Numerical Multiphase Flow Model Research Articles

Estimation of Fracture–Matrix Transport Properties from Saturation Profiles Using a Multivariate Automatic History Matching Method

This study focuses on the development and implementation of a numerical model of multiphase flow in a fractured core sample by describing the capillary pressure–relative permeability characteristics. An automated history matching approach is proposed to determine relative permeability and capillary pressure curves simultaneously for both matrix and fracture consistent with a core flood reservoir model performance, which relies on a commercial reservoir simulator coupled with an optimization protocol. The results indicate that the proposed approach successfully predicts relative permeability and capillary pressure curves of a fractured core sample and provides a foundation for field-scale history matching with simultaneous estimation of transport properties.

The impact of heterogeneity on the distribution of CO 2: Numerical simulation of CO 2 storage at Ketzin

Numerical modelling of multiphase flow is an essential tool to ensure the viability of long-term and safe CO 2 storage in geological formations. Uncertainties arising from the heterogeneity of the formation and lack of knowledge of formation properties need to be assessed in order to create a model that can reproduce the data available from monitoring. In this study, we investigated the impact of unknown spatial variability in the petrophysical properties within a sandy channel facies of a fluviatile storage formation using stochastic methods in a Monte Carlo approach. The stochastic method has been applied to the Ketzin test site (CO 2SINK), and demonstrates that the deterministic homogeneous model satisfactorily predicts the first CO 2 arrival time at the Ketzin site. The equivalent permeability was adjusted to the injection pressure and is in good agreement with the hydraulic test. It has been shown that with increasing small-scale heterogeneity, the sharpness of the CO 2 front decreases and a greater volume of the reservoir is affected, which is also seen in an increased amount of dissolved CO 2. Increased anisotropy creates fingering effects, which result in higher probabilities for earlier arrival times. Generally, injectivity decreases with increasing heterogeneity.

Parameter estimation from flowing fluid temperature logging data in unsaturated fractured rock using multiphase inverse modeling

Parameter Estimation From Flowing Fluid Temperature Logging Data In Unsaturated Fractured Rock Using Multiphase Inverse Modeling Sumit Mukhopadhyay, Yvonne W. Tsang, and Stefan Finsterle Lawrence Berkeley National Laboratory, Berkeley, CA 94720 Abstract A simple conceptual model has been recently developed for analyzing pressure and temperature data from flowing fluid temperature logging (FFTL) in unsaturated fractured rock. Using this conceptual model, we developed an analytical solution for FFTL pressure response, and a semi-analytical solution for FFTL temperature response. We also proposed a method for estimating fracture permeability from FFTL temperature data. The conceptual model was based on some simplifying assumptions, particularly a single- phase air flow model was used. In this paper, we develop a more comprehensive numerical model of multiphase flow and heat transfer associated with FFTL. Using this numerical model, we perform a number of forward simulations to determine the parameters that have the strongest influence on the pressure and temperature response from FFTL. We then use the iTOUGH2 optimization code to estimate these most sensitive parameters through inverse modeling and to quantify the uncertainties associated with these estimated parameters. We conclude that FFTL can be utilized to determine permeability, porosity, and thermal conductivity of the fracture rock. Two other parameters, which are not properties of the fractured rock, have strong influence on FFTL response. These are pressure and temperature in the borehole that were at equilibrium with the fractured rock formation at the beginning of FFTL. We illustrate how these parameters can also be estimated from FFTL data. Introduction In a recent paper [Mukhopadhyay and Tsang, 2008], hereafter referred to as Paper I, we presented a simple conceptual model and a semi-analytical solution to analyze the data from flowing fluid temperature logging (FFTL). In Paper I, we also presented a procedure to estimate the effective permeability of the fractured rock using the temperature data from FFTL (see Section 2 for a recapitulation of FFTL). The conceptual model described in Paper I assumes single-phase flow of air and ignores the presence of the water phase in the unsaturated rock. The model includes heat transfer by convection but neglects heat conduction. It also assumes that pumping of air from the borehole during FFTL does not change the pressure and temperature in the surrounding rock (a reasonable assumption, considering the short duration of the test and the large volume of the surrounding rock compared to the volume of the borehole). However, it is possible that these simplifying assumptions could introduce some uncertainties into the estimated

Multiphase flow model to study channel flow dynamics of PEM fuel cells: deformation and detachment of water droplets

Deformation and detachment conditions for a water droplet adhering to the surfaces of the cathode in PEM fuel cells are investigated. This problem is numerically modelled by considering the dynamic behaviour of a droplet located between two parallel plates. The numerical multiphase flow model is based on solving Navier–Stokes equations for Newtonian fluids in the channel. The study includes the effect of interfacial forces with constant surface tension. The volume-of-fluid method is used to numerically determine the deformation of free surfaces. Water droplet and channel fluid properties, inlet velocity and droplet size determine whether a droplet can separate from the surface or just deforms and remains stationary. The critical conditions for the droplet break-up are determined based on the Reynolds and Capillary numbers. Effects of droplet size relative to the channel width, density and viscosity ratios between the water droplet and oxidant fluid are addressed.

EXPERIMENTAL AND THEORETICAL INVESTIGATION OF LNAPL MOVEMENT IN STRATIFIED MEDIA DURING SOIL REMEDIATION

The saturation distribution and clean up efficiency of light non-aqueous phase liquid (LNAPL) in the strata beneath the earth has been the subject of many studies. Better understanding of LNAPL infiltration into layered soil is important for the effective design of remediation strategies. The objective of this study was to simulate LNAPL movement in homogenous and stratified porous media using gravity assisted inert gas injection (GAIGI) process as a cleaning technique. We used homogeneous and layered sandpacked transparent models that allows for visual observation of LNAPL movement in order to study LNAPL redistribution in a layered porous medium. Pore volume, porosity, absolute permeability, connate water saturation, and oil saturation of the models were determined experimentally. Seasonal water table movement and contaminated zone were established and then, under GAIGI process, clean up efficiency was determined. The downward displacement of LNAPL by gas drive resulted in very high LNAPL clean up efficiency. Using the contaminant production history in the homogeneous model, the LNAPL relative permeability was calculated and the results were extended to layered media. The numerical multi-phase flow model in porous media was validated with regard to the experimental results. This model is able to adequately reproduce the experimental LNAPL saturation profile and clean up efficiency.

Development of Three-Dimensional Numerical Model of Multiphase Flow “DOLPHIN-3D” and Dynamic Analysis of Drifting Bodies under Wave Actions

Development of Three-Dimensional Numerical Model of Multiphase Flow “DOLPHIN-3D” and Dynamic Analysis of Drifting Bodies under Wave Actions

Numerical modelling of multiphase flow and transport processes in landfills

Waste material in municipal landfills can be described as heterogeneous porous media, where flow and transport processes of gases and liquids are combined with local material degradation. This paper deals with the basic formulation of a multiphase flow and transport model applicable to the numerical analysis of coupled transport and reaction processes inside landfills. The transport model treats landfills within the framework of continuum mechanics, where flow and transport processes are described on a macroscopic level. The composition of organic and inorganic matter in the solid phase and its degradation are modelled on a microscopic scale. The degradation model captures the different reaction schemes of various microbial activities. Subsequently, transport and reaction processes have to be coupled, since emissions at the surface and from the drainage layer depend on the flow of leachate and gas, the transport of various substances and heat, and the biodegradation of organic matter. The theoretical considerations presented here are fundamental to the development of numerical models for the simulation of multiphase flow and transport processes inside landfills coupled with biochemical reactions and heat generation. The implicit modelling of leachate and gas flows including growth and decay of micro-organisms are innovative contributions to landfill modelling

Direct simulation of spray cooling: Effect of vapor bubble growth and liquid droplet impact on heat transfer

Numerical modeling of multiphase flow using level set method is discussed. The 2-D model considers the effect of surface tension between liquid and vapor, gravity, phase change and viscosity. The level set method is used to capture the movement of the free surface. The detail of incorporating the mechanism of phase change in the incompressible Navier–Stokes equations using the level set method is described. The governing equations are solved using the finite difference method. The computer model is used to study the spray cooling phenomenon in the micro environment of about 40 μm thick liquid layer with vapor bubble growing due to nucleation. The importance of studying the heat transfer mechanism in thin liquid film for spray cooling is identified. The flow and heat transfer details are presented for two cases: (1) when the vapor bubble grows due to nucleation and (2) merges with the vapor layer above the liquid layer and when a liquid droplet impacts the thin liquid layer with vapor bubble growing.

Correction to “Dense nonaqueous phase liquid (DNAPL) source zone characterization: Influence of hydraulic property correlation on predictions of DNAPL infiltration and entrapment”

[1] The influence of aquifer property correlation on multiphase fluid migration and entrapment was explored through the use of correlated and uncorrelated porosity, permeability, and capillary pressure-saturation (Pc-Sat) parameter fields in a cross-sectional numerical multiphase flow model. Data collected from core samples in a nonuniform sandy aquifer were used to generate three-dimensional aquifer parameter fields. Porosity was assumed to be uniform or simulated using sequential Gaussian simulation (SGS). Permeability (k) was modeled independently of porosity using SGS as well as simulated geostatistical indicator classes derived from measured grain size distribution curves. Retention characteristics were assigned employing Leverett scaling of a representative Pc-Sat curve to the geostatistical k fields or, alternatively, on the basis of simulated indicator classes and porosity values. Ensemble dense nonaqueous phase liquid (DNAPL) infiltration and entrapment behavior for a hypothetical tetrachloroethylene (PCE) spill was simulated in four sets of two-dimensional profiles extracted from these realizations. Comparisons of saturation profiles and spatial moments from point source DNAPL infiltration simulations suggest that choices involving the geostatistical algorithm used to model k and the incorporation of variable versus uniform porosity have a smaller influence than choices involving the scaling of capillary retention properties to k. From these simulations it is apparent that the degree of spatial correlation in Pc-Sat parameters exerts a controlling influence on predicted DNAPL spreading and redistribution in saturated aquifers. The resultant distribution of mass within a DNAPL source zone will have implications for DNAPL recovery and subsequent mass fluxes in remediation operations.

Infiltration and redistribution of LNAPL into unsaturated layered porous media

Enhanced understanding of light non-aqueous phase liquid (LNAPL) infiltration into heterogeneous porous media is important for the effective design of remediation strategies. We used a 2-D experimental facility that allows for visual observation of LNAPL contours in order to study LNAPL redistribution in a layered porous medium. The layers are situated in the unsaturated zone near the watertable and they are inclined to be able to observe the effect of discontinuities in capillary forces and relative permeabilities. Two experiments were performed. The first experiment consisted of LNAPL infiltration into a fine sand matrix with a coarse sand layer, and the second experiment consisted of a coarse sand matrix and a fine sand layer. The numerical multi-phase flow model STOMP was validated with regard to the experimental results. This model is able to adequately reproduce the experimental LNAPL contours. Numerical sensitivity analysis was also performed. The capillarity contrast between sands was found to be the main controlling factor determining the final LNAPL distribution.

Dense nonaqueous phase liquid (DNAPL) source zone characterization: Influence of hydraulic property correlation on predictions of DNAPL infiltration and entrapment

The influence of aquifer property correlation on multiphase fluid migration and entrapment was explored through the use of correlated and uncorrelated porosity, permeability, and capillary pressure‐saturation (Pc‐Sat) parameter fields in a cross‐sectional numerical multiphase flow model. Data collected from core samples in a nonuniform sandy aquifer were used to generate three‐dimensional aquifer parameter fields. Porosity was assumed to be uniform or simulated using sequential Gaussian simulation (SGS). Permeability (k) was modeled independently of porosity using SGS as well as simulated geostatistical indicator classes derived from measured grain size distribution curves. Retention characteristics were assigned employing Leverett scaling of a representative Pc‐Sat curve to the geostatistical k fields or, alternatively, on the basis of simulated indicator classes and porosity values. Ensemble dense nonaqueous phase liquid (DNAPL) infiltration and entrapment behavior for a hypothetical tetrachloroethylene (PCE) spill was simulated in four sets of two‐dimensional profiles extracted from these realizations. Comparisons of saturation profiles and spatial moments from point source DNAPL infiltration simulations suggest that choices involving the geostatistical algorithm used to model k and the incorporation of variable versus uniform porosity have a smaller influence than choices involving the scaling of capillary retention properties to k. From these simulations it is apparent that the degree of spatial correlation in Pc‐Sat parameters exerts a controlling influence on predicted DNAPL spreading and redistribution in saturated aquifers. The resultant distribution of mass within a DNAPL source zone will have implications for DNAPL recovery and subsequent mass fluxes in remediation operations.

Predicting DNAPL entrapment and recovery: the influence of hydraulic property correlation

The influence of aquifer property correlation on multiphase fluid migration, entrapment and recovery was explored by incorporating correlated and uncorrelated porosity, permeability, and capillary pressure-saturation (Pc-Sat) parameter fields in a cross-sectional numerical multiphase flow model. Comparison of two-dimensional entrapped organic saturation distributions for a simulated tetrachloroethylene (PCE) spill in ensembles of aquifer realizations suggests that the degree of spatial correlation in Pc-Sat parameters exerts a controlling influence on dense nonaqueous phase liquid (DNAPL) spreading and redistribution in saturated aquifers. The predicted evolution of DNAPL source zones and resultant remediation efficiency under surfactant enhanced aquifer remediation (SEAR) also appear to be strongly influenced by the spatial correlation of aquifer parameters and multiphase flow constitutive relationships. Results for a limited number of realizations selected from each ensemble showed that removal of 60% to 99% of entrapped PCE could reduce dissolved contaminant concentration and mass flux by approximately two orders of magnitude under natural gradient conditions. Aqueous phase contaminant mass flux did not vary uniformly as a function of % DNAPL removed, however, and notable differences in behavior were observed for models incorporating correlated versus uncorrelated Pc-Sat and permeability fields. Although these results must be confirmed through analysis of additional realizations, it is likely that similar or larger differences between correlated and uncorrelated system behavior will be observed in aquifers with greater spatially variability than that of the nonuniform, homogeneous sand aquifer studied here.

NUMERICAL EXPERIMENT OF GAS-LIQUID PHASE AND SOLID-GAS-LIQUID PHASE FLOWS

Understanding the mechanism of air-water interaction is very important from the viewpoint of fluid dynamics in estuaries, lakes, and coastal sea areas. However, it is difficult to simulate the multi-phase flow for the incompressible and compressible fluids simultaneously because the physical properties of gas and liquid are quite different.The purpose of the present study is to develop a numerical model of multi-phase flow with a CIP method and a generalized SMAC method. In order to validate the proposed numerical model, complicated hydraulic phenomena with not only gas-liquid interface but also solid-gas-liquid interface have been computed; for example, dam break problem, exchange flow with two different densities in the liquid phase, and collision problem between water and a solid body. It has been demonstrated from the calculation results that the numerical model can give stable results for both gas-liquid phase flow and solid-gas-liquid phase flow and reproduce the complicated hydraulic phenomena precisely.

Effects of heterogeneities on capillary pressure–saturation–relative permeability relationships

In theories of multiphase flow through porous media, capillary pressure–saturation and relative permeability–saturation curves are assumed to be intrinsic properties of the medium. Moreover, relative permeability is assumed to be a scalar property. However, numerous theoretical and experimental works have shown that these basic assumptions may not be valid. For example, relative permeability is known to be affected by the flow velocity (or pressure gradient) at which the measurements are carried out. In this article, it is suggested that the nonuniqueness of capillary pressure–relative permeability–saturation relationships is due to the presence of microheterogeneities within a laboratory sample. In order to investigate this hypothesis, a large number of “numerical experiments” are carried out. A numerical multiphase flow model is used to simulate the procedures that are commonly used in the laboratory for the measurement of capillary pressure and relative permeability curves. The dimensions of the simulation domain are similar to those of a typical laboratory sample (a few centimeters in each direction). Various combinations of boundary conditions and soil heterogeneity are simulated and average capillary pressure, saturation, and relative permeability for the “soil sample” are obtained. It is found that the irreducible water saturation is a function of the capillary number; the smaller the capillary number, the larger the irreducible water saturation. Both drainage and imbibition capillary pressure curves are found to be strongly affected by heterogeneities and boundary conditions. Relative permeability is also found to be affected by the boundary conditions; this is especially true about the nonaqueous phase permeability. Our results reveal that there is much need for laboratory experiments aimed at investigating the interplay of boundary conditions and microheterogeneities and their effect on capillary pressure and relative permeability.

Multiphase flow modeling of molten material-vapor-liquid mixtures in thermal nonequilibrium

This paper presents a numerical model of multiphase flow of the mixtures of molten material-liquid-vapor, particularly in thermal nonequilibrium. It is a two-dimensional, transient, three-fluid model in Eulerian coordinates. The equations are solved numerically using the finite difference method that implicitly couples the rates of phase changes, momentum, and energy exchange to determine the pressure, density, and velocity fields. To examine the model’s ability to predict an experimental data, calculations have been performed for tests of pouring hot particles and molten material into a water pool. The predictions show good agreement with the experimental data. It appears, however, that the interfacial heat transfer and breakup of molten material need improved models that can be applied to such high temperature, high pressure, multiphase flow conditions.

On two‐phase relative permeability and capillary pressure of rough‐walled rock fractures

This paper presents a conceptual and numerical model of multiphase flow in fractures. The void space of real rough‐walled rock fractures is conceptualized as a two‐dimensional heterogeneous porous medium, characterized by aperture as a function of position in the fracture plane. Portions of a fracture are occupied by wetting and nonwetting phase, respectively, according to local capillary pressure and global accessibility criteria. Phase occupancy and permeability are derived by assuming a parallel‐plate approximation for suitably small subregions in the fracture plane. For lognormal aperture distributions, a simple approximation to fracture capillary pressure is obtained in closed form; it is found to resemble the typical shape of Leverett's j function. Approximations to wetting and nonwetting phase relative permeabilities are calculated by numerically simulating single phase flows separately in the wetted and nonwetted pore spaces. Illustrative examples indicate that relative permeabilities depend sensitively on the nature and range of spatial correlation between apertures. It is also observed that interference between fluid phases flowing in a fracture tends to be strong, with the sum of wetting and nonwetting phase relative permeabilities being considerably less than 1 at intermediate saturations.

Numerical modelling of multiphase flow in porous media : Allen, M B In: Advances in Transport Phenomena in Porous Media, edited by J Bear and M Y CorapciogluP849–920. Publ Dordrecht: Martinus Nijhoff, 1987

Numerical modelling of multiphase flow in porous media : Allen, M B In: Advances in Transport Phenomena in Porous Media, edited by J Bear and M Y CorapciogluP849–920. Publ Dordrecht: Martinus Nijhoff, 1987

Numerical modelling of multiphase flow in porous media

The simultaneous flow of immiscible fluids in porous media occurs in a wide variety of applications. The equations governing these flows are inherently nonlinear, and the geometries and material properties characterizing many problems in petroleum and groundwater engineering can be quite irregular. As a result, numerical simulation often offers the only viable approach to the mathematical modelling of multiphase flows. This paper provides an overview of the types of models that are used in this field and highlights some of the numerical techniques that have appeared recently. The exposition includes discussions of multiphase, multispecies flows in which chemical transport and interphase mass transfers play important roles. The paper also examines some of the outstanding physical and mathematical problems in multiphase flow simulation. The scope of the paper is limited to isothermal flows in natural porous media; however, many of the special techniques and difficulties discussed also arise in artificial porous media and multiphase flows with thermal effects.