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

Pore-scale visualization of hydrogen storage in a sandstone at subsurface pressure and temperature conditions: Trapping, dissolution and wettability

HYPOTHESIS

Underground hydrogen (H2) storage is a potentially viable solution for large-scale cyclic H2 storage; however, the behavior of H2 at subsurface pressure and temperature conditions is poorly known. This work investigates if the pore-scale displacement processes in H2-brine systems in a porous sandstone can be sufficiently well defined to enable effective and economic storage operations. In particular, this study investigates trapping, dissolution, and wettability of H2-brine systems at the pore-scale, at conditions that are realistic for subsurface H2 storage.

EXPERIMENTS

We have performed in situ X-ray imaging during a flow experiment to investigate pore-scale processes during H2 injection and displacement in a brine saturated Bentheimer sandstone sample at temperature and pressure conditions representative of underground reservoirs. Two injection schemes were followed for imbibition: displacement of H2 with H2-equilibrated brine and with non-H2-equilibrated brine. The results from the two cycles were compared with each other.

FINDINGS

The sandstone was found to be wetting to the brine and non-wetting to H2 after both displacement cycles, with average contact angles of 54° and 53° for H2-equilibrated and non-H2-equilibrated brine respectively. We also found a higher recovery of H2 (43.1%) when displaced with non-H2-equilibrated brine compared to that of H2-equilibrated brine (31.6%), indicating potential dissolution of H2 in the unequilibrated imbibing brine at reservoir conditions. Our results suggest that underground H2 storage may indeed be a suitable strategy for energy storage, but considerable further research is needed to fully comprehend the pore-scale interactions at reservoir conditions.

Study on Oil Recovery Mechanism of Polymer-Surfactant Flooding Using X-ray Microtomography and Integral Geometry

Understanding pore-scale morphology and distribution of remaining oil in pore space are of great importance to carry out in-depth tapping of oil potential. Taking two water-wet cores from a typical clastic reservoir in China as an example, X-ray CT imaging is conducted at different experimental stages of water flooding and polymer-surfactant (P-S) flooding by using a high-resolution X-ray microtomography. Based on X-ray micro-CT image processing, 3D visualization of rock microstructure and fluid distribution at the pore scale is achieved. The integral geometry newly developed is further introduced to characterize pore-scale morphology and distribution of remaining oil in pore space. The underlying mechanism of oil recovery by P-S flooding is further explored. The results show that the average diameter of oil droplets gradually decreases, and the topological connectivity becomes worse after water flooding and P-S flooding. Due to the synergistic effect of “1 + 1 > 2” between the strong sweep efficiency of surfactant and the enlarged swept volume of the polymer, oil droplets with a diameter larger than 124.58 μm can be gradually stripped out by the polymer-surfactant system, causing a more scattered distribution of oil droplets in pore spaces of the cores. The network-like oil clusters are still dominant when water flooding is continued to 98% of water cut, but the dominant pore-scale oil morphology has evolved from network-like to porous-type and isolated-type after P-S flooding, which can provide strong support for further oil recovery in the later stage of chemical flooding.

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.

New type of pore-snap-off and displacement correlations in imbibition

HYPOTHESIS

Imbibition of a fluid into a porous material involves the invasion of a wetting fluid in the pore space through piston-like displacement, film and corner flow, snap-off and pore bypassing. These processes have been studied extensively in two-dimensional (2D) porous systems; however, their relevance to three-dimensional (3D) natural porous media is poorly understood. Here, we investigate these pore-scale processes in a natural rock sample using time-resolved 3D (i.e., four-dimensional or 4D) X-ray imaging.

EXPERIMENTS

We performed a capillary-controlled drainage-imbibition experiment on an initially brine-saturated carbonate rock sample. The sample was imaged continuously during imbibition using 4D X-ray imaging to visualize and analyze fluid displacement and snap-off processes at the pore-scale.

FINDINGS

We discover a new type of snap-off that occurs in pores, resulting in the entrapment of a small portion of the non-wetting phase in pore corners. This contrasts with previously-observed snap-off in throats which traps the non-wetting phase in pore centers. We relate the new type of pore-snap-off to the pinning of fluid-fluid interfaces at rough surfaces, creating contact angles close to 90°. Subsequently, we provide correlations for displacement events as a function of pore-throat geometry. Our findings indicate that having a small throat does not necessarily favor snap-off: the key criterion is the throat radius in relation to the pore radius involved in a displacement event, captured by the aspect ratio.

Direct Numerical Simulation of Pore-Scale Trapping Events During Capillary-Dominated Two-Phase Flow in Porous Media

This study focuses on direct numerical simulation of imbibition, displacement of the non-wetting phase by the wetting phase, through water-wet carbonate rocks. We simulate multiphase flow in a limestone and compare our results with high-resolution synchrotron X-ray images of displacement previously published in the literature by Singh et al. (Sci Rep 7:5192, 2017). We use the results to interpret the observed displacement events that cannot be described using conventional metrics such as pore-to-throat aspect ratio. We show that the complex geometry of porous media can dictate a curvature balance that prevents snap-off from happening in spite of favourable large aspect ratios. We also show that pinned fluid-fluid-solid contact lines can lead to snap-off of small ganglia on pore walls; we propose that this pinning is caused by sub-resolution roughness on scales of less than a micron. Our numerical results show that even in water-wet porous media, we need to allow pinned contacts in place to reproduce experimental results.

Application of percolation, critical-path, and effective-medium theories for calculation of two-phase relative permeability

There has been active development of numerical pore-network simulation of two-phase immiscible flows in porous media in recent years. These models allow for generation of capillary pressure and relative permeability curves. However, percolation models provide an efficient alternative, with reduced reliance on numerical techniques. Implementation of effective medium or critical path theory along with the percolation model allows for evaluation of the relative permeability curves. Both approximations failed to match the irreducible water saturation for water relative permeability. While the effective medium approximation poorly matches the pore network simulator, the critical path approximation is shown to match the result of the oil relative permeability. Despite the difference in end points, there is qualitative agreement between critical path approximation and the pore network simulator. Moreover, observed differences are not necessarily a drawback due to important boundary effects as discussed in the paper. Our results indicate that percolation-theory based predictions have the potential to become an efficient tool for upscaling by computing two-phase flow properties for numerous porosity subdomains.

Pore-by-Pore Modelling, Validation and Prediction of Waterflooding in Oil-Wet Rocks Using Dynamic Synchrotron Data

We predict waterflood displacement on a pore-by-pore basis using pore network modelling. The pore structure is captured by a high-resolution image. We then use an energy balance applied to images of the displacement to assign an average contact angle, and then modify the local pore-scale contact angles in the model about this mean to match the observed displacement sequence. Two waterflooding experiments on oil-wet rocks are analysed where the displacement sequence was imaged using time-resolved synchrotron imaging. In both cases the capillary pressure in the model matches the experimentally obtained values derived from the measured interfacial curvature. We then predict relative permeability for the full saturation range. Using the optimised contact angles distributed randomly in space has little effect on the predicted capillary pressures and relative permeabilities, indicating that spatial correlation in wettability is not significant in these oil-wet samples. The calibrated model can be used to predict properties outside the range of conditions considered in the experiment.

Pore Structure Characterization of Undisturbed Weathered Crust Elution-Deposited Rare Earth Ore Based on X-ray Micro-CT Scanning

As an environmentally compliant hydrometallurgical process, in situ leaching is extensively used by the mining industry to recover rare earth from weathered crust elution-deposited rare earth ore. In the in situ leaching system, the pore structure plays a dominant role in the permeability of the rare earth orebody and is one of the most important factors that influence the leaching performance. To study the pore structure characteristics of the rare earth ore, an undisturbed ore sample was scanned using X-ray micro-computed tomography. Based on the image processing techniques, visualization of the pore structure was realized and several parameters of 2D and 3D pore structures, such as porosity, pore volume, length, width, aspect ratio, and orientation, were obtained and statistically analyzed. The ball-and-stick model of large pore clusters was built by the maximal ball algorithm, and some of their detailed characteristics were obtained. The results indicate that the pore structure of weathered crust elution-deposited rare earth ore exhibits a multi-scale and strong heterogeneity characteristic. The distribution characteristics of pores between the vertical direction and the horizontal direction are obviously different. The small pores are more prevalent in number, but they make only a small contribution to the total pore volume. In addition, the orientation of the pores is anisotropic in both vertical and horizontal directions. Furthermore, the ball-and-stick model reveals that large pore clusters are composed of several interconnected void spaces, and most of them are small and irregular.

Dynamic fluid configurations in steady-state two-phase flow in Bentheimer sandstone

Fast synchrotron tomography is used to study the impact of capillary number, Ca, on fluid configurations in steady-state two-phase flow in porous media. Brine and n-decane were co-injected at fixed fractional flow, f_{w}=0.5, in a cylindrical Bentheimer sandstone sample for a range of capillary numbers 2.1×10^{-7}≤Ca≤4.2×10^{-5}, while monitoring the pressure differential. As we have demonstrated in Gao et al. [Phys. Rev. Fluids 5, 013801 (2020)2469-990X10.1103/PhysRevFluids.5.013801], dependent on Ca, different flow regimes have been identified: at low Ca only fixed flow pathways exist, while after a certain threshold dynamic effects are observed resulting in intermittent fluctuations in fluid distribution which alter fluid connectivity. Additionally, the flow paths, for each capillary number, were imaged multiple times to quantify the less frequent changes in fluid occupancy, happening over timescales longer than the duration of our scans (40 s). In this paper we demonstrate how dynamic connectivity results from the interaction between oil ganglia populations. At low Ca connected pathways of ganglia are fixed with time-independent small, medium, and large ganglia populations. However, with an increase in Ca we see fluctuations in the size and numbers of the larger ganglia. With the onset of intermittency, fluctuations occur mainly in pores and throats of intermediate size. When Ca is further increased, we see rapid changes in occupancy in pores of all size. By combining observations on pressure fluctuations and flow regimes at various capillary numbers, we summarize a phase diagram over a range of capillary numbers for the wetting and nonwetting phases, Ca_{w} and Ca_{nw}, respectively, to quantify the degree of intermittent flow. These different regimes are controlled by a competition between viscous forces on the flowing fluids and the capillary forces acting in the complex pore space. Furthermore, we plot the phase diagrams of the transition from Darcy flow to intermittent flow over a range of Reynolds and Weber numbers for the wetting and nonwetting phases to evaluate the balance among capillary, viscous, and inertial forces, incorporating data from the literature. We demonstrate that pore geometry has a significant control on flow regime.

Validation of pore network modeling for determination of two-phase transport in fibrous porous media

Pore network modeling (PNM) has been widely investigated in the study of multiphase transport in porous media due to its high computational efficiency. The advantage of PNM is achieved in part at the cost of using simplified geometrical elements. Therefore, the validation of pore network modeling needs further verification. A Shan-Chen (SC) multiphase lattice Boltzmann model (LBM) was used to simulate the multiphase flow and provided as the benchmark. PNM using different definitions of throat radius was performed and compared. The results showed that the capillary pressure and saturation curves agreed well when throat radius was calculated using the area-equivalent radius. The discrepancy of predicted phase occupations from different methods was compared in slice images and the reason can be attributed to the capillary pressure gradients demonstrated in LBM. Finally, the relative permeability was also predicted using PNM and provided acceptable predictions when compared with the results using single-phase LBM.

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.

Dynamics of fluid displacement in mixed-wet porous media

We identify a distinct two-phase flow invasion pattern in a mixed-wet porous medium. Time-resolved high-resolution synchrotron X-ray imaging is used to study the invasion of water through a small rock sample filled with oil, characterized by a wide non-uniform distribution of local contact angles both above and below 90°. The water advances in a connected front, but throats are not invaded in decreasing order of size, as predicted by invasion percolation theory for uniformly hydrophobic systems. Instead, we observe pinning of the three-phase contact between the fluids and the solid, manifested as contact angle hysteresis, which prevents snap-off and interface retraction. In the absence of viscous dissipation, we use an energy balance to find an effective, thermodynamic, contact angle for displacement and show that this angle increases during the displacement. Displacement occurs when the local contact angles overcome the advancing contact angles at a pinned interface: it is wettability which controls the filling sequence. The product of the principal interfacial curvatures, the Gaussian curvature, is negative, implying well-connected phases which is consistent with pinning at the contact line while providing a topological explanation for the high displacement efficiencies in mixed-wet media.

Intermittent fluid connectivity during two-phase flow in a heterogeneous carbonate rock

Subsurface fluid flow is ubiquitous in nature, and understanding the interaction of multiple fluids as they flow within a porous medium is central to many geological, environmental, and industrial processes. It is assumed that the flow pathways of each phase are invariant when modeling subsurface flow using Darcy's law extended to multiphase flow, a condition that is assumed to be valid during steady-state flow. However, it has been observed that intermittent flow pathways exist at steady state even at the low capillary numbers typically encountered in the subsurface. Little is known about the pore structure controls or the impact of intermittency on continuum scale flow properties. Here we investigate the impact of intermittent pathways on the connectivity of the fluids for a carbonate rock. Using laboratory-based micro computed tomography imaging we observe that intermittent pathway flow occurs in intermediate-sized pores due to the competition between both flowing fluids. This competition moves to smaller pores when the flow rate of the nonwetting phase increases. Intermittency occurs in poorly connected pores or in regions where the nonwetting phase itself is poorly connected. Intermittent pathways lead to the interrupted transport of the fluids; this means they are important in determining continuum scale flow properties, such as relative permeability. The impact of intermittency on flow properties is significant because it occurs at key locations, whereby the nonwetting phase is otherwise disconnected.

Minimal surfaces in porous media: Pore-scale imaging of multiphase flow in an altered-wettability Bentheimer sandstone

High-resolution x-ray imaging was used in combination with differential pressure measurements to measure relative permeability and capillary pressure simultaneously during a steady-state waterflood experiment on a sample of Bentheimer sandstone 51.6 mm long and 6.1 mm in diameter. After prolonged contact with crude oil to alter the surface wettability, a refined oil and formation brine were injected through the sample at a fixed total flow rate but in a sequence of increasing brine fractional flows. When the pressure across the system stabilized, x-ray tomographic images were taken. The images were used to compute saturation, interfacial area, curvature, and contact angle. From this information relative permeability and capillary pressure were determined as functions of saturation. We compare our results with a previously published experiment under water-wet conditions. The oil relative permeability was lower than in the water-wet case, although a smaller residual oil saturation, of approximately 0.11, was obtained, since the oil remained connected in layers in the altered wettability rock. The capillary pressure was slightly negative and 10 times smaller in magnitude than for the water-wet rock, and approximately constant over a wide range of intermediate saturation. The oil-brine interfacial area was also largely constant in this saturation range. The measured static contact angles had an average of 80^{∘} with a standard deviation of 17^{∘}. We observed that the oil-brine interfaces were not flat, as may be expected for a very low mean curvature, but had two approximately equal, but opposite, curvatures in orthogonal directions. These interfaces were approximately minimal surfaces, which implies well-connected phases. Saddle-shaped menisci swept through the pore space at a constant capillary pressure and with an almost fixed area, removing most of the oil.

Time-resolved synchrotron X-ray micro-tomography datasets of drainage and imbibition in carbonate rocks

Multiphase flow in permeable media is a complex pore-scale phenomenon, which is important in many natural and industrial processes. To understand the pore-scale dynamics of multiphase flow, we acquired time-series synchrotron X-ray micro-tomographic data at a voxel-resolution of 3.28 μm and time-resolution of 38 s during drainage and imbibition in a carbonate rock, under a capillary-dominated flow regime at elevated pressure. The time-series data library contains 496 tomographic images (gray-scale and segmented) for the complete drainage process, and 416 tomographic images (gray-scale and segmented) for the complete imbibition process. These datasets have been uploaded on the publicly accessible British Geological Survey repository, with the objective that the time-series information can be used by other groups to validate pore-scale displacement models such as direct simulations, pore-network and neural network models, as well as to investigate flow mechanisms related to the displacement and trapping of the non-wetting phase in the pore space. These datasets can also be used for improving segmentation algorithms for tomographic data with limited projections.