Scale Up Reactive Flow in Heterogeneous Porous Media Using Continuous Time Random Walk Approach

Reservoir heterogeneities strongly affect the fluid flow in porous media. The behavior of transport and reaction of fluid varies at different scales, leading to the discrepancies between laboratory experiments and field observations. The reactive processes in porous media may alter reservoir properties with different spatial and temporal scale, varying future transport and reaction behaviors. This thesis provides an efficient probabilistic approach to scale up coupled transport and reaction processes in heterogeneous porous media to field scale based on laboratory-scale information. The continuous time random walk (CTRW) is a probabilistic framework which is always incorporating with particle tracking (PT) approach to model solute transport in heterogeneous porous medium. In CTRW-PT approach, the motion of solute particles is described as combination of random independent spatial and temporal increments in each walk step. The spatial and temporal increments, or normally called as transition distance and time, are chosen from a joint space-time probability density function by a stochastic process. The CTRW-PT approach simulates reactive fluid transport as non-reactive fluid. The modelling of reaction and dissolution is followed by in each time step, updating the change of porous medium and its effect on following transport and reaction. The characteristic probability density function (pdf) is used to simulate the transport of fluid. Adjusting the ensemble parameter β and t_2 accounts for the effects of heterogeneity which leads to anomalous flow behavior: the fluid propagates along the “preferential” pathways with short transition times and “trapped” in some zones with long transition times. It mimics the macroscopic behavior that fluid has the tendency to propagate in high-permeability zones and bypass the low-permeability zones. Simulations of non-reactive tracer flow and nanofluid flow under various conditions are performed at core-scale to obtain the key parameters in characteristic pdf by matching the experimental results. The effect of reactive process, heterogeneity and flow rate on flow behavior is analyzed. The CTRW-PT simulation captures the characters of anomalous behavior of delayed breakthrough. The model is run at larger scale as reservoir properties are scaled up properly. The core-scale simulation based on the characteristic pdf agrees with the experimental results. The large-scale simulation is implemented by using the characteristic pdf to describe flow behaviors in a large-scale domain. It is shown that CTRW-PT approach is more effective in large-scale modeling than solving advection-diffusion-reaction equation (ADRE) by finite difference method (FDM). The simulation results at large scale show that the flow response is spatial-dependent. Compared to solving traditional ADRE, the utilization of CTRW-PT approach to model reactive fluid flow captures the characters of anomalous flow behavior, especially in highly heterogeneous porous media. By the probabilistic framework and stochastic process, this approach is more computational-efficient for scaling up lab-scale results to larger scale. It can consolidate the lab-scale understanding with field prediction to optimize the field treatment design

Transport Phenomena Modelled on Pore-Space Images

Fluid flow and dispersion of solute particles are modelled directly on three-dimensional pore-space images of rock samples. To simulate flow, the finite-difference method combined with a standard predictor-corrector procedure to decouple pressure and velocity is applied. We study the permeability and the size of representative elementary volume (REV) of a range of consolidated and unconsolidated porous media. We demonstrate that the flow-based REV is larger than for geometry-based properties such as porosity and specific surface area, since it needs to account for the tortuosity and connectedness of the flow paths. For solute transport we apply a novel streamline-based algorithm that is similar to the Pollock algorithm common in field-scale reservoir simulation, but which employs a semi-analytic formulation near solid boundaries to capture, with sub-grid resolution, the variation in velocity near the grains. A random walk method is used to account for mixing by molecular diffusion. The algorithm is validated by comparison with published results for Taylor-Aris dispersion in a single capillary with a square cross-section. We then accurately predict experimental data available in the literature for longitudinal dispersion coefficient as a function of Peclet number. We study a number of sandpack, sandstone and carbonate samples for which we have good quality three-dimensional images. There is a power-law dependence of dispersion coefficient as a function of Peclet number, with an exponent that is a function of pore-space heterogeneity: the carbonates we study have a distinctly different behaviour than sandstones and sandpacks. This is related to the differences in transit time probabilities of solute particles travelling between two neighbouring voxels. We then study the non-Fickian behaviour of solute transport in porous media by modelling the NMR propagators and the time-dependent dispersion coefficients of different rock types. The behaviour is explained using Continuous Time Random Walk (CTRW) theory: transport is qualitatively different for the complex porous media such as carbonates compared to the sandstone or sandpack, with long tailing and an almost immobile peak concentration. We discuss extensions of the work to reactive transport and the simulation of transport in finely-resolved images with billions of voxels

Coupled Pore-to-Continuum Multiscale Modeling of Dynamic Particle Filtration Processes in Porous Media

Modeling particle transport and retention in porous media is important in fields such as hydrocarbon extraction, groundwater filtration, and membrane separation. While the continuum-scale (\u3e1 m) is usually of practical interest, pore-scale (1-100 μm) dynamics govern the transport and retention of particles. Therefore, accurate modeling of continuum-scale behavior requires an effective incorporation of pore-scale dynamics. Due to current computational limits however, the large spatial and temporal discrepancies of these scales prohibit modeling an entire continuum-scale system as a single pore-scale model. Even if a pore-scale model could incorporate every pore contained in a continuum-scale system, an upscaling scheme that coupled pore- and continuum-scale models should in principle be more efficient and achieve acceptable accuracy. In this work, a continuum-scale model for particle transport and retention has been developed using the concurrent coupling method. In the model, pore network models (PNMs) were embedded within continuum-scale finite difference grid blocks. As simulations progressed the embedded PNMs periodically provided their continuum-scale grid blocks with updated petrophysical properties. The PNMs used a Lagrangian particle tracking method to identify particle dispersion and retention coefficients. Any changes in permeability and porosity due to particle trapping were also determined. Boundary conditions for the PNM simulations were prescribed by fluid velocity and influent particle concentration information from the continuum-scale grid blocks. Coupling in this manner allowed for a dynamic understanding of how particle induced changes at the pore-scale impact continuum-scale behavior

Characterisation of solute transport in heterogeneous porous media by multidimensional imaging and modelling

The study of solute transport in porous media continues to find applications in both traditional and emerging engineering problems, many of which occur in natural environments. Key applications include CO2 sequestration, enhanced oil recovery and soil remediation. Transport is a fundamental component in the analysis of these systems, because it provides the driving force for physical and chemical interactions between the fluid and the solid phase. However, the inherent heterogeneity of the subsurface leads to what is classically referred to as anomalous transport, which challenges classic interpretations of both field and laboratory experiments. In this context, novel laboratory protocols are needed to probe transport in heterogeneous medium by measuring the spatial structure of the concentration field in the medium, rather than relying exclusively on the analysis of breakthrough curves (BTCs). In this thesis, a combined experimental and modelling study of solute transport in a range of porous media has been presented, including sandstone and carbonate rocks, to cover a range of pore structures. At the core of the experimental work is the combination of two imaging methods, X-ray Computed Tomography and Positron Emission Tomography. While the former is used to characterise rock properties spatially, the latter allows visualising the temporal evolution of the full tracer plume within the medium in three dimensions. To this aim, a core-flooding system has been built to carry out pulse-tracer tests over a wide range of Péclet numbers (Pe=15-500) using brine- and radio-tracers. In addition to the experiments on the three rock samples (Bentheimer Sandstone, Ketton Limestone and Edwards Carbonate), control experiments on uniform beadpacks were carried out to verify the accuracy of the in-situ measurements. The experimental BTCs have been analysed in the framework of residence time distribution functions, which revealed mass transfer limitations in the microporous carbonates in the form of a characteristic flow-rate effect. Three transport models: the Advection Dispersion Equation (ADE), the Multi-Rate Mass Transfer (MRMT) and the Continuous Time Random Walk (CTRW) framework have been thoroughly evaluated with both the BTCs and the internal concentration profiles. It is shown that the ADE provides an accurate description of the results on the beadpack and the sandstone. The data on the carbonates are better described by the MRMT, which uses a fraction of stagnant, intra-granular pore space and an external fluid film resistance model to account for mass transfer between the flowing fluid and the porous particles. The CTRW theory, applied here for the first time to carbonate cores, provides a further improvement in describing the BTC, because of its ability to account for unresolved heterogeneities. In the application of the models, a distinction was made between parameters that are rocks-specific (e.g., the dispersivity) and those that depend on the flow rate, by treating the former as global fitting parameters in the optimisation routine. Accordingly, the obtained results provide a more consistent picture than what the current literature may suggest regarding the use of these models to the analysis of BTCs. The dataset obtained from the PET has been used to quantify the extent and rate of mixing in the different porous media. The 3-D images clearly reveal the presence of spreading caused by subcore-scale heterogeneities. To quantify their effects on the core-scale dispersion, various measures has been used, namely the dilution index (Π), the spreading length-scale (K) and the intensity of segregation (I). It was observed that the microporosity has a pronounced effect on mixing, thereby greatly accelerating the time scale to reach the asymptotic regime. Notably, both Π and K scale vary linearly with the square-root of time, indicating the suitability of a Fickian-based model to quantify macrodispersion. This observation suggests that the strength of heterogeneity in the rock samples investigated is moderate and that anomalous transport has evolved to normal behaviour on a length-scale O(l)∼10 cm (∼ length of the samples). In this context, to provide a more comprehensive picture of anomalous transport in laboratory rock samples, future studies should aim at increasing the spatial resolution of the measurement. Non-invasive, imaging tools such as PET are likely to go a long way in addressing this problem and provide significant opportunities to advance our understanding of miscible displacements in consolidated porous media, thus including those involving additional phenomena, such as adsorption and chemical reactions.Open Acces

Range separation: The divide between local structures and field theories

This work presents parallel histories of the development of two modern theories of condensed matter: the theory of electron structure in quantum mechanics, and the theory of liquid structure in statistical mechanics. Comparison shows that key revelations in both are not only remarkably similar, but even follow along a common thread of controversy that marks progress from antiquity through to the present. This theme appears as a creative tension between two competing philosophies, that of short range structure (atomistic models) on the one hand, and long range structure (continuum or density functional models) on the other. The timeline and technical content are designed to build up a set of key relations as guideposts for using density functional theories together with atomistic simulation.Comment: Expanded version of a 30 minute talk delivered at the 2018 TSRC workshop on Ions in Solution, to appear in the March, 2019 issue of Substantia (https://riviste.fupress.net/index.php/subs/index

Investigations into Heavy Oil Recovery by Vapour Extraction (VAPEX)

It is anticipated that resources from extra-heavy oils and bitumen may resolve the expected future escalation in oil demand. Such oils are usually recovered by thermal methods, however these can be energy intensive, especially for reservoirs with thin net-pay or those bounded with large aquifers or gas caps. This is primarily due to excessive heat losses. On the other hand, VAPour EXtraction of heavy oil (VAPEX) is a more energy-efficient, economically attractive and pollution-free alternative, especially for these problematic scenarios. Despite all the potential benefits of this process, there are many uncertainties associated with the actual physics of the process. The question as to whether the oil drainage rates are sufficient for the mechanism to be economically feasible for field scale application remains unanswered. Prediction of field scale recovery factors by numerical simulation is challenging since a very fine grid is needed to ensure that the physical diffusion dominates the numerical diffusion and then to model the subsequent gravity drainage. Thus, there is a tendency to rely upon the Butler-Mokrys (1989) analytical equation to estimate oil rates. A further uncertainty in field scale application, which has only been investigated in a few studies, is the impact of geological heterogeneity on the process, since this can influence the solvent-oil dispersive mixing as well as the shape of the solvent chamber. This research first investigated the oil drainage rates with VAPEX by performing a series of laboratory experiments in both homogenous and heterogeneous systems (including layered and single discontinuous shales). All experiments were performed in well-characterized glass bead packs using glycerol and ethanol as analogues of heavy oil and solvent, respectively. The porous medium and fluid properties were measured independently. The experimentally measured rates were compared to the estimates derived from the Butler-Mokrys (1989) analytical model. In addition, numerical simulations were performed to validate whether the physical diffusion boundaries were captured correctly. Our experiments revealed that the Butler-Mokrys analytical model substantially underestimated the drainage rates in all cases, even when the effects of convective dispersion and end-point density difference were factored in. Results from the heterogeneous models further suggested that layering may not reduce VAPEX oil drainage rates significantly. The performance in systems with layers and discontinuous shale barriers, however, was less than in homogenous models with higher or equivalent permeabilities. The numerical simulations, therefore, under-predicted the physical oil drainage rates, although the pattern of solvent-oil distribution was correctly captured. The research was then extended from lab-scale experiments to field-scale numerical investigations, using a fine grid, high resolution model with realistic petro-physical properties. The solvent–oil PVT were based on real field properties. Three key criteria were examined: the oil production rates and the recovery factors that it is possible to achieve; the full range of static parameters influencing VAPEX, and; identification of the most sensitive parameters (i.e. reservoir thickness (h), vertical permeability (kv/kh) and average arithmetic permeability). In addition, we compared the performance of VAPEX against Steam Assisted Gravity Drainage (SAGD). These, field scale numerical simulations revealed that VAPEX oil extraction rates incorporating diffusional mixing alone were insufficient for the mechanism to be feasible. Although incorporating single-well tracer test (SWTT) dispersivities into the numerical simulations significantly improved the recovery rates, they still remained unacceptably low.Open Acces

Reservoir Heterogeneity: Should It Be Modelled as Conformance or Dispersion?

Imperial Users onl

High resolution modeling of transport in porous media

This dissertation presents research on the pore-level modeling of transport in porous media. The focus of this work is on high-resolution modeling, a rigorous approach that represents detailed geometry and first-principle physics at the streamline scale. Three major topics are presented in this dissertation: an efficient approach for solving Stokes flow in essentially arbitrary disordered porous media, high-resolution versus network simulations of dispersion phenomena, and a stochastic model for solving interfacial mass transfer from source spheres in porous media. First an approach was developed for solving the Stokes flow problem in a comparatively large, very heterogeneous two-dimensional porous media with high efficiency using a combined domain decomposition and boundary element method. The second topic discussed in this dissertation is the high-resolution and network simulation of dispersion in the porous media for the purpose of evaluating network discretization effects for the hydrodynamic model and the nodal mixing assumption for the solute transport model. It was found that molecular diffusion is not resolved properly with the nodal mixing assumption in the high Peclet number range. The third topic was the development of a stochastic model for simulating interfacial mass transfer from the surface of a single source sphere in a heterogeneous porous medium, which is valid in both low and high Peclet number range