Generalized network modeling of capillary-dominated two-phase flow

Percolation without trapping: How Ostwald ripening during two-phase displacement in porous media alters capillary pressure and relative permeability

Conventional measurements of two-phase flow in porous media often use completely immiscible fluids, or are performed over time scales of days to weeks. If applied to the study of gas storage and recovery, these measurements do not properly account for Ostwald ripening, significantly overestimating the amount of trapping and hysteresis. When there is transport of dissolved species in the aqueous phase, local capillary equilibrium is achieved: this may take weeks to months on the centimeter-sized samples on which measurements are performed. However, in most subsurface applications where the two phases reside for many years, equilibrium can be achieved. We demonstrate that in this case, two-phase displacement in porous media needs to be modeled as percolation without trapping. A pore network model is used to quantify how to convert measurements of trapped saturation, capillary pressure and relative permeability made ignoring Ostwald ripening to account for this effect. We show that conventional measurements overestimate the amount of capillary trapping by 20-25%.

Pore-scale modeling of two-phase flow: A comparison of the generalized network model to direct numerical simulation

Despite recent advances in pore-scale modeling of two-phase flow through porous media, the relative strengths and limitations of various modeling approaches have been largely unexplored. In this work, two-phase flow simulations from the generalized network model (GNM) [Phys. Rev. E 96, 013312 (2017)2470-004510.1103/PhysRevE.96.013312; Phys. Rev. E 97, 023308 (2018)2470-004510.1103/PhysRevE.97.023308] are compared with a recently developed lattice-Boltzmann model (LBM) [Adv. Water Resour. 116, 56 (2018)0309-170810.1016/j.advwatres.2018.03.014; J. Colloid Interface Sci. 576, 486 (2020)0021-979710.1016/j.jcis.2020.03.074] for drainage and waterflooding in two samples-a synthetic beadpack and a micro-CT imaged Bentheimer sandstone-under water-wet, mixed-wet, and oil-wet conditions. Macroscopic capillary pressure analysis reveals good agreement between the two models, and with experiments, at intermediate saturations but shows large discrepancy at the end-points. At a resolution of 10 grid blocks per average throat, the LBM is unable to capture the effect of layer flow which manifests as abnormally large initial water and residual oil saturations. Critically, pore-by-pore analysis shows that the absence of layer flow limits displacement to invasion-percolation in mixed-wet systems. The GNM is able to capture the effect of layers, and exhibits predictions closer to experimental observations in water and mixed-wet Bentheimer sandstones. Overall, a workflow for the comparison of pore-network models with direct numerical simulation of multiphase flow is presented. The GNM is shown to be an attractive option for cost and time-effective predictions of two-phase flow, and the importance of small-scale flow features in the accurate representation of pore-scale physics is highlighted.

Paired and Unpaired Deep Learning Methods for Physically Accurate Super-Resolution Carbonate Rock Images

X-ray micro-computed tomography (micro-CT) has been widely leveraged to characterise the pore-scale geometry of subsurface porous rocks. Recent developments in super-resolution (SR) methods using deep learning allow for the digital enhancement of low-resolution (LR) images over large spatial scales, creating SR images comparable to high-resolution (HR) ground truth images. This circumvents the common trade-off between resolution and field-of-view. An outstanding issue is the use of paired LR and HR data, which is often required in the training step of such methods but is difficult to obtain. In this work, we rigorously compare two state-of-the-art SR deep learning techniques, using both paired and unpaired data, with like-for-like ground truth data. The first approach requires paired images to train a convolutional neural network (CNN), while the second approach uses unpaired images to train a generative adversarial network (GAN). The two approaches are compared using a micro-CT carbonate rock sample with complicated micro-porous textures. We implemented various image-based and numerical verifications and experimental validation to quantitatively evaluate the physical accuracy and sensitivities of the two methods. Our quantitative results show that the unpaired GAN approach can reconstruct super-resolution images as precise as the paired CNN method, with comparable training times and dataset requirements. This unlocks new applications for micro-CT image enhancement using unpaired deep learning methods; image registration is no longer needed during the data processing stage. Decoupled images from data storage platforms can be exploited to train networks for SR digital rock applications. This opens up a new pathway for various applications related to multi-scale flow simulations in heterogeneous porous media.

Discrimination between Pore and Throat Resistances against Single-Phase Flow in Porous Media

This study investigates the critical agents that cause non-Darrian flow in porous media. Four porous media different in morphology but similar in topology were studied numerically. By varying the throat diameters, the distinct roles of pores and throats in total dissipation were investigated using direct numerical simulation. Forchheimer model was selected to analyze the non-Darcian flow. In our simplified geometry, the ratio KappKD can best be correlated by non-Darcy effect (E). Total dissipation is directly related to the porous medium resistance against fluid flow. The energy dissipated in pores and throats was calculated by summing the dissipation in each computational segment. Pores are more prone to disobey the Darcy model than throats due to irregularity in fluid flow, and they are introduced as the cause of Darcy-model cessation. By increasing the pore-to-throat ratio, the non-Darcian flow in the pores begins sooner. The results show that the energy dissipation due to eddies is negligible. The dissipation in pores and throats was simulated through separate power-law equations, and their exponents were also extracted. The exponent for the pore body is equal to two when the viscous forces are dominant, and it increases by increasing the inertia force. The dissipation due to pore bodies is more apparent when the size of pore and throats are of the same order of magnitude. The relative losses of pore body increase as the velocity increases, in contrast to throats.

Precursor Film Spreading during Liquid Imbibition in Nanoporous Photonic Crystals

When a macroscopic droplet spreads, a thin precursor film of liquid moves ahead of the advancing liquid-solid-vapor contact line. Whereas this phenomenon has been explored extensively for planar solid substrates, its presence in nanostructured geometries has barely been studied so far, despite its importance for many natural and technological fluid transport processes. Here we use porous photonic crystals in silicon to resolve by light interferometry capillarity-driven spreading of liquid fronts in pores of few nanometers in radius. Upon spatiotemporal rescaling the fluid profiles collapse on master curves indicating that all imbibition fronts follow a square-root-of-time broadening dynamics. For the simple liquid (glycerol) a sharp front with a widening typical of Lucas-Washburn capillary-rise dynamics in a medium with pore-size distribution occurs. By contrast, for a polymer (PDMS) a precursor film moving ahead of the main menisci entirely alters the nature of the nanoscale transport, in agreement with predictions of computer simulations.

Pore-by-pore modeling, analysis, and prediction of two-phase flow in mixed-wet rocks

A pore-network model is an upscaled representation of the pore space and fluid displacement, which is used to simulate two-phase flow through porous media. We use the results of pore-scale imaging experiments to calibrate and validate our simulations, and specifically to find the pore-scale distribution of wettability. We employ energy balance to estimate an average, thermodynamic, contact angle in the model, which is used as the initial estimate of contact angle. We then adjust the contact angle of each pore to match the observed fluid configurations in the experiment as a nonlinear inverse problem. The proposed algorithm is implemented on two sets of steady state micro-computed-tomography experiments for water-wet and mixed-wet Bentheimer sandstone. As a result of the optimization, the pore-by-pore error between the model and experiment is decreased to less than that observed between repeat experiments on the same rock sample. After calibration and matching, the model predictions for capillary pressure and relative permeability are in good agreement with the experiments. The proposed algorithm leads to a distribution of contact angle around the thermodynamic contact angle. We show that the contact angle is spatially correlated over around 4 pore lengths, while larger pores tend to be more oil-wet. Using randomly assigned distributions of contact angle in the model results in poor predictions of relative permeability and capillary pressure, particularly for the mixed-wet case.

Validation of model predictions of pore-scale fluid distributions during two-phase flow

Pore-scale two-phase flow modeling is an important technology to study a rock's relative permeability behavior. To investigate if these models are predictive, the calculated pore-scale fluid distributions which determine the relative permeability need to be validated. In this work, we introduce a methodology to quantitatively compare models to experimental fluid distributions in flow experiments visualized with microcomputed tomography. First, we analyzed five repeated drainage-imbibition experiments on a single sample. In these experiments, the exact fluid distributions were not fully repeatable on a pore-by-pore basis, while the global properties of the fluid distribution were. Then two fractional flow experiments were used to validate a quasistatic pore network model. The model correctly predicted the fluid present in more than 75% of pores and throats in drainage and imbibition. To quantify what this means for the relevant global properties of the fluid distribution, we compare the main flow paths and the connectivity across the different pore sizes in the modeled and experimental fluid distributions. These essential topology characteristics matched well for drainage simulations, but not for imbibition. This suggests that the pore-filling rules in the network model we used need to be improved to make reliable predictions of imbibition. The presented analysis illustrates the potential of our methodology to systematically and robustly test two-phase flow models to aid in model development and calibration.