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

Enhanced Reaction Kinetics in Stationary Two-Phase Flow through Porous Media

Understanding the interaction between multiphase flow and reactive transport in porous media is critical for many environmental and industrial applications. When a nonwetting immiscible phase is present within the pore space, it can remain immobile, which we call unsaturated flow, or move, resulting in multiphase flow. Previous studies under unsaturated flow conditions have shown that, for a given flow rate, the product of a mixing-driven reaction increases as wetting phase saturation decreases. Conversely, the opposite effect is observed for a given Péclet number (i.e., the flow rate is adapted depending on the wetting phase saturation). However, the impact of multiphase flow dynamics on mixing-driven reactions is poorly understood due to experimental and numerical challenges. To assess the impact of multiphase flow conditions on product formation, we use an optimized chemiluminescence reaction and an experimental setup that allows the separate injection of reactants along with a stationary two-phase flow. In our experiments, the mass of the reaction product under stationary two-phase flow conditions increases faster than Fickian beyond the diffusive time. The global kinetics initially increase before experiencing a monotonic decrease with significant fluctuations caused by the displacement of the nonwetting phase. For a given flow rate of the wetting phase, product formation depends on the flow rate of the nonwetting immiscible phase.

A Statistical Analysis of Fluid Interface Fluctuations: Exploring the Role of Viscosity Ratio

Understanding multiphase flow through porous media is integral to geologic carbon storage or hydrogen storage. The current modelling framework assumes each fluid present in the subsurface flows in its own continuously connected pathway. The restriction in flow caused by the presence of another fluid is modelled using relative permeability functions. However, dynamic fluid interfaces have been observed in experimental data, and these are not accounted for in relative permeability functions. In this work, we explore the occurrence of fluid fluctuations in the context of sizes, locations, and frequencies by altering the viscosity ratio for two-phase flow. We see that the fluctuations alter the connectivity of the fluid phases, which, in turn, influences the relative permeability of the fluid phases present.

4D microvelocimetry reveals multiphase flow field perturbations in porous media

Many environmental and industrial processes depend on how fluids displace each other in porous materials. However, the flow dynamics that govern this process are still poorly understood, hampered by the lack of methods to measure flows in optically opaque, microscopic geometries. We introduce a 4D microvelocimetry method based on high-resolution X-ray computed tomography with fast imaging rates (up to 4 Hz). We use this to measure flow fields during unsteady-state drainage, injecting a viscous fluid into rock and filter samples. This provides experimental insight into the nonequilibrium energy dynamics of this process. We show that fluid displacements convert surface energy into kinetic energy. The latter corresponds to velocity perturbations in the pore-scale flow field behind the invading fluid front, reaching local velocities more than 40 times faster than the constant pump rate. The characteristic length scale of these perturbations exceeds the characteristic pore size by more than an order of magnitude. These flow field observations suggest that nonlocal dynamic effects may be long-ranged even at low capillary numbers, impacting the local viscous-capillary force balance and the representative elementary volume. Furthermore, the velocity perturbations can enhance unsaturated dispersive mixing and colloid transport and yet, are not accounted for in current models. Overall, this work shows that 4D X-ray velocimetry opens the way to solve long-standing fundamental questions regarding flow and transport in porous materials, underlying models of, e.g., groundwater pollution remediation and subsurface storage of CO2 and hydrogen.

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.

Pore-Scale Investigation of Dynamic Immiscible Displacement in Layered Media using Synchrotron X-ray Microtomography

Understanding the dynamics of immiscible fluid in a porous media is critical in many chemical and environmental engineering processes. However, the geological heterogeneity effect on multiphase flow behavior remains unclear. Here, the dynamics of immiscible fluid displacement and entrapment were experimentally demonstrated at pore-level using time-lapse synchrotron X-ray microtomography. A drainage-imbibition experiment was designed using an unconsolidated layered sand pack that comprised coarse sand and fine sand zones. There were significant differences between the two zones, with regard to the temporal variations in fluid saturation and morphological evolution of nonwetting fluid (oil) during imbibition. Highly connected oil clusters in the coarse zone broke up into many small fragments, whereas the cluster in the fine zone remained connected while spanning multiple pores. To further understand the impacts of pore size and connectivity on multiphase fluid dynamics, a new approach that tracks the temporal variation of immiscible fluid in individual pores was conducted. The surface area at the oil-water interface increased during imbibition, which is expected to facilitate mass transfer and surface interactions. Understanding immiscible fluid displacement in layered porous media at the pore-level could lead to more effective environmental remediation.

Improved dynamic imaging of multiphase flow by constrained tomographic reconstruction

Dynamic tomography has become an important technique to study fluid flow processes in porous media. The use of laboratory X-ray tomography instruments is, however, limited by their low X-ray brilliance. The prolonged exposure times, in turn, greatly limit temporal resolution. We have developed a tomographic reconstruction algorithm that maintains high image quality, despite reducing the exposure time and the number of projections significantly. Our approach, based on the Simultaneous Iterative Reconstruction Technique, mitigates the problem of few and noisy exposures by utilising a high-quality scan of the system before the dynamic process is started. We use the high-quality scan to initialise the first time step of the dynamic reconstruction. We further constrain regions of the dynamic reconstruction with a segmentation of the static system. We test the performance of the algorithm by reconstructing the dynamics of fluid separation in a multiphase system. The algorithm is compared quantitatively and qualitatively with several other reconstruction algorithms and we show that it can maintain high image quality using only a fraction of the normally required number of projections and with a substantially larger noise level. By robustly allowing fewer projections and shorter exposure, our algorithm enables the study of faster flow processes using laboratory tomography instrumentation but it can also be used to improve the reconstruction quality of dynamic synchrotron experiments.

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.

Upscaling the porosity-permeability relationship of a microporous carbonate for Darcy-scale flow with machine learning

The permeability of a pore structure is typically described by stochastic representations of its geometrical attributes (e.g. pore-size distribution, porosity, coordination number). Database-driven numerical solvers for large model domains can only accurately predict large-scale flow behavior when they incorporate upscaled descriptions of that structure. The upscaling is particularly challenging for rocks with multimodal porosity structures such as carbonates, where several different type of structures (e.g. micro-porosity, cavities, fractures) are interacting. It is the connectivity both within and between these fundamentally different structures that ultimately controls the porosity–permeability relationship at the larger length scales. Recent advances in machine learning techniques combined with both numerical modelling and informed structural analysis have allowed us to probe the relationship between structure and permeability much more deeply. We have used this integrated approach to tackle the challenge of upscaling multimodal and multiscale porous media. We present a novel method for upscaling multimodal porosity–permeability relationships using machine learning based multivariate structural regression. A micro-CT image of Estaillades limestone was divided into small 60³ and 120³ sub-volumes and permeability was computed using the Darcy–Brinkman–Stokes (DBS) model. The microporosity–porosity–permeability relationship from Menke et al. (Earth Arxiv, https://doi.org/10.31223/osf.io/ubg6p, 2019) was used to assign permeability values to the cells containing microporosity. Structural attributes (porosity, phase connectivity, volume fraction, etc.) of each sub-volume were extracted using image analysis tools and then regressed against the solved DBS permeability using an Extra-Trees regression model to derive an upscaled porosity–permeability relationship. Ten test cases of 360³ voxels were then modeled using Darcy-scale flow with this machine learning predicted upscaled porosity–permeability relationship and benchmarked against full DBS simulations, a numerically upscaled Darcy flow model, and a Kozeny–Carman model. All numerical simulations were performed using GeoChemFoam, our in-house open source pore-scale simulator based on OpenFOAM. We found good agreement between the full DBS simulations and both the numerical and machine learning upscaled models, with the machine learning model being 80 times less computationally expensive. The Kozeny–Carman model was a poor predictor of upscaled permeability in all cases.

Mechanisms controlling fluid breakup and reconnection during two-phase flow in porous media

The use of Darcy's law to describe steady-state multiphase flow in porous media has been justified by the assumption that the fluids flow in continuously connected pathways. However, a range of complex interface dynamics have been observed during macroscopically steady-state flow, including intermittent pathway flow where flow pathways periodically disconnect and reconnect. The physical mechanisms controlling this behavior have remained unclear, leading to uncertainty concerning the occurrence of the different flow regimes. We observe that the fraction of intermittent flow pathways is dependent on the capillary number and viscosity ratio. We propose a phase diagram within this parameter space to quantify the degree of intermittent flow.