous porous media is studied, considering immiscible and incompressible displacement. This model is numerically solved using the Finite Volume Method (FVM) and we compare four numerical schemes for the approximation of fluxes on the faces of the discrete volumes. We describe briefly how to obtain the mathematical and computational models applying axiomatic formulations and generic programming. Two strategies of parallelization are implemented in order to reduce the execution time. We study distributed (cluster of CPUs) and shared (Graphics Processing Units) memory architectures. A performance comparison of these two architectures is done along with an analysis of the four numerical schemes, for a water-flooding five-spot pattern model.

Survey on Efficient Linear Solvers for Porous Media Flow Models on Recent Hardware Architectures

In the past few years, High Performance Computing (HPC) technologies led to General Purpose Processing on Graphics Processing Units (GPGPU) and many-core architectures. These emerging technologies offer massive processing units and are interesting for porous media flow simulators may used for CO<sub>2<sub/> geological sequestration or Enhanced Oil Recovery (EOR) simulation. However the crucial point is “are current algorithms and software able to use these new technologies efficiently?”The resolution of large sparse linear systems, almost ill-conditioned, constitutes the most CPU-consuming part of such simulators. This paper proposes a survey on various solver and preconditioner algorithms, analyzes their efficiency and performance regarding these distinct architectures. Furthermore it proposes a novel approach based on a hybrid programming model for both GPU and many-core clusters. The proposed optimization techniques are validated through a Krylov subspace solver; BiCGStab and some preconditioners like ILU0 on GPU, multi-core and many-core architectures, on various large real study cases in EOR simulation.

Two-Level Domain Decomposition Methods for Highly Heterogeneous Darcy Equations. Connections with Multiscale Methods

Multiphase, compositional porous media flow models lead to the solution of highly heterogeneous systems of Partial Differential Equations (PDE). We focus on overlapping Schwarz type methods on parallel computers and on multiscale methods. We present a coarse space [Nataf F., Xiang H., Dolean V., Spillane N. (2011) <i>SIAM J. Sci. Comput.<i/> <b>33<b/>, 4, 1623-1642] that is robust even when there are such heterogeneities. The two-level domain decomposition approach is compared to multiscale methods.

A two-grid expanded mixed element method for nonlinear non-Fickian flow model in porous media

The full discrete scheme of expanded mixed finite element approximation is introduced for nonlinear parabolic integro-differential equations modelling non-Fickian flow in porous media. To solve the nonlinear problem efficiently, a two-grid algorithm is considered and analysed. This approach allows us to perform all of the nonlinear iterations on a coarse grid space and just execute a linear system on a fine grid space. Based on RTk mixed element space, error estimates and convergence results are presented for solutions of the two-grid method. Some numerical examples are given to verify the theoretical predictions and show the efficiency of the two-grid method.

Predicting Natural Gas Viscosity with a Mixture Viscosity Model for the Entire Fluid Region

A new predictive corresponding-states mixture viscosity model for the entire fluid region and large range of temperature and pressure is reported here. Using previously published parameters for pure n-alkanes, viscosity predictions with this model were made for the methane–ethane system and twelve component Qatari synthetic natural gas mixtures. For the synthetic natural gas mixtures studied, the new model presented here has comparable predictability to other literature models and superior predictability at higher (11 mol %) levels of N2 and CO2 content. The integral use of the PC-SAFT equation of state with the fluid mixture viscosity model introduced here provides an attractive unified approach for modeling flow in porous media.

Adaptive moving grid methods for two-phase flow in porous media

In this paper, we present an application of the moving mesh method for approximating numerical solutions of the two-phase flow model in porous media. The numerical schemes combine a mixed finite element method and a finite volume method, which can handle the nonlinearities of the governing equations in an efficient way. The adaptive moving grid method is then used to distribute more grid points near the sharp interfaces, which enables us to obtain accurate numerical solutions with fewer computational resources. The numerical experiments indicate that the proposed moving mesh strategy could be an effective way to approximate two-phase flows in porous media.

Porous media flow models for maternal placental circulation

s / Placenta 34 (2013) A1–A99 A15 Conclusion: Detailed placental measures collected by simple imaging methods illuminate placental functional efficiency, a key factor in gestational life that is likely important in fetal programming. PCA demonstrates the complex interactions between lateral expansion of the chorionic plate surface, branching growth of chorionic surface vessels, and arborisation of the fetal stem villi to create the placental surface exchange area that makes up disk thickness. Measurement of any single dimension can lead to misleading conclusions because in different combinations, specific measures may have opposite effects on beta. http://dx.doi.org/10.1016/j.placenta.2013.06.044 P1.8. POROUS MEDIA FLOW MODELS FOR MATERNAL PLACENTAL CIRCULATION Christopher Ball , David Grynspan , Andree Gruslin 3,4 Department of Pathology and Laboratory Medicine, The Ottawa Hospital, Ottawa, Ontario, Canada; Department of Pathology and Laboratory Medicine, Children's Hospital of Eastern Ontario, Ottawa, Ontario, Canada; Department of Obstetrics and Gynecology, The Ottawa Hospital, Ottawa, Ontario, Canada; Department of Cellular Molecular Medicine, The Ottawa Hospital, Ottawa, Ontario, Canada Introduction: It is reasonable to believe that the presence of abnormal flow patterns in the chorionic vessels is an earlier and more sensitive predictor of IUGR than altered end diastolic flow in the umbilical artery. It furthermore appears that the prediction of IUGR becomes increasingly sensitive as predictive flowmeasurements are taken increasingly distal (to the fetus) in the umbilical cord. This, we hypothesize, results from remodelling of the villous circulatory beddthe most proximate correlate of the factors that lead to IUGR. The effect of lacunar blood flow, the intimately connected maternal side of placental flow, cannot be ignored. Aim:Our aim is tomodel the fluidmechanics of the normalmaternal lacunar blood flows in order to assess its influence on flow within the measurable parts of the fetal arterial tree. In view of the placental structure, we aim to apply a model of flow through porous media to the maternal flow bed. Methods: Preliminary inquiry has lead us to suspect that this flowproblem is analogous to the problem of laminar flow through a porous medium (such as in models of fuel cells, ground water, etc.). Here we will illustrate application of this canonical flow model to that of the maternal placenta. Discussion: The problem of modelling EDFR provides an example where interdisciplinary collaboration between medicine and engineering hopefully will permit rapid progress through novel application to one field of established constructs from another. http://dx.doi.org/10.1016/j.placenta.2013.06.045 P1.9. ECHOCARDIOGRAPHIC ANALYSES OF PREGNANCIES IN THE PLACENTAL GROWTH FACTOR KNOCKOUT MOUSE Kristiina Aasa , Bruno Zavan , Philip Wong , Yat Tse , Stephen Pang , B. Anne Croy 1 Queen's University, Kingston, ON, Canada; UNIFAL-MG, Alfenas, Minas

Approximating the vanishing capillarity limit of two‐phase flow in multi‐dimensional heterogeneous porous medium

AbstractNeglecting capillary pressure effects in two‐phase flow models for porous media may lead to non‐physical solutions: indeed, the physical solution is obtained as limit of the parabolic model with small but non‐zero capillarity. In this paper, we propose several numerical strategies designed specifically for approximating physically relevant solutions of the hyperbolic model with neglected capillarity, in the multi‐dimensional case. It has been shown in [Andreianov &amp; Cancès, Comput. Geosci., DOI: 10.1007/s10596‐012‐9329‐8, 2013] that in the case of the one‐dimensional Buckley‐Leverett equation with distinct capillary pressure properties of adjacent rocks, the interface may impose an upper bound on the transmitted flux. This transmission condition may reflect the oil trapping phenomenon. We recall the theoretical results for the one‐dimensional case which are used to motivate the construction of multi‐dimensional finite volume schemes. We describe and discuss a coupled scheme resulting as the limit of the scheme constructed in [Brenner &amp; Cancès &amp; Hilhorst, HAL preprint no.00675681, 2012] and two IMplicit Pressure – Explicit Saturation (IMPES) schemes with different level of coupling. We finally provide numerical evidences of the good behavior of the fully decoupled version of the IMPES scheme.

Simulation of Multiphase Flow of the Oil-Water Separation in a Rotating Packed Bed for Oil Purification

HIGEE (High Gravity Rotary Device) rotating oil purifier which consists of two parts: hydrocyclone separator and rotating packed bed (abbr. RPB) is considered to be capable of removing the solid particle contaminant, moisture and gas simultaneously. As the major unit of HIGEE, the RPB uses centrifugal force to intensify mass transfer. Because of the special structure of RPB, the hydraulic characteristics of the RPB are very important. In this study, the multiphase flow model in porous media of the RPB is presented, and the dynamical oil-water separation in the RPB is simulated using a commercial computational fluid dynamics code. The operating conditions and configuration on the hydraulic performance of the RPB are investigated. The results have indicated that the separation efficiency of HIGEE rotating oil purifier is predominantly affected by operating conditions and the configurations. The best inlet pressure is 0.002 MPa. When the liquid inlet is placed in the outside of the lower surface of RPB; oil outlet is placed in the upper surface, where it is near the rotation axis; and water outlet is placed in the middle of the RPB, where it is far away from the oil outlet, the separating efficiency is the best.

Numerical Simulation of Two-Phase Flow in a Rotating Packed Bed

According to the development of a new type of oil purifier——HIGEE rotating oil purifier, this paper has carried out related numerical simulations. The two-phase porous medium flow model in the rotating packed bed (RPB) was built, and by using CFD software, the distribution of the phases in the RPB which is on the condition of high gravity (HIGEE) field and the porous media has been simulated. The paper has developed the influencing rule of key technologies parameters which affect the separating efficiency of the rotating packed bed.

Numerical Modeling of Degenerate Equations in Porous Media Flow

In this paper is introduced a new numerical formulation for solving degenerate nonlinear coupled convection dominated parabolic systems in problems of flow and transport in porous media by means of a mixed finite element and an operator splitting technique, which, in turn, is capable of simulating the flow of a distinct number of fluid phases in different porous media regions. This situation naturally occurs in practical applications, such as those in petroleum reservoir engineering and groundwater transport. To illustrate the modelling problem at hand, we consider a nonlinear three-phase porous media flow model in one- and two-space dimensions, which may lead to the existence of a simultaneous one-, two- and three-phase flow regions and therefore to a degenerate convection dominated parabolic system. Our numerical formulation can also be extended for the case of three space dimensions. As a consequence of the standard mixed finite element approach for this flow problem the resulting linear algebraic system is singular. By using an operator splitting combined with mixed finite element, and a decomposition of the domain into different flow regions, compatibility conditions are obtained to bypass the degeneracy in order to the degenerate convection dominated parabolic system of equations be numerically tractable without any mathematical trick to remove the singularity, i.e., no use of a parabolic regularization. Thus, by using this procedure, we were able to write the full nonlinear system in an appropriate way in order to obtain a nonsingular system for its numerical solution. The robustness of the proposed method is verified through a large set of high-resolution numerical experiments of nonlinear transport flow problems with degenerating diffusion conditions and by means of a numerical convergence study.

Two-Component Two-Compressible Flow in a Porous Medium

We prove existence of solutions of a two-compressible (liquid and gas) phase flow model in porous media with two components (water and hydrogen). This model is obtained by writing the mass conservation for each component in each phase. We suppose that the mass exchange between dissolved hydrogen and hydrogen in the gas phase is supposed finite. This mass exchange is modeled by a source term on each mass conservation equations.

Assessment of groundwater inflows into Kuteshwar Limestone Mines through flow modeling study, Madhya Pradesh, India

The development of limestone mining activities in Katni, Madhya Pradesh becomes necessary to increase the depth of exploration to produce ore. Increase in the exploration depth means that mining pits were subjected to water inrush. A hydrological and a hydrogeological model for the Katni area have been developed using USGS flow code, MODFLOW 2000. Collected GIS-based information was synthesized in a finite difference numerical model. The regional steady flow was calibrated under pre-development conditions assuming an equivalent porous medium approach. Water budget calculations show that the total groundwater flow into the aquifer system due to interaction with river amounts to 14,783 m3/day. Infiltration from precipitation provides 1,600 m3/day of the groundwater supply, while 1,446 m3/day comes from lateral inflow and the remaining. The inflows into mine pit area amounts to 15,725 m3/day. Although the karstic nature of the limestone aquifer the equivalent porous medium flow model is appropriate to represent hydraulic heads and recharge/discharge relationships on a regional scale. The results of this study can be used to predict the required amounts of pumping and the possible locations to dewater the groundwater in the mining pits.

Dispersive Stresses at the Canopy Upstream Edge

The derivation of flow and mass transfer models in canopy and porous media environments involves the spatial-averaging of the flow properties and their subscale equations. The averaging of the momentum equation generates the dispersive stress terms that represent the subscale spatial variations of the unresolved velocity field. While previous studies ignored the dispersive stresses in their flow models, recent evidence indicates that the dispersive stresses may be important. Here we focus our attention on the magnitude of the normal dispersive stresses in the entry region of a ‘forest patch’, where the in-canopy velocities are large and the longitudinal derivatives do not cancel out. Highly detailed particle image velocimetry measurements, at a temporal and spatial resolution of 5 Hz and 1.4 mm, are obtained inside and around a 1-m long model canopy which consists of transparent vertical cylinders 6 mm in diameter and 74.3 mm high (h). The cylinders are randomly distributed to form a relatively sparse forest patch with a leaf area density of 7.56 m−1 and a fluid volume fraction (porosity) of 0.965. We present results of the double averaged flow properties at three different regions of the forest patch; the upstream edge (x ≈ 0), the fully-developed interior region (x ≈ 10h) and the downstream edge (x ≈ 13h). We find that the normal dispersive stresses around the entry region of the forest patch are significantly larger than the normal Reynolds stresses. An order of magnitude analysis of the relevant terms in the momentum equation indicates that the longitudinal derivatives of the dispersive stresses are of the same order of magnitude as that of the drag force and similar to that of the horizontal convection term. The longitudinal derivatives of the Reynolds stresses are smaller, though cannot be ignored. Comparing these results with the characteristic profiles measured in the fully-developed region indicates that the dispersive stresses, which are generated at the forest patch entrance, decrease along an adjustment region while maintaining their profile shape. We find that the dispersive stresses influence the rate at which momentum penetrates into the canopy. These observations suggest that under certain flow conditions, dispersive stresses may dominate the momentum balance and therefore must be considered in future canopy and porous media flow models.

A novel meshing and finite element flow model for porous media

This work presents a new fully-unstructured meshing scheme for generating simulation meshes, coupled with a novel simulation method for fluid flow models in porous media. We use unstructured tetrahedral meshing algorithms to generate meshes that rigorously adhere to structural and depositional heterogeneity in geological reservoir models at multiple scales. Geological heterogeneity is represented using numerous surfaces, in contrast with traditional pixel- or grid-based methods. This approach allows the generation of meshes which capture heterogeneity more efficiently and accurately than structured or partially-structured grids. The flow simulations are performed using a new hybrid discontinuous Galerkin/control volume based method which combines continuous pressure and discontinuous velocities. Our approach rigorously enforces material balance equations while ensuring crucial scalar fields such as pressure and saturation remain positive and bounded. This research has direct application to aquifer flow systems. We report the results of single-phase flow simulations on unstructured meshes for complex geological systems. These simulations accurately model the spread of groundwater contaminants such as methyl tertiary butyl ether (MTBE) ormetals such as arsenic that behave as tracers in aquifers. Initially, simulations are run on simple anisotropic geological systems for two-dimensional flow to benchmark against analytical solutions and validate the accuracy of the simulator for simple flow problems. Next, simulations for tracer flow are performed on 3D channelized and fractured reservoir systems to demonstrate the robustness and accuracy of the new grids and simulator in complex reservoir geology. We present numerical simulations of single-phase flow for a variety of geological systems of increasing complexity, culminating in systems which would be impossible to mesh and solve with structured meshes. This is also a first step towards a more complex multi-phase and multi-component implementation of the novel methods for flow through porous media.

Quasi-Newton acceleration of ILU preconditioners for nonlinear two-phase flow equations in porous media

In this work, preconditioners for the iterative solution by Krylov methods of the linear systems arising at each Newton iteration are studied. The preconditioner is defined by means of a Broyden-type rank-one update of a given initial preconditioner, at each nonlinear iteration, as described in [5] where convergence properties of the scheme are theoretically proved. This acceleration is employed in the solution of the nonlinear system of algebraic equations arising from the finite element discretization of two-phase flow model in porous media. We report numerical results of the application of this approach when the initial preconditioner is chosen to be the incomplete LU decomposition of the Jacobian matrix at the initial nonlinear stage. It is shown that the proposed acceleration reduces the number of linear iterations needed to achieve convergence. Also, the cost of computing the preconditioner is reduced as this operation is made only once at the beginning of the Newton iteration.

Modeling of unrest signals in heterogeneous hydrothermal systems

Monitoring of quiescent volcanoes, such as Campi Flegrei (Italy), involves the measurement of geochemical and geophysical parameters that are expected to change as eruptive conditions approach. Some of these changes are associated with the hydrothermal activity that is driven by the release of heat and magmatic fluids. This work focuses on the properties of the porous medium and on their effects on the signals generated by the circulating fluids. The TOUGH2 porous media flow model is applied to simulate a shallow hydrothermal system fed by a source of magmatic fluids. The simulated activity of the source, with periods of increased fluid discharge, generates changes in gas composition, gravity, and ground deformation. The same boundary conditions and source activity were applied to simulate the evolution of homogeneous and heterogeneous systems, characterized by different rock properties. Phase distribution, fluid composition, and the related signals depend on the nature and properties of the rock sequence through which the fluids propagate. Results show that the distribution of porosity and permeability affects all the observable parameters, controlling the timing and the amplitude of their changes through space and time. Preferential pathways for fluid ascent favor a faster evolution, with larger changes near permeable channels. Slower changes over wider areas characterize less permeable systems. These results imply that monitoring signals do not simply reflect the evolution of the magmatic system: intervening rocks leave a marked signature that should be taken into account when monitoring data are used to infer system conditions at depth.

THE ROLE OF POROUS MEDIA IN MODELING FLUID FLOW WITHIN HOLLOW FIBER MEMBRANES OF THE TOTAL ARTIFICIAL LUNG

A numerical study was conducted to analyze fluid flow within hollow fiber membranes of the artificial lungs. The hollow fiber bundle was approximated using a porous media model. In addition, the transport equations were solved using the finite-element formulation based on the Galerkin method of weighted residuals. Comparisons with previously published work on the basis of special cases were performed and found to be in excellent agreement. A Newtonian viscous fluid model for the blood was used. Different flow models for porous media, such as the Brinkman-extended Darcy model, Darcy's law model, and the generalized flow model, were considered. Results were obtained in terms of streamlines, velocity vectors, and pressure distribution for various Reynolds numbers and Darcy numbers. The results from this investigation showed that the pressure drop across the artificial lung device increased with an increase in the Reynolds number. In addition, the pressure drop was found to increase significantly for small Darcy numbers.