Image-based modelling of coke combustion in a multiscale porous medium using a micro-continuum framework

Abstract

Non-isothermal reactive transport in complicated porous media is diverse in nature and industrial applications. There are challenges in the modelling of multiple physicochemical processes in multiscale pore structures with various length scales ranging from nanometres to micrometres. This study focuses on coke combustion during in situ crude oil combustion techniques. A micro-continuum model was developed to perform an image-based simulation of coke combustion through a multiscale porous medium. The simulation coupled weakly compressible gas flow, species transport, conjugate heat transfer, heterogeneous coke oxidation kinetics and structural evolution. The unresolved nanoporous coke region was treated as a continuum, for which the random pore model, permeability model and species diffusivity model were integrated as sub-grid models to account for the sub-resolution reactive surface area, Darcy flow and Knudsen diffusion, respectively. A Pe–Da diagram was provided to present five characteristic combustion regimes covering the ignition temperature and air flux in realistic field operations and laboratory measurements. The present model proved to achieve more accurate predictions of the feasible ignition temperature than previous models. Compared with the air flux of $\phi \sim O\textrm{(1) s}{\textrm{m}^\textrm{3}}(\textrm{air})\;{({\textrm{m}^\textrm{2}}\ \textrm{h})^{ - 1}}$ in the field, the increasing air flux in the laboratory transformed the combustion regime from diffusion-limited to convection-limited, which led to an overpredicted burning temperature. Reactive fingering combustion was analysed to understand the potential risks in some experimental measurements. The findings provide a better understanding of coke combustion and can help engineers design sustainable combustion methods. The developed image-based model allows other types of multiscale and nonlinear reactive transport to be simulated.

Multiscale Digital Rock Imaging and Modeling for Measuring the Heterogeneous Carbonate and Conglomerate Permeability at the Laboratory Plug Scale

“…Therefore, the simulated permeability difference further highlighted the importance of multiscale modeling on permeability prediction. The present multiscale imaging and modeling are validated to provide a more accurate and robust method to predict the permeability of the fracture-cemented carbonates than the previous single-scale approaches based on the standard Navier–Stokes , and Navier–Stokes-like simulations. , …”

“…For a more quantitative comparison, it is desirable to use the Navier–Stokes-like simulation via the DBS model to approximate a single-scale simulation of fluid flow through the fractures and assess the corresponding permeability. According to the previous work, , the DBS model can be reduced to the Naiver–Stokes equation when the permeability of the microporous matrix is tuned to a sufficiently low value, such as 10 –3 mD, resulting in near-zero velocity inside the matrix and recovering the non-slip boundary condition on the matrix surface. The results of the FC-1 sample, as shown in Figure c, indicate that the Navier–Stokes-like simulation underpredicted the permeability of the fractured carbonates by at least 1 order of magnitudes.…”

“…The steady-state DBS equation was written as where ε is the local porosity at each computational cell, p is the pressure, and K is the local permeability. For modeling multiscale fluid flow in the low-resolution plug image, the DBS approach introduced bounding values of the local porosity ε = 1 and ε = 0 ≡ 0.01 to represent the resolved large pores and the impermeable grains, and intermediate 0 < ε < 1 to represent the unresolved matrix pores below image resolution. , Meanwhile, the permeability of the impermeable grains was reduced to O­(10 –3 ) mD based on the given porosity and Kozeny–Carman relation . According to these physical definitions, the DBS model can employ a single momentum equation to simulate Darcy flow in the microporous matrix and recover Stokes flow in the fractures and vugs .…”

“…27,30 Meanwhile, the permeability of the impermeable grains was reduced to O(10 −3 ) mD based on the given porosity and Kozeny−Carman relation. 31 According to these physical definitions, the DBS model can employ a single momentum equation to simulate Darcy flow in the microporous matrix and recover Stokes flow in the fractures and vugs. 27 The use of the single-field equation can ensure that the velocities and stresses are continuous throughout the entire computational domain.…”

“…The present multiscale imaging and modeling are validated to provide a more accurate and robust method to predict the permeability of the fracture-cemented carbonates than the previous single-scale approaches based on the standard Navier−Stokes 35,36 and Navier−Stokes-like simulations. 27,31 In addition, the extended four-step workflow was also implemented for the fractured carbonate permeability computation. The critical point of the four-step workflow is introducing the subdomain division and integration steps into the basic two-step workflow.…”