A continuum model of multi-phase reactive transport in igneous systems

Multi-phase reactive transport processes are ubiquitous in igneous systems. A challenging aspect of modelling igneous phenomena is that they range from solid-dominated porous to liquid-dominated suspension flows and therefore entail a wide spectrum of rheological conditions, flow speeds, and length scales. Most previous models have been restricted to the two-phase limits of porous melt transport in deforming, partially molten rock and crystal settling in convecting magma bodies. The goal of this paper is to develop a framework that can capture igneous system from source to surface at all phase proportions including not only rock and melt but also an exsolved volatile phase. Here, we derive an n-phase reactive transport model building on the concepts of Mixture Theory, along with principles of Rational Thermodynamics and procedures of Non-equilibrium Thermodynamics. Our model operates at the macroscopic system scale and requires constitutive relations for fluxes within and transfers between phases, which are the processes that together give rise to reactive transport phenomena. We introduce a phase- and process-wise symmetrical formulation for fluxes and transfers of entropy, mass, momentum, and volume, and propose phenomenological coefficient closures that determine how fluxes and transfers respond to mechanical and thermodynamic forces. Finally, we demonstrate that the known limits of two-phase porous and suspension flow emerge as special cases of our general model and discuss some ramifications for modelling pertinent two- and three-phase flow problems in igneous systems.Comment: Revised preprint submitted for peer-reviewed publication: main text with 8 figures, 1 table; appendix with 3 figures and 2 table

A new pore-scale numerical simulator for investigating special core analysis data

The study presented in this thesis addresses various pore-scale phenomena related to the oil industry by implementing new numerical models capable of simulating a wide range of multiphase flow processes such as depressurisation, water flooding, gas injection and various EOR techniques. The aim is not to produce quantitative predictions per se but rather to examine the effect of key petrophysical parameters on oil recovery when different production protocols are applied to specific rock analogues. In order to facilitate this, a new pore-scale process simulator is developed – numSCAL (numerical Special Core Analysis Laboratory) – with different modules associated with different mechanisms. A steady-state depletion model is described first and used to investigate the impact of numerous parameters on solution gas drive. We show that parameter combinations that increase bubble density can lead to delayed gas breakthrough and can result in high critical gas saturations. The model is extended to support three-phase flow by incorporating concepts from graph theory. Simulation results highlight the interaction between the underlying phase saturations, spreading conditions and wetting films and emphasise the competition among mechanisms acting in three-phase systems. Two unsteady-state models are also presented to study water flooding processes in porous media – the first mainly applied to simulate drainage processes and the second used to study the onset of ganglia mobilisation. Results show that parameters affecting the capillary number and viscous ratio play a crucial role in determining the observed invasion regime and final oil recoveries. Conditions required for ganglia mobilisation are derived and used to predict the likelihood of mobilisation at different parts of the reservoir. The dynamic drainage model is then extended to simulate low salinity (LS) water flooding and polymer injection – secondary and tertiary effects are shown to depend on interactions amongst several key flow parameters (including initial reservoir wettability, flow rate and viscous ratio). In addition, a positive synergistic effect is identified, where the combined injection of LS brine and polymer leads to increased recovery in several scenarios. The study concludes with an application of the pore-scale modelling technique in a novel research area. A new approach is presented to model drug perfusion surrounding Glioblastoma Multiform (GBM) tumours. Results show that blood flow, transmural transport and tissue diffusion have a direct impact on the average drug concentrations that develop in the vascular network and the surrounding tissue

Lattice and Continuum Modelling of a Bioactive Porous Tissue Scaffold

A contemporary procedure to grow artificial tissue is to seed cells onto a porous biomaterial scaffold and culture it within a perfusion bioreactor to facilitate the transport of nutrients to growing cells. Typical models of cell growth for tissue engineering applications make use of spatially homogeneous or spatially continuous equations to model cell growth, flow of culture medium, nutrient transport, and their interactions. The network structure of the physical porous scaffold is often incorporated through parameters in these models, either phenomenologically or through techniques like mathematical homogenization. We derive a model on a square grid lattice to demonstrate the importance of explicitly modelling the network structure of the porous scaffold, and compare results from this model with those from a modified continuum model from the literature. We capture two-way coupling between cell growth and fluid flow by allowing cells to block pores, and by allowing the shear stress of the fluid to affect cell growth and death. We explore a range of parameters for both models, and demonstrate quantitative and qualitative differences between predictions from each of these approaches, including spatial pattern formation and local oscillations in cell density present only in the lattice model. These differences suggest that for some parameter regimes, corresponding to specific cell types and scaffold geometries, the lattice model gives qualitatively different model predictions than typical continuum models. Our results inform model selection for bioactive porous tissue scaffolds, aiding in the development of successful tissue engineering experiments and eventually clinically successful technologies.Comment: 38 pages, 16 figures. This version includes a much-expanded introduction, and a new section on nonlinear diffusion in addition to polish throughou

Effects of natural micro-fracture morphology, temperature and pressure on fluid flow in coals through fractal theory combined with lattice Boltzmann method

Acknowledgements: This research was funded by the National Natural Science Foundation of China (grant nos. 343 41830427, 41922016 and 41772160) and the Fundamental Research Funds for Central Universities (grant no. 2652019255). The authors also want to thank the Royal Society Edinburgh and NSFC to support their collaborations.Peer reviewedPostprin

Pore-to-continuum Multiscale Modeling of Two-phase Flow in Porous Media

Abstract Pore-scale network modeling using 3D X-ray computed tomographic images (digital rock technology) has become integral to both research and commercial simulations in recent years. While this technology provides tremendous insight into pore-scale behavior, computational methods for integrating the results into practical, continuum-scale models remain fairly primitive. The general approach is to run pore-scale models and continuum models sequentially, where macroscopic parameters are simulated using the pore-scale models and then used in the continuum models as if they have been obtained from laboratory experiments. While a sequential coupling approach is appealing in some cases, an inability to run the two models concurrently (exchanging parameters and boundary conditions in real numerical time) will prevent using pore-scale image-based modeling to its full potential. In this work, an algorithm for direct coupling of a dynamic pore-network model for multiphase flow with a traditional continuum-scale simulator is presented. The ability to run the two models concurrently is made possible by a novel dynamic pore-network model that allows simultaneous injection of immiscible fluids under either transient or steady-state conditions. The dynamic network algorithm can simulate both drainage and imbibition. Consequently, the network algorithm can be used to model a complete time-dependent injection process that comprises a steady-state relative permeability test, and also allows for coupling to a continuum model via exchange of information between the two models. Results also include the sensitivity analysis of relative permeability to pore-level physics and simulation algorithms. A concurrent multiscale modeling approach is presented. It allows the pore-scale properties to evolve naturally during the simulated reservoir time step and provide a unique method for reconciling the dramatically different time and length scales across the coupled models. The model is tested for examples associated with oil production and groundwater transport in which relative permeability depends on flowrate, thus demonstrating a situation that cannot be modeled using a traditional approach. This work is significant because it represents a fundamental change in the way we might obtain continuum-scale parameters in a reservoir simulation