On the validity of effective formulations for transport through heterogeneous porous media

International audienceGeological heterogeneity enhances spreading of solutes, and causes transport to be anomalous (i.e., non-Fickian), with much less mixing than suggested by dispersion. This implies that modeling transport requires adopting either stochastic approaches that model heterogeneity explicitly or effective transport formulations that acknowledge the effects of heterogeneity. A number of such formulations have been developed and tested as upscaled representations of enhanced spreading. However, their ability to represent mixing has not been formally tested, which is required for proper reproduction of chemical reactions and which motivates our work. We propose that, for an effective transport formulation to be considered a valid representation of transport through Heterogeneous Porous Media (HPM), it should honor mean advection, mixing and spreading. It should also be flexible enough to be applicable to real problems. We test the capacity of the Multi-Rate Mass Transfer (MRMT) to reproduce mixing observed in HPM, as represented by the classical multi-Gaussian log-permeability field with a Gaussian correlation pattern. Non-dispersive mixing comes from heterogeneity structures in the concentration fields that are not captured by macrodispersion. These fine structures limit mixing initially, but eventually enhance it. Numerical results show that, relative to HPM, MRMT models display a much stronger memory of initial conditions on mixing than on dispersion because of the sensitivity of the mixing state to the actual values of concentration. Because MRMT does not restitute the local concentration structures, it induces smaller non-dispersive mixing than HPM. However long-lived trapping in the immobile zones may sustain the deviation from dispersive mixing over much longer times. While spreading can be well captured by MRMT models, non-dispersive mixing cannot

Numerical Monte-Carlo analysis of the influence of pore-scale dispersion on macrodispersion in heterogeneous porous media

Macrodispersion is the result of molecular diffusion and hydrodynamic dispersion. Molecular diffusion comes from the random motion of molecules. Hydrodynamic dispersion comes from the spreading of solutes due to the heterogeneous flow. From pore scale to Darcy scale, dispersion is modeled by fixed dispersivities. At larger scales, dispersion comes both from the smaller scale dispersion and from the fluctuations of flow issued by the heterogeneous permeability. In this study, we investigate the influences of pore-scale dispersion and heterogeneous permeability on the macrodispersion

Development of RWHet to Simulate Contaminant Transport in Fractured Porous Media

Accurate simulation of matrix diffusion in regional-scale dual-porosity and dual-permeability media is a critical issue for the DOE Underground Test Area (UGTA) program, given the prevalence of fractured geologic media on the Nevada National Security Site (NNSS). Contaminant transport through regional-scale fractured media is typically quantified by particle-tracking based Lagrangian solvers through the inclusion of dual-domain mass transfer algorithms that probabilistically determine particle transfer between fractures and unfractured matrix blocks. UGTA applications include a wide variety of fracture aperture and spacing, effective diffusion coefficients ranging four orders of magnitude, and extreme end member retardation values. This report incorporates the current dual-domain mass transfer algorithms into the well-known particle tracking code RWHet [LaBolle, 2006], and then tests and evaluates the updated code. We also develop and test a direct numerical simulation (DNS) approach to replace the classical transfer probability method in characterizing particle dynamics across the fracture/matrix interface. The final goal of this work is to implement the algorithm identified as most efficient and effective into RWHet, so that an accurate and computationally efficient software suite can be built for dual-porosity/dual-permeability applications. RWHet is a mature Lagrangian transport simulator with a substantial user-base that has undergone significant development and model validation. In this report, we also substantially tested the capability of RWHet in simulating passive and reactive tracer transport through regional-scale, heterogeneous media. Four dual-domain mass transfer methodologies were considered in this work. We first developed the empirical transfer probability approach proposed by Liu et al. [2000], and coded it into RWHet. The particle transfer probability from one continuum to the other is proportional to the ratio of the mass entering the other continuum to the mass in the current continuum. Numerical examples show that this method is limited to certain ranges of parameters, due to an intrinsic assumption of an equilibrium concentration profile in the matrix blocks in building the transfer probability. Subsequently, this method fails in describing mass transfer for parameter combinations that violate this assumption, including small diffusion coefficients (i.e., the free-water molecular diffusion coefficient 1×10-11 meter2/second), relatively large fracture spacings (such as meter), and/or relatively large matrix retardation coefficients (i.e., ). These “outliers” in parameter range are common in UGTA applications. To address the above limitations, we then developed a Direct Numerical Simulation (DNS)-Reflective method. The novel DNS-Reflective method can directly track the particle dynamics across the fracture/matrix interface using a random walk, without any empirical assumptions. This advantage should make the DNS-Reflective method feasible for a wide range of parameters. Numerical tests of the DNS-Reflective, however, show that the method is computationally very demanding, since the time step must be very small to resolve particle transfer between fractures and matrix blocks. To improve the computational efficiency of the DNS approach, we then adopted Roubinet et al.’s method [2009], which uses first passage time distributions to simulate dual-domain mass transfer. The DNS-Roubinet method was found to be computationally more efficient than the DNS-Reflective method. It matches the analytical solution for the whole range of major parameters (including diffusion coefficient and fracture aperture values that are considered “outliers” for Liu et al.’s transfer probability method [2000]) for a single fracture system. The DNS-Roubinet method, however, has its own disadvantage: for a parallel fracture system, the truncation of the first passage time distribution creates apparent errors when the fracture spacing is small, and thus it tends to erroneously predict breakthrough curves (BTCs) for the parallel fracture system. Finally, we adopted the transient range approach proposed by Pan and Bodvarsson [2002] in RWHet. In this method, particle transfer between fractures and matrix blocks can be resolved without using very small time steps. It does not use any truncation of the first passage time distribution for particles. Hence it does not have the limitation identified above for the DNS-Reflective method and the DNS-Roubinet method. Numerical results were checked against analytical solutions, and also compared to DCPTV2.0 [Pan, 2002]. This version of RWHet (called RWHet-Pan&Bodvarsson in this report) can accurately capture contaminant transport in fractured porous media for a full range of parameters without any practical or theoretical limitations

Statistical characteristics of flow as indicators of channeling in heterogeneous porous and fractured media

International audienceWe introduce two new channeling indicators Dic and Dcc based on the Lagrangian distribution of flow rates. On the basis of the participation ratio, these indicators characterize the extremes of both the flow-tube width distribution and the flow rate variation along flow lines. The participation ratio is an indicator biased toward the larger values of a distribution and is equal to the normalized ratio of the square of the first-order moment to the second-order moment. Compared with other existing indicators, they advantageously provide additional information on the flow channel geometry, are consistently applicable to both porous and fractured media, and are generally less variable for media generated using the same parameters than other indicators. Based on their computation for a broad range of porous and fracture permeability fields, we show that they consistently characterize two different geometric properties of channels. Dic gives a characteristic scale of low-flow zones in porous media and a characteristic distance between effectively flowing structures in fractured cases. Dcc gives a characteristic scale of the extension of high-flow zones in porous media and a characteristic channel length in fractured media. Dic is mostly determined by channel density and permeability variability. Dcc is, however, more affected by the nature of the correlation structure like the presence of permeability channels or fractures in porous media and the length distribution in fracture networks

Adaptive Kalman Filtering Scheme For The Simulation Of Benzene In Subsurface Environment

Environmental legislation in several states has become more stringent on the clean up procedures for benzene and other toxic chemicals since the enactment of the Comprehensive Environmental Response, Compensation, and Liability Act (Superfund). In order to comply with the Superfund requirements for hazardous pollutants, accurate information about the nature of contaminants is required to carry out risk assessment and effective site remediation. The use of subsurface contaminant transport models, coupled with stochastic data assimilation schemes, can provide accurate predictions of contaminant transport to enhance the reliability of risk assessment in the area of environmental remediation. In this study, a two-dimensional deterministic model was used to simulate the advective and diffusive transport of benzene in the subsurface. A robust Adaptive Kalman Filter (AKF) has been constructed as a stochastic data assimilation scheme to improve the prediction of the benzene contaminant plume. The AKF has been proposed to improve the performance of the conventional Kalman Filter (KF) by reducing the uncertainties associated with the process and observation noise statistics. The impact of the adaptive filter on the KF performance was examined by comparing model predictions with a simulated true field which was created by introducing some random Gaussian noise into an observation model. The simulation results indicated an improvement in filter performance after the implementation of the adaptive Kalman filter scheme. Although the Kalman filter was successful in reducing the prediction error of the deterministic model from 5.0 mg/L to 1.1 mg/L at the end of the simulation period, the introduction of the AKF scheme further improved the prediction accuracy of the KF by about 18%. In all, the AKF scheme successfully improved the prediction accuracy of the deterministic model by about 82%. Furthermore, the results of sensitivity test suggest that for the AKF under consideration, using a window size of five can give a much improved accuracy and stability

A Literature Review and Transport Modelling of Nanoparticles for Enhanced Oil Recovery

Master's thesis in Petroleum engineeringNanotechnology has been envisioned to transform every sector of industries, particularly in the petroleum industry. Numerous researches, especially on nano-EOR, have been done in the past few years and shown promising results for improving oil recovery. Injected nanoparticles (NPs) are believed to be able to form adsorption layers on the top of grain surface. The adsorptions layers then alter the wettability of the rock and reduce the interfacial tension. Due to the importance of the adsorption, numerous theoretical studies were performed to simulate the transport behavior of NPs in the porous media. The purpose of this thesis is to i) review the state-of-the-art progress of nanoparticles application in the petroleum industry especially in EOR, and ii) simulate the transport and adsorption of nanoparticles in the porous media. Literatures show that various types of nanoparticles can improve oil recovery through several mechanisms such as wettability alteration, interfacial tension reduction, disjoining pressure and mobility control. Parameters such as salinity, temperature, size, and concentration are substantial for nano-EOR. Several experiments indicate that NPs can improve the oil recovery significantly up to 20% after the primary recovery period. Classical Advection-Dispersion Equation (ADE) is commonly used to simulate particles flow in the porous media, but it fails to simulate NPs flow due to the adsorption that occurs. The colloidal filtration theory (CFT) is used in the study to accommodate the adsorption. Several modifications on CFT, such as dual site model (ISTM), increase the number of unknown variables that reduce the efficiency and the accuracy of the model. Therefore, a simple modified linear adsorption model (ML) is proposed by the author, followed by parameter sensitivity study to reduce the unknown parameters and understand each parameter affecting on the model. The simulation result indicates that CFT model is unable to predict the effluent history data. Differently, ML model demonstrates that it can predict the effluent history quite well. The comparison with ISTM indicates that both can simulate the behavior of NPs, and our ML model gives slightly better result than ISTM model. Therefore, the transport and adsorption of NPs can be predicted by the simple linear adsorption model

Small Particle Transport in Fibrin Gels and High Throughput Clot Characterization

The formation, function, and lysis of blood clots is largely governed by the transport of nano- and micro-scale particles. Yet there is not fully established physics that relates clot structure to transport phenomena such as fluid permeation and particle diffusion. This dissertation explores small particle transport in fibrin. I report on the size-dependence of particle mobility in fibrin, and discuss the implications of these results for fibrinolytic drug design. I measure the relationship between fibrin permeability and diffusion of 0.2--2.8 micron particles in fibrin gels, then determine the time and length scales at which small particle diffusion is directly related to bulk gel permeability. This result implies that one could develop a high throughput clot characterization assay that provides more detail than turbidity, the predominant high throughput measurement. I also present my work designing and developing systems to perform these and other experiments in high throughput, which include novel technologies for optical microscopy and magnetic force application.Doctor of Philosoph

Mathematical and numerical modelling of shock initiation in heterogeneous solid explosives

In the field of explosive science, the existence of the ‘hot-spot’ is generally accepted as essential to any theory on shock initiation. Continuum-based shock initiation models only account for ‘hot-spots’ implicitly, and the majority of these models use pressure-dependent reaction rates. The development of a simple but physically realistic model to predict desensitisation (double shock) effects within the confines of an existing pressure-based model is described and simulations compared with experimental data with mixed results. The need to invoke a separate desensitisation model for double shocks demonstrates that reaction rates are not substantially dependent on local pressure. The newly developed continuum, entropy-dependent, CREST model has been implemented and validated in a number of hydrocodes. However, the move to entropy-based reaction rates introduces a number of computational problems not associated with pressure-based models. These problems are described, in particular, an entropy-dependent model over-predicts the rate of energy release in an explosive adjacent an impact surface, and requires a finer mesh than a pressure-dependent model to achieve mesh converged results. The CREST model, fitted only to onedimensional data of the shock to detonation transition, is shown to be able to accurately simulate two-dimensional detonation propagation data. This gives confidence in the predictive capability of the model. To account for ‘hot-spots’ explicitly, a simple model to describe ‘hot-spot’ initiation has been developed. The simple model is presented where ‘hot-spots’ are formed as a result of elastic-viscoplastic stresses generated in the solid explosive during pore collapse. Results from the model compare well with corresponding results from direct numerical simulations, and both are consistent with observations and commonly held ideas regarding the shock initiation and sensitivity of heterogeneous solid explosives. The results also indicate that viscoplastic ‘hot-spot’ models described in the literature are built on an invalid assumption.EThOS - Electronic Theses Online ServiceGBUnited Kingdo