Abstract Instantaneous heat transfer between different phases, known as local thermal equilibrium (LTE), is commonly assumed for modeling heat transfer in porous media. This assumption may not hold in certain technical and environmental applications, particularly with large temperature gradients, large differences in thermal properties, or high velocities. Local thermal non-equilibrium (LTNE) models aim to describe heat transfer processes when the LTE assumption may fail. We compare three continuum-scale models from the pore to the representative elementary volume (REV) scale. Specifically, dual-network and REV-scale models are evaluated against a pore-resolved model used as a reference in the absence of experimental results. Different effective models are used to obtain upscaled properties on the REV scale and to compare resulting temperature profiles. The systems investigated are fully saturated, consisting of one fluid and one solid phase. This study focuses on purely conductive systems without significant differences in thermal properties. Results show that LTE holds for low interfacial resistances. However, for large interfacial resistances, solid and fluid temperatures differ. The REV-scale model with effective parameters obtained by homogenization leads to similar results as the pore-resolved model, whereas the dual-network model deviates more due to fixed spatial resolution. Among the evaluated REV-scale formulations, only the homogenization-based approach captures the LTNE behavior, as it incorporates the interfacial heat transfer coefficient. Our results provide a basis for conduction-dominated heat transfer in saturated porous media and for further systematic comparisons that incorporate convection relevant to a broader range of applications.

Abstract Multiphase flow simulation in porous media is a challenging task with significant industrial implications. Pore Network Modeling (PNM) is an effective method that provides accurate results within a reasonable computational timeframe. However, as the complexity of these systems increases, particularly when simulating whole-core-sized pore networks (Digital Plugs) with millions of elements, there is a growing demand to improve the computational efficiency of PNM. The primary computational bottleneck is the pressure field update process, which involves solving a linear system of balance equations. To address this issue, our research focuses on evaluating the performance of a recently developed multiscale preconditioner for solving this system. We compare its performance against a state-of-the-art algebraic multigrid (AMG) method. Networks where the multiscale preconditioner outperforms AMG are identified, and a multilevel strategy is implemented to extend the capabilities of the method to networks with up to 200 million pore bodies. This shows the multiscale method is a promising alternative to accelerate multiphase simulations in Pore Network Modeling.

Abstract Cement-based material fabrication typically involved cement-mix curing, followed by drying, which partially removed the evaporable water. The post-curing drying of cement-based materials is addressed with unprecedented determination of the drying-participating water (DPW) and drying-induced air voids (DIAV), which in this work involve drying at 23 °C and 40% relative humidity, and differ from the widely reported greater quantities for elevated-temperature drying. This work also provides a simple method for the determination in real time during drying. Prior methods, such as porosimetry and density measurement, are inadequate. Of significance is the finding that increasing the water/cement ratio caused the DPW and DIAV contents to grow, but the fraction of the drying-induced pore volume occupied by air remained unaffected. Here, “complete drying” means complete removal of the part of the evaporable water that can be removed under the drying conditions used (23 °C, 40% relative humidity, 30 days), i.e., DPW during post-curing drying. The cured material was saturated with water before drying started. During drying, the DPW content diminished while the drying-induced air voids (DIAV, the part of the total air voids resulting from drying under the drying conditions used) content grew, with air (rather than water) increasingly occupying the drying-induced pores. The density and DPW + DIAV (drying-induced porosity) decreased slightly during drying. Increasing the water/cement ratio caused the DPW and DIAV contents to grow, but the fraction of the drying-induced pore volume occupied by air remained unaffected. This work provides a new method of real-time determination of DPW and DIAV during drying.

Abstract The tortuosity of a porous medium has a significant effect on heat transfer through it, but this effect is difficult to quantify. In this study, we have developed the concept of applied thermal tortuosity and the thermal tortuosity function which characterizes the effect of porous medium geometry and the thermal conductivity ratio on the averaged path length of heat conduction in a porous medium. We have also proposed new macroscopic geometric parameters of porous media that can better describe the complexity of the porous media geometry. The relationship between the macroscopic geometric parameters and the developed thermal tortuosity function was established by using a neural network model. We used the developed thermal tortuosity function to calculate effective thermal conductivity, which can be applied in the thermal energy equation. Computations were performed for arbitrary two-dimensional porous media. Despite the model’s uncertainties, the developed neural network model is significantly more accurate than empirical correlations for determining the effective thermal conductivity. Optimization of the neural network architecture can further improve the accuracy of the model, but the problem of uncertainty cannot be completely solved. The study shows the importance of embedding the established knowledge of transport in porous media into the neural network model to improve its accuracy.

Abstract The usability of enzymatically induced calcium carbonate precipitation (EICP) as a method for altering porous media properties, soil stabilization, or biocementation depends on our ability to predict the spatial distribution of the precipitated calcium carbonate in porous media. While current REV-scale models can reproduce the main features of laboratory experiments, they neglect effects like the formation of preferential flow paths and the appearance of multiple polymorphs of calcium carbonate with differing properties. We show that extending an existing EICP model by the conceptual assumption of a mobile precipitate, amorphous calcium carbonate (ACC), allows for the formation of preferential flow paths when the initial porosity is heterogeneous. We apply sensitivity analysis to understand the influence of characteristic parameters of ACC that are uncertain or unknown, and compare two model variations based on different formulations of the ACC detachment term to analyze the plausibility of our hypothesis. An arbitrary polynomial chaos (aPC) surrogate model is trained based on the full model and used to reduce the computational cost of this study.