Elucidating the Role of Interfacial Tension for Hydrological Properties of Two-Phase Flow in Natural Sandstone by an Improved Lattice Boltzmann Method

We investigated the interfacial tension (IFT) effect on fluid flow characteristics inside micro-scale, porous media by a highly efficient multi-phase lattice Boltzmann method using a graphics processing unit. IFT is one of the most important parameters for carbon capture and storage and enhanced oil recovery. Rock pores of Berea sandstone were reconstructed from micro-CT scanned images, and multi-phase flows were simulated for the digital rock model at extremely high resolution (3.2  \(\upmu \) m). Under different IFT conditions, numerical analyses were carried out first to investigate the variation in relative permeability, and then to clarify evolution of the saturation distribution of injected fluid. We confirmed that the relative permeability decreases with increasing IFT due to growing capillary trapping intensity. It was also observed that with certain pressure gradient \(\Delta P\) two crucial IFT values, \(\sigma _{1}\) and \(\sigma _{2}\) , exist, creating three zones in which the displacement process has totally different characteristics. When \(\sigma _{1}< \sigma < \sigma _{2}\) , the capillary fingering patterns are observed, while for \(\sigma < \sigma _{1}\) viscous fingering is dominant and most of the passable pore spaces were invaded. When \(\sigma > \sigma _{2}\) the invading fluid failed to break through. The pore-throat-size distribution estimated from these crucial IFT values ( \(\sigma _{1 }\) and \(\sigma _{2})\) agrees with that derived from mercury porosimetry measurements of Berea sandstone. This study demonstrates that the proposed numerical method is an efficient tool for investigating hydrological properties from pore structures.     

Correlation of Water Vapor Permeability with Microstructure Characteristics of Building Materials Using Robust Chemometrics

This paper studies various microstructure parameters of natural and artificial building materials and aims to their correlation to the water vapor permeability. Three categories of building materials were investigated: stones, bricks, and plasters. Mercury intrusion porosimetry was applied in order to obtain the materials microstructure characteristics, a variety of pore size distributions and pore structure measurements, such as total porosity. The water vapor permeability of materials was determined experimentally according to ASTM standard E96-00. A robust principal component regression approach, coupled with multiple outlier detection, was applied in order to correlate water vapor permeability values to pore size distributions. A good quality correlation model was found by utilizing relative specific pore volume and relative specific pore surface distributions, whereas using pore structure measurements, such as total porosity, the correlation results were very poor. From the results, specific ranges of pore size distribution, corresponding to pores radius sizes greater than $10\,\upmu \text{ m }$ 10 μ m and between 1.778 and $0.421\,\upmu \text{ m }$ 0.421 μ m , contribute to the water vapor permeability of the materials.     

Estimation of Shale Intrinsic Permeability with Process-Based Pore Network Modeling Approach

A multi-scale pore network model is developed for shale with the process-based method (PBM). The pore network comprises three types of sub-networks: the \(\upmu \)m-scale sub-network, the nm-scale pore sub-network in organic matter (OM) particles and the nm-scale pore sub-network in clay aggregates. Process-based simulations mimic shale-forming geological processes and generate a \(\upmu \)m-scale sub-network which connects interparticle pores, OM particles and clay aggregates. The nm-scale pore sub-networks in OM and clay are extracted from monodisperse sphere packing. Nm-scale throats in OM and clay are simplified to be cylindrical and cuboid-shaped, respectively. The nm-scale pore sub-networks are inserted into selected OM particles and clay aggregates in the \(\upmu \)m-scale sub-network to form an integrated multi-scale pore network. No-slip permeability is evaluated on multi-scale pore networks. Permeability calculations verify that shales permeability keeps decreasing when nm-scale pores and throats replace \(\upmu \)m-scale pores. Soft shales may have higher porosity but similar range of permeability with hard shales. Small compaction leads to higher permeability when nm-scale pores dominate a pore network. Nm-scale pore networks with higher interconnectivity contribute to higher permeability. Under constant shale porosity, the shale matrix with cuboid-shaped nm-scale throats has lower no-slip permeability than that with cylindrical throats. Different from previous reconstruction processes, the new reconstruction process first considers the porous OM and clay distribution with PBM. The influence of geological processes on the multi-scale pore networks is also first analyzed for shale. Moreover, this study considers the effect of OM porosities and different pore morphologies in OM and clay on shale permeability.     

Experimental Study of Nonlinear Flow in Micropores Under Low Pressure Gradient

As throat radius decrease to micro-nanoscale, seepage in unconventional reservoirs such as ultra-low permeability and tight reservoirs differs from conventional ones. Flow experiment in micropores is a promising approach to study characteristics of microflow. In this paper, a visual experimental device was established. Water flow through micropores with radius of 1.38–10.03 \(\upmu \hbox {m}\) was investigated, under 0.033–16 MPa/m. The results showed that in microscale, water flow did not agree with Poiseuille equation. Flow rate was lower than theoretical value and showed nonlinear characteristics. In the near wall area, due to the attraction of solid wall, a stagnant fluid layer was formed. It occupied flow space and thus lowered flow rate. Its thickness declined with pressure gradient increasing, which led to nonlinear flow characteristics. When the pressure gradient was very high, the thickness stopped declining and kept constant. Afterward, the flow transited to linear. In pores with smaller radius, the steady stagnant layer was thinner, but took a larger proportion of the flow space. For tubes of \(r = 1.38, 4.81, 10.03\,\upmu \hbox {m}\), the thickness of steady stagnant layer was 0.11, 0.23, 0.27 \(\upmu \hbox {m}\), respectively.     

On the Potential of Tomographic Methods when Applied to Compacted Crushed Rock Salt

Compacted crushed rock salt is considered as potential backfill material in repositories for nuclear waste. To evaluate the sealing properties of this material knowledge concerning the nature of the pore space is of eminent interest. Here, the pore microstructures of crushed rock salt samples with different compaction states were investigated by X-ray (XCT) computed tomography and Focused Ion Beam nanotomography (FIB-nt). Based on these methods the pore microstructures were reconstructed and quantitatively analyzed with respect to porosity, connectivity and percolation properties. Regarding pores with radii \(> 4\,\upmu \hbox {m}\) , porosity differs substantially in the two analyzed samples ( \(\phi = 0.01\) and 0.10). The pore microstructures are considered isotropic in connectivity and percolation threshold. Using two finite-scaling schemes we found percolation thresholds with critical porosities \(\phi _{c} > 0.05\) . Based on statistical considerations, the millimeter size samples that can be analyzed by XCT are large enough to provide a meaningful picture of the pore geometry related to macroporosity. The samples contain also a small fraction (i.e. \(< 0.01\) ) of pores with radii \(< 1\,\upmu \hbox {m}\) , which were resolved by FIB-nt. Often these pores can be found along grain boundaries. These pores are granular shaped and are not connected to each other. Typical samples size that can be analyzed by FIB-nt is on the order of tens of microns, which turned out to be too small to provide representative geometric information unless an effort is made that involves several FIB-nt realizations per sample.     

Flow Dynamics of \hbox {CO}_{2}/brine at the Interface Between the Storage Formation and Sealing Units in a Multi-layered Model

Pressure distribution and \(\hbox {CO}_{2}\) plume migration are two major interests in \(\hbox {CO}_{2}\) geologic storage as they determine the injectivity and storage capacity. In this study, we adopted a three-layer model comprising a storage formation and the over- and underlying seals and determined three distinct flow regions based on the vertical flux exchange of \(\hbox {CO}_{2}\) and native brine. Regions 1 and 2 showed \(\hbox {CO}_{2}\) flowing from the storage formation to adjacent seals with counter-flowing brine. The characteristics of these fluxes in Region 1 were governed by permeability change due to salt precipitation whereas buoyancy force controlled the flux pattern in Region 2. Region 3 showed brine flowing from storage formation toward the over- and underlying seals, which enabled the displaced brine to escape from the storage formation and make room for \(\hbox {CO}_{2}\) to store as well as reduce the pressure build-up. In the multi-layered model, the counter-flowing brine in flow Region 1 resulted in localized salt precipitation at the upper and lower boundary of storage formation. We assessed the bottom-hole pressure and \(\hbox {CO}_{2}\) mass in caprock with respect to reservoir size. While the formation thickness influenced the bottom-hole pressure in the early stage of injection, the horizontal extension of the reservoir was more influential to pressure build-up during the injection period, and to the stabilized pressure during the post-injection period. The \(\hbox {CO}_{2}\) mass in caprock gently increased during the injection period as well as during the post-injection period and reached about 4–5 % of injected \(\hbox {CO}_{2}\) . The percentage of escaped brine from the storage formation ranged from 80–100 % of the \(\hbox {CO}_{2}\) mass stored in the storage formation depending on the reservoir scale.     

Identification of Molecular Transport Mechanisms in Micro-Porous Hydrotalcite–Silica Membrane

Hydrotalcite (HT) materials have been known to be able to adsorb \(\hbox {CO}_{2}\) even at high temperature. However, HT has not been made into a micro-porous membrane because of its meso-porous nature. In order to form a micro-porous HT membrane, silica was selected as a host matrix due to its ability to retain its micro-porosity. In this paper, a micro-porous hydrotalcite–silica membrane was formed on a meso-porous \(\upgamma \) -alumina layer supported by a macro-porous \(\upalpha \) -alumina substrate. Most of the micro-porosity determined from nitrogen adsorption measurement was found to be either closed or open but not interconnected, whereas most of the meso-porosity (at ca. 11.2 nm) in the micro-porous membrane was open and interconnected, thereby promoting gas flow. Viscous flow mechanism was observed to dominate transport of gases in macro-porous membrane. Knudsen diffusion dominated transport of gases in meso-porous membrane. On the other hand, surface affinity influenced the transport of carbon dioxide through the micro-porous membrane rather significantly. While permeability of pure hydrogen and carbon dioxide were independent of pressure, the permeability of the gases in the binary mixtures decreased with increasing pressure. Both experiment and simulation demonstrated consistent results.     

Grain Shape Effects on Permeability,Formation Factor,and Capillary Pressure from Pore-Scale Modeling

We invoke pore-scale models to evaluate grain shape effects on petrophysical properties of three-dimensional (3D) images from micro-CT scans and consolidated grain packs. Four sets of grain-packs are constructed on the basis of a new sedimentary algorithm with the following shapes: exact angular grain shapes identified from micro-CT scans, ellipsoids fitted to angular grains, and spheres with volume and surface-to-volume ratio equal to original angular grains on a grain-by-grain basis. Subsequently, a geometry-based cementation algorithm implements pore space alteration due to diagenesis. Eight micro-CT scans and 144 grain-pack images with $500 \times 500 \times 500$ voxels (the resolution units of 3D images) are analyzed in this study. Absolute permeability, formation factor, and capillary pressure are calculated for each 3D image using numerical methods and compared to available core measurements. Angular grain packs give rise to the best agreement with experimental measurements. Cement volume and its spatial distribution in the pore space significantly affect all calculated petrophysical properties. Available empirical permeability correlations for non-spherical grains underestimate permeability between 30 and 70 % for the analyzed samples. Kozeny–Carman’s predictions agree with modeled permeability for spherical grain packs but overestimate permeability for micro-CT images and non-spherical grain packs when volume-based radii are used to calculate the average grain size in a pack. We identify surface-to-volume ratio and grain shape as fundamental physical parameters that control fluid distribution and flow in porous media for equivalent porosity samples.     

Miscible and Immiscible Foam Injection for Mobility Control and EOR in Fractured Oil-Wet Carbonate Rocks

Foam injection is a proven enhanced oil recovery (EOR) technique for heterogeneous reservoirs, but is less studied for EOR in fractured systems. We experimentally investigated tertiary \(\text {CO}_{2}\) injections, and \(\text {N}_{2}\) - and \(\text {CO}_{2}\) -foam injections for enhanced oil recovery in fractured, oil-wet limestone core plugs. Miscible \(\text {CO}_{2}\) and \(\text {CO}_{2}\) -foam was compared with immiscible \(\text {CO}_{2}\) - and \(\text {N}_{2}\) -foam as tertiary recovery techniques, subsequent to waterfloods, in fractured rocks with different wettability preferences. At water-wet conditions waterfloods produced approximately 40 % OOIP, by spontaneous imbibition. Waterflood oil recovery at oil-wet conditions was below 20 % OOIP, due to suppressed imbibition where water predominantly flowed through the fractures, unable to mobilize the oil trapped in the matrix. Tertiary, supercritical \(\text {CO}_{2}\) -mobilized oil trapped in the matrix, particularly at weakly oil-wet conditions, by diffusion. Recovery by diffusion was high due to small core samples, high initial oil saturation and a continuous oil phase at oil-wet conditions. Both immiscible \(\text {CO}_{2}\) - and \(\text {N}_{2}\) -foams and miscible, supercritical \(\text {CO}_{2}\) -foam demonstrated high ultimate oil recoveries, but immiscible foam was less efficient (30 pore volumes injected) compared to miscible foam (2 pore volumes injected) to reach ultimate recovery. This is explained by the capillary threshold pressure preventing the injected \(\text {N}_{2}\) gas from entering the matrix, verified by computed X-ray tomography, and the mobilized oil was displaced by the aqueous surfactant in the foam. At miscible conditions, there exists no capillary entry pressure between the oil-saturated matrix and the injected \(\text {CO}_{2}\) , allowing foam to invade the matrix for efficient oil recovery.     

The Effects of Brine Species on the Formation of Residual Water in a \hbox {CO}_{2}–Brine System

Geological storage of \(\hbox {CO}_{2}\) in deep saline aquifers is achieved by injecting \(\hbox {CO}_{2}\) into the aquifers and displacing the brine. Although most of the brine is displaced, some residual groundwater remains in the rock pores. We conducted experiments to investigate factors that influence how much of this residual water remains after \(\hbox {CO}_{2}\) is injected. A rock sample was saturated with brines of two different salts. Supercritical \(\hbox {CO}_{2}\) was injected into the samples at aquifer temperature and pressure, and the displaced water and water–gas mixtures were collected and measured. The results show that deionized water drains more completely than either of the two brines, and NaCl brine drains more completely than \(\hbox {CaCl}_{2}\) brine. The ranking of the irreducible water saturation at the end of the experiment is deionized \(\hbox {water}<\hbox {NaCl brine } <\hbox {CaCl}_{2}\) brine. The process of drainage can be divided into three stages according to the drainage flow rates; the Pushing Drainage, Portable Drainage, and Dissolved Drainage stages. This paper proposed a capillary model which is used to interpret the mechanisms that characterize these three stages.     

Thermal Conduction in Deforming Isotropic and Anisotropic Granular Porous Media with Rough Grain Surface

The measurement of fluid pressure inside pores is a major challenge in experimental studies of two-phase flow in porous media. In this paper, we describe the manufacturing procedure of a micro-model with integrated fibre optic pressure sensors. They have a circular measurement window with a diameter of 260 \(\upmu \hbox {m}\), which enables the measurement of pressure at the pore scale. As a porous medium, we used a PDMS micro-model with known physical and surface properties. A given pore geometry was produced following a procedure we had developed earlier. We explain the technology behind fibre optic pressure sensors and the procedure for integrating these sensors into a micro-model and demonstrate their utility for the measurement of pore pressure under transient two-phase flow conditions. Finally, we present and analyse results of single and two-phase flow experiments performed in the micro-model and discuss the link between small-scale fast pressure changes with pore-scale events.     

A Procedure for the Accurate Determination of Sub-Core Scale Permeability Distributions with Error Quantification

We present a new method for non-destructively calculating sub-core scale permeability distributions within a core. The new method integrates experimentally measured capillary pressure data and sub-core scale saturation and porosity data collected using a computed tomography-scanner, to construct an accurate and unique sub-core scale permeability distribution. Using this procedure, it is possible to conduct highly refined simulations of core flooding experiments without typical assumptions requiring the core to be homogeneous, or relying on inaccurate porosity-based methods for estimating permeability distributions. The calculation procedure is described and results from two example rock cores are presented, a Berea Sandstone and a sandstone from the Otway Basin Pilot Project in Australia. Drainage coreflooding experiments of carbon dioxide ( $\text{ CO }_{2})$ CO 2 ) injection into water are first conducted on both cores and permeability distributions are calculated using the experimental data. Numerical simulations of the very same experiments are then conducted to demonstrate the accuracy of the calculated sub-core scale permeability distribution. Results from both cores show that the input sub-core scale saturation distributions are predicted with an $R^{2}$ R 2 correlation of greater than 0.93. This is compared to having no correlation when using simple porosity-only based permeability distributions, or assuming homogeneous core properties (Krause et al., SPE J 16(4):768–777, 2011). The uniqueness of the calculated permeability distribution is then demonstrated by calculating permeability distributions for the same core using data collected at different $\text{ CO }_{2}$ CO 2 injection fractional flows. Results show that the two independently calculated permeability distributions agree within the limits of experimental measurement error.     

Advection–Dispersive Mechanisms of Electrolyte Species in Porous Matrix

Advection–dispersive phenomena inside two geometries of porous media, corresponding to a structured and unstructured network of minichannels, are studied from a combination of analytical, numerical, and electrodiffusion techniques. The instantaneous limiting diffusion current, connected to the concentration of electroactive species flowing in the porous matrix, is recorded and measured during flow experimentation. Transport phenomena investigation consists of the step injection of a tracer of higher concentration than the bulk flow in order to characterize the mixing of electrolyte species inside two arrangements of network, so called \(\times \) _network and T_network. The experimental results are supported by 2D-numerical simulations performed in the \(\times \) _network. A pore model is proposed in order to predict the pore velocity, which is used within the resolution of the diffusion–convection balance. The numerical simulations, based on a second-order finite difference scheme, give rise to a good agreement in terms of mixing index and the methodology employed for the numerical injection concentration appears suitable. The numerical experiments are quite-well representative in laminar regime below the critical Reynolds number ( \(Re_{\mathrm{crit}}\approx \,200\) ). Above \(Re_{\mathrm{crit}}\) , the inertial effects are not negligible and the momentum transfer needs to be taken into account. This latter phenomenon is analyzed at the pore-scale in term of local skin friction measured at the channels crossing, then compared and discussed from analytical solutions.     

Numerical Simulation of Porosity in Cements

The pores in cementitious materials, their sizes and connectivity have an important influence on the durability of concrete. Several microstructural models have been developed to simulate the three-dimensional pore network in cement pastes. In this article, microstructures with the $\upmu $ μ ic model are compared with experimental results. It is seen that despite having a resolution for the capillary pores very close to reality, the experimentally observed breakthrough diameter from mercury intrusion is much lower than the values obtained by applying an algorithm of mercury intrusion to the simulated microstructure. The effect of some of the most important input parameters on the pore sizes in the simulated microstructure explored. The phenomenon which seems best able to explain this discrepancy is that C–S–H is not in fact a phase with a smooth surface as represented in microstructural models, but a phase which grows as needles into the pore space, leading to very small water-filled capillary pores from quite young ages. The results demonstrate it will be extremely challenging to represent the porosity of real microstructures in microstructural models on the scale of hundreds of microns necessary to study macroscopic transport.     

Effects of Particle Size Non-Uniformity on Transport and Retention in Saturated Porous Media

Short-pulse injection experiments are investigated to study the effects of particle size non-uniformity on the transport and retention in saturated porous media. Monodisperse particles (3, 10, and 16 \(\upmu \hbox {m}\) latex microspheres) and polydisperse particles (containing 3, 10, and 16 latex microspheres) were explored. The obtained results suggest considering not only the particle sizes but also their polydispersivity (particle size non-uniformity) in transport and retention. Although, the density of the suspended particles is close to that of water, results reveal a slow transport of particles compared to the dissolved tracer whatever their size and flow velocity. The recovered particles in the mixture experiments show that the retention of large particles (10 and 16 \(\upmu \hbox {m}\)) enhances the retention of small ones (3 \(\upmu \hbox {m}\)). However, the straining of 10 and 16 \(\upmu \hbox {m}\) particles in “mixture experiments” is smaller than their straining in “monodisperse experiments”. A linear relationship summarizing the simultaneous effect of particle sizes and flow velocity on deposition kinetics coefficient is proposed.     

Gas Sorption and the Consequent Volumetric and Permeability Change of Coal II: Numerical Modeling

The permeability of coalbed methane reservoirs may evolve during the recovery of methane and injection of gas, due to the change of effective stress and gas adsorption and desorption. Experimental and numerical studies were conducted to investigate the sorption-induced permeability change of coal. This paper presents the numerical modeling part of the work. It was found that adsorption of pure gases on coal was well represented by parametric adsorption isotherm models in the literature. Based on the experimental data of this study, adsorption of pure \(\hbox {N}_2\) was modeled using the Langmuir equation, and adsorption of pure \(\hbox {CO}_2\) was well represented by the N-Layer BET equation. For the modeling of CO \(_2\) & N \(_2\) binary mixture adsorption, the ideal adsorbed solution (IAS) model and the real adsorbed solution (RAS) model were used. The IAS model estimated the total amount of mixture adsorption and the composition of the adsorbed phase based on the pure adsorption isotherms. The estimated total adsorption and adsorbed-phase composition were very different from the experimental results, indicating nonideality of the CO \(_2\) –N \(_2\) –Coal-adsorption system. The measured sorption-induced strain was linearly proportional to the total amount of adsorption despite the species of the adsorbed gas. Permeability reduction followed a linear correlation with the volumetric strain with the adsorption of pure \(\hbox {N}_2\) and the tested CO \(_2\) & N \(_2\) binary mixtures, and an exponential correlation with the adsorption of pure \(\hbox {CO}_2\) .     

Shear Rate Determination from Pore-Scale Flow Fields

Aqueous solutions with polymer additives often used to improve the macroscopic sweep efficiency in oil recovery typically exhibit non-Newtonian rheology. In order to predict the Darcy-scale effective viscosity \(\mu _{\mathrm{eff}} \) required for practical applications often, semi-empirical correlations such as the Cannella or Blake–Kozeny correlation are employed. These correlations employ an empirical constant (“C-factor”) that varies over three orders of magnitude with explicit dependency on porosity, permeability, fluid rheology and other parameters. The exact reasons for this dependency are not very well understood. The semi-empirical correlations are derived under the assumption that the porous media can be approximated by a capillary bundle for which exact analytical solutions exist. The effective viscosity \(\mu _{\mathrm{eff}} (v_{\mathrm{Darcy}} )\) as a function of flow velocity is then approximated by a cross-sectional average of the local flow field resulting in a linear relationship between shear rate \(\gamma \) and flow velocity. Only with such a linear relationship, the effective viscosity can be expressed as a function of an average flow rate instead of an average shear rate. The local flow field, however, does in general not exhibit such a linear relationship. Particularly for capillary tubes, the velocity is maximum at the center, while the shear rate is maximum at the tube wall indicating that shear rate and flow velocity are rather anti-correlated. The local flow field for a sphere pack is somewhat more compatible with a linear relationship. However, as hydrodynamic flow simulations (using Newtonian fluids for simplicity) performed directly on pore-scale resolved digital images suggest, flow fields for sandstone rock fall between the two limiting cases of capillary tubes and sphere packs and do in general not exhibit a linear relationship between shear rate and flow velocity. This indicates that some of the shortcomings of the semi-empirical correlations originate from the approximation of the shear rate by a linear relationship with the flow velocity which is not very well compatible with flow fields from direct hydrodynamic calculations. The study also indicates that flow fields in 3D rock are not very well represented by capillary tubes.     

Suspended Particles Transport and Deposition in Saturated Granular Porous Medium: Particle Size Effects

An experimental study on the transport and deposition of suspended particles (SP) in a saturated porous medium (calibrated sand) was undertaken. The influence of the size distribution of the SP under different flow rates is explored. To achieve this objective, three populations with different particles size distributions were selected. The median diameter $d_{50}$ of these populations was 3.5, 9.5, and $18.3~\upmu \hbox {m}$ . To study the effect of polydispersivity, a fourth population noted “Mixture” ( $d_{50} = 17.4\; \upmu \hbox {m}$ ) obtained by mixing in equal proportion (volume) the populations 3.5 and $18.3\;\upmu \hbox {m}$ was also used. The SP transfer was compared to the dissolved tracer (DT) one. Short pulse was the technique used to perform the SP and the DT injection in a column filled with the porous medium. The breakthrough curves were competently described with the analytical solution of a convection–dispersion equation with first-order deposition kinetics. The results showed that the transport of the SP was less rapid than the transport of the DT whatever the flow velocity and the size distribution of the injected SP. The mean diameter of the recovered particles increases with flow rate. The longitudinal dispersion increases, respectively, with the increasing of the flow rates and the SP size distribution. The SP were more dispersive in the porous medium than the DT. The results further showed that the deposition kinetics depends strongly on the size of the particle transported and their distribution.     

Reconstructing the 3D shapes of droplets in glass microchannels with application to Bretherton’s problem

The outstanding potential of absorbance imaging for the 3D shape analysis of dynamic scenes in multiphase flows is demonstrated and experimentally confirmed. The experimental procedures and workflows have been extended and applied to the 3D shape analysis of droplets moving in microchannels. Using this technique, the problem of measuring the thickness of the lubrication layer and the droplet geometry with sub- \(\upmu\) m resolution could be solved. The obtained data generally conform to models based on Bretherton’s theory and allow its extension even for non-circular microchannel geometries.     

Experimental Characterization of Porosity Structure and Transport Property Changes in Limestone Undergoing Different Dissolution Regimes

Limestone dissolution by $\hbox {CO}_2$ -rich brine induces critical changes of the pore network geometrical parameters such as the pore size distribution, the connectivity, and the tortuosity which govern the macroscopic transport properties (permeability and dispersivity) that are required to parameterize the models, simulating the injection and the fate of $\hbox {CO}_2$ . A set of four reactive core-flood experiments reproducing underground conditions ( $T = 100\,^{\circ }\hbox {C}$ and $P = 12$ MPa) has been conducted for different $\hbox {CO}_2$ partial pressures $(0.034 < P_{\mathrm{CO}_2}< 3.4\; \hbox {MPa})$ in order to study the different dissolution regimes. X-ray microtomographic images have been used to characterize the changes in the structural properties from pore scale to Darcy scale, while time-resolved pressure loss and chemical fluxes enabled the determination of the sample-scale change in porosity and permeability. The results show the growth of localized dissolution features associated with high permeability increase for the highest $P_{\mathrm{CO}_2}$ , whereas dissolution tends to be more homogeneously distributed for lower values of $P_{\mathrm{CO}_2}$ . For the latter, the higher the $P_{\mathrm{CO}_2}$ , the more the dissolution patterns display ramified structures and permeability increase. For the lowest value of $P_{\mathrm{CO}_2}$ , the preferential dissolution of the calcite cement associated with the low dissolution kinetics triggers the transport that may locally accumulate and form a microporous material that alters permeability and produces an anti-correlated porosity–permeability relationship. The combined analysis of the pore network geometry and the macroscopic measurements shows that $P_{\mathrm{CO}_2}$ regulates the tortuosity change during dissolution. Conversely, the increase of the exponent value of the observed power law permeability–porosity trend while $P_{\mathrm{CO}_2}$ increases, which appears to be strongly linked to the increase of the effective hydraulic diameter, depends on the initial rock structure.