Two methods for determining the pore critical point (PCP), i.e., the critical point of confined fluid, are currently available in the literature. The better-known method is based on the analysis of data obtained from adsorption isotherms, while the newer method analyzes the heat of capillary condensation data obtained from differential scanning calorimetry (DSC). For the first time, these two methods are implemented on the same confined system for comparison to explore which method provides the true PCP. While the heat released at the PCP derived from adsorption isotherms is measurably nonzero, implying that a phase transition still occurs in the pores, no heat is released at the PCP derived from the DSC measurements, which indicates the true critical point of the first-order phase transition. With this true PCP, the Peng-Robinson cubic equation of state (EOS), without any modification, is shown to accurately represent the whole capillary-condensation curve of confined pure fluids with small and large molecules as well as a confined mixture.

The purpose of this study is to determine the dispersion in a channel with leaky walls. First, the velocity field for the main and leakage flows is described. Then, the unsteady-state two-dimensional advection-diffusion equation is utilized to govern the solute transport. Finally, by applying the Reynolds decomposition and performing cross-sectional averaging, the reduced-order model for advection-dispersion solute transport in the channel with leaky walls provides expressions for both the effective mean flow velocity and the associated dispersion coefficient. The results show that the effective velocity of the main stream increases with increasing axial and transverse Péclet numbers, the cross-sectional average velocity, and the leakage to main flow velocity ratio. However, as the velocity ratio increases, the effective velocity may display either monotonic or non-monotonic behavior at small transverse Péclet numbers. This behavior depends on the axial Péclet number, based on the cross-sectional average velocity. It is also observed that, for each cross-sectional average velocity, the dispersion coefficient increases with increasing axial Péclet number. In contrast, it decreases with increasing transverse Péclet number. In addition, the dispersion coefficient tends to increase with the cross-sectional average velocity. The results find applications in the design of microfluidic and biomedical flow systems.

The solute transport due to mixed electro-osmotic and pressure-driven flows of viscoelastic fluids in microchannels is studied here. The Reynolds decomposition technique, in combination with the assumptions underlying the Taylor-Aris theory, is used to derive a reduced-order model that yields the dispersion coefficient, which is then solved using the general Duhamel theorem to obtain the cross-sectional average concentration. The dispersion is evaluated for the general case of mixed electro-osmotic and pressure-driven flows of viscoelastic fluids, and for three special cases: combined electro-osmotic and pressure-driven flows of a Newtonian fluid, electro-osmotic flow of a viscoelastic fluid, and pressure-driven flow of a viscoelastic fluid. The dispersion coefficient is characterized by four main nondimensional parameters: the ratio of advection to diffusion (Pe), the inverse of the electric double-layer thickness (κ), the ratio of pressure-driven to electro-osmotic forces (λ), and the fluid viscoelasticity (ɛDe^{2}). As expected, the larger the Peclet number, the greater the dispersion for fixed λ and ɛDe^{2} values. It is generally observed that the dispersion coefficient increases as the fluid viscoelasticity increases, for constant values of the Peclet number and the ratio of pressure-driven to electro-osmotic forces. The results also indicate that the dispersion exhibits nonmonotonic behavior as λ increases from negative to positive values, for fixed Peclet number and fluid viscoelasticity. The dispersion coefficient and the cross-sectional average concentration are examined for special cases and compared with the general case. The developed mathematical model and findings have implications for the design of solute transport in microfluidic systems.

The effect of pore size distribution on the phase transition of confined mixtures in nanoporous media is a field of study that still has a significant knowledge gap in the literature. This study presents experimental measurements on the phase transition of a methane/propane gas mixture confined in multimodal nanoporous media with independent domains, marking the first measurements of its kind. Accurate experiments are conducted by employing the isochoric cooling procedure using differential scanning calorimetry (DSC). The capillary condensation conditions occur at distinct temperatures and pressures in accordance with the pore size, which agrees well with the independent domain theory. The thermogram peaks for multimodal pores with independent domains are observed to be a linear combination of the peaks measured for each individual pore size. This supports the superimposition principle, which is shown to be valid for both pure gases and gas mixtures. Additionally, for the first time, the three-line approach is employed to pinpoint the pore critical point (PCP) of the gas mixture. Although the pore critical pressure of confined fluids is consistently lower than the bulk critical pressure, this study demonstrates that the pore critical temperature of a confined mixture can be higher than the bulk critical temperature.

Flow in shale differs substantially from that in conventional reservoirs due to unfavorable reservoir features such as ultra-low permeability and very poor porosity. Shale also exhibits considerable anisotropy and heterogeneity, with clay laminae and bedding angle being the primary variables influencing anisotropy. As a result, shale is subjected to high stress sensitivity and deformation during depressurization, which affects fluid flow. Furthermore, non-Darcy flow mechanisms exist thereby making flow in shale a complex phenomenon. Nonetheless, many studies have recently focused on the geophysical and geomechanical characterization of shale. Various works have equally examined the complexity of fluid flow. Numerous studies were particularly interested in the influence of non-linear flow parameters and stress sensitivity on apparent permeability, intrinsic permeability, and porosity during pressure depletion. However, relatively few works, mostly theoretical, have been carried out on coupled flow and geomechanical reactions. This review thus includes a report on fluid flow and geomechanical characterization of shale formation, as well as an identification of the factors that influence rock deformation and fluid flow during production. The review showed that flow regimes are predominantly dependent on pore pressure and pore size, whereas flow regimes regulate apparent permeability. For example, at low pressures and pore radius less than 10 nm, flow regims were found to significantly increase the apparent permeability. However, at higher bulk modulus (>10 GPa), pore radius has essentially no impact, hence, pore pressure becomes the dominant factor influencing flow. In addition, the review shows that during depressurization, geophysical metrics are more sensitive to pressure changes than geomechanical properties. Finally, some results in literature revealed that the impact of geomechanical characteristics on cumulative production can be ignored in competent formations with high Young's modulus (about 6 × 106-10 × 106 psi). In conclusion, recovery from shale could be optimized by integrating experimental studies with hydromechanical models during initial reservoir studies.

Tracer tests are widely performed for the characterization of reservoir properties during the hydraulic fracturing operation. The dispersion of the tracer depends on the interaction of the proppant-packed hydraulic fracture and the tight porous medium through the naturally porous walls. However, the effects of the interaction of the porous walls and dynamics of flow in the proppant-packed hydraulic fracture on the tracer dispersion and reservoir dynamic mass/heat storage capacity have not yet been reported in the literature. In this work, the tracer dispersion in a proppant-packed hydraulic fracture surrounded by a tight porous medium is theoretically modeled and the dynamic storage capacity is evaluated. The Darcy-Brinkman equation is used to describe the fully developed laminar Stokes fluid flow in the proppant-packed hydraulic fracture. We used the Taylor dispersion theory and Reynolds decomposition approach to derive the exact equivalent transport parameters, including dispersion and advection coefficients, as well as the storage capacity of the tight porous medium. It is found that the tracer dispersion is controlled by the Darcy and the Peclet numbers in the proppant-packed hydraulic fracture. The results indicate that the ratio of tracer dispersion in the proppant-packed hydraulic fracture with porous walls to that with nonporous walls ranges from zero for very small Darcy numbers to 0.3 for large Darcy numbers. The ratio of the advection velocity in the proppant-packed hydraulic fracture with porous walls to that with nonporous walls ranges from unity for very small Darcy numbers to 7/5 for large Darcy numbers. The results also indicate that tracer mass storage capacity in the tight porous medium increases as the Peclet number for fluid flow in the proppant-packed hydraulic fracture increases. Conversely, storage decreases as the Darcy number in the proppant-packed hydraulic fracture rises. A comparison reveals that a flow transport model based on proppant-free hydraulic fracture may lead to the overestimation of the tracer mass/heat storage capacity. The findings of this study pave the way to advance our understanding of tracer tests for evaluating reservoir characteristics during fracturing operations in enhanced geothermal systems.

Crossflow filtration is a separation technique where fluid flows tangentially across a membrane or porous media, reducing clogging by sweeping away retained particles and allowing continuous filtration. Dispersion of solute matter in crossflow filtration plays an essential role in the separation performance of many industrial processes. The current work aims to generalize the Taylor dispersion theory and study the solute transport in a slit–porous medium system with a crossflow. The solute is depleted by the porous medium at the slit top porous wall or the interface between the slit and the porous medium, where the continuity of the solute concentration and mass flux is applied. The solute is simultaneously transported axially by the main flow along the slit and vertically by the crossflow perpendicular to the slit. Using the Reynolds decomposition and cross-sectional averaging techniques, the generalized reduced-order model for the advection-dispersion solute transport in the slit–porous medium system with the presence of a crossflow is established, where the effective velocity of the main flow and the effective dispersion coefficient are obtained. The analysis of the results reveals that the nondimensional Taylor dispersion coefficient scales with the Peclet numbers for the crossflow and the main flow, respectively, as DT∼Pev−5/3 (when Pev≥20) and DT∼Peu2. The proposed theoretical model, along with the findings of this study, paves the way for the fundamental study of dispersion in more complex systems.

Summary As a clean energy carrier, hydrogen (H2) is considered an indispensable part of the energy transition roadmap. To meet increasing energy demand, extremely large storage capacities are required. Previous studies have focused on underground H2 storage in conventional depleted gas reservoirs, salt caverns, and saline aquifers. The increasing number of depleted shale gas reservoirs may be good candidates for H2 storage. In this work, we analyze the potential of H2 storage in depleted gas reservoirs using Monte Carlo (MC) simulations. The competitive adsorption of a methane-hydrogen (C1-H2) system under nanoscale conditions is investigated, including the effects of pore size, temperature, pressure, boundary material, and fluid composition. Our results show that C1 is preferentially adsorbed in a C1-H2 system. C1 forms the adsorption layer near the boundary surface, while H2 molecules are freely distributed in the pore. The fluid distribution indicates that H2 can be easily produced during H2 recovery processes, which contributes to H2 storage in depleted shale gas reservoirs. In addition, the effect of water on C1-H2 competitive adsorption is analyzed. The strong interactions between water and boundary atoms force C1 molecules away from the adsorbed region. This work provides a foundation for hydrogen storage in depleted shale gas reservoirs at a molecular level.

The purpose of this study is to address the two-dimensional counter-current capillary dominant imbibition of a wetting phase into a water-wet porous cylindrical matrix block partially submerged in the wetting phase. A two-dimensional unsteady-state diffusion equation is used to model the process. The governing equation is solved using a combination of the Laplace and the finite Fourier sine transforms to find and analyze the solutions for the normalized water saturation and the volume of the imbibed wetting phase. The results reveal that the volume of the imbibed wetting phase and the capillary diffusion shape factor for a partially submerged matrix block are significantly lower compared to those of a fully submerged matrix block, highlighting the overestimation of imbibed volume using available models based on full immersion in the wetting phase. It has been observed that the volume of the imbibed wetting phase increases over time until reaching a state of equilibrium. In the case of a partially submerged matrix block, the shape factor is inversely proportional to the square root of time (σ ∼ 1/t) during the early time and decreases sharply as the imbibed wetting phase reaches an equilibrium. In the case of a fully submerged matrix block, the shape factor is inversely proportional to the square root of time (σ ∼ 1/t) during the early time and later reaches a pseudo-steady-state value. The proposed model, along with the findings obtained, advances our understanding of capillary imbibition in porous media.

An accurate measurement of the isothermal heat of capillary condensation in nanopores by the tandem use of differential scanning calorimetry (DSC) and adsorption/desorption experiments, for the first time, has been developed. To demonstrate the method, propane confined in SBA-15 mesoporous silica is used as the system. This is also the first time that the conditions of capillary condensation measured by those two different experimental methods using identical mesoporous adsorbent-adsorbate systems are compared and found to agree with each other, the fact of which allows us to accurately determine the isothermal heat of capillary condensation. The isothermal heat of capillary condensation of this system is found to be lower than the heat of bulk condensation and to decrease with temperature following the trend of that of bulk, just the opposite behavior of the isosteric enthalpy of capillary condensation, the magnitude of which is constant and higher than the heat of bulk condensation.

Viscosity modification of injected fluids is a vital mechanism for successful oil recovery from an oil reservoir. Various studies have demonstrated that nanoparticles (NPs) possess the tendency to alter the wettability of reservoir rocks, reduce the interfacial tension between injected fluids and crude oil, and modify the viscosity of injected fluids. Zirconia (ZrO2) and gamma-alumina (gamma-Al2O3) NPs have demonstrated huge prospects for enhanced oil recovery (EOR) in various studies. Recently, experimental investigations have attributed the viscosity behavior of silica nanofluids to the interaction between the ions of the silica NPs and electrolytes at the electrical double layer. Therefore, this study investigates the viscosity behavior of ZrO2 and gamma-Al2O3 NPs with their increasing concentrations in different aqueous solutions present in reservoir brine by employing techniques such as dynamic light scattering and transmission electron microscopy in addition to viscosity and pH measurements at ambient conditions of approximately 25celcius and 1 atm. The viscosity behavior of spherical particles in suspensions is well suited for the viscosity profile of the nanofluids with increasing concentrations of ZrO2 and gamma-Al2O3 NPs. The viscosity of the ZrO2 and gamma-Al2O3 nanofluids containing the chloride salts increases in the order of Ca2+ > Na+ > K+ while those containing the sulfate salts increase in the order Mg2+ > Na+ > K+. Comparatively, the model proposed by Williams et al. predicts the viscosities of the electrolyte-based zirconia and gamma-Al2O3 nanofluids with percentage absolute average deviation (%AAD) of 2.07 and 2.52 %, respectively, whereas those by Einstein's model records %AAD of 3.15 and 3.68 %, respectively. The findings from this study provide experimental data and illuminate the understanding of the viscosity behavior of the nanofluids containing electrolytic ions and set the stage for further investigations, which are relevant for EOR purposes.

Depleted oil and gas reservoirs have been recognized as prevailing alternatives to store hydrogen (H-2). However, only a few attempts have been perused to evaluate hydrogen storage in these formations. Our study is among the first to experimentally investigate hydrogen storage in oil-wet Berea sandstones under elevated temperature and pressure conditions. This study involves experimental investigations of hydrogen-brine steady-state drainage and imbibition relative permeability in the presence and absence of methane (CH4) as a cushion gas. Core flood experiments are also conducted to assess the effect of CH4 addition to H-2 on the formation pressurization effectiveness and the displacement of original fluids. Furthermore, we analyze the influence of hydrogen exposure on rock petrophysical properties such as porosity and permeability under subsurface conditions. Our findings show that adding 50% CH4 to H-2 improves gas relative permeability by 70.5%. The results also indicate that hydrogen storage and recovery are significantly enhanced with CH4. The gas saturation increases from 0.277 to 0.611 at the end of gas flooding with a 50%-50% H2-CH4 gas mixture. The addition of CH4 as a cushion gas considerably accelerates core pressurization during hydrogen injection, resulting in a reduction of 30.3% in the gas volume required to achieve 1000 psi pressurization. This study demonstrates minor alterations in the porosity and permeability of rock samples as a result of pure H-2 and 50%-50% H-2-CH4 exposure. The generated experimental data are crucial for predicting flow, optimizing storage and recovery, ensuring safety, supporting modeling, designing injection/extraction strategies, and understanding recovery techniques.

Tracer transport in hydraulic fractures is substantially affected by the rock matrix surrounding them. Nevertheless, there is not yet an expression in literature to address the relationship among the transport coefficients, porous walls, hydraulic fracture geometries, and non-Newtonian fluid properties. Therefore, the tracer dispersion due to non-Newtonian fluid flows in hydraulic fractures with different geometries and porous walls is mathematically derived and studied in the current work. Rectangular, triangular, and elliptical models and power-law model are considered here to describe the hydraulic fracture geometry and the non-Newtonian fluid rheology, respectively. The results reveal that as the flow behavior index grows, the coefficient of the shear dispersion term in the case of the shear thinning and Newtonian fluids follows an order of triangular > elliptical > rectangular and in the case of the shear thickening while the same order is followed at the beginning, it turns first to triangular > rectangular > elliptical, then to rectangular > triangular > elliptical, and finally to rectangular > elliptical > triangular. The coefficient of the shear dispersion term increases sharply for each geometrical model with the flow behavior index when the fluid is shear thinning while it first increases slightly and then flattens when the fluid is shear thickening. However, the coefficient of the shear dispersion term for porous walls is lower than the one for nonporous walls. It is also found that the average tracer dispersion coefficients in rectangular, triangular, and elliptical nonporous-walled and porous-walled hydraulic fractures and their ratio dictate that the hydraulic fracture-rock matrix communication through the continuity of the tracer concentration and the mass flux needs to be considered for determination of the tracer dispersion during the transition for intermediate Peclet numbers and the advection-dominated tracer transport for large Peclet numbers. This study along with its findings can pave the way for future investigations on the tracer dispersion in a network of hydraulic fractures with rough and porous walls.

The technique of sequentially injecting low salinitywater (LSW),nanoparticles (NPs), and surfactant (abbreviated collectively as LNS)into fractured carbonate reservoirs (FCRs) has been successfully appliedin our previous work. In this study, the technique is further investigatedexperimentally to include other types of surfactants and NPs. Theselection criteria used for assessing the two surfactants (TritonX-100 and C(19)TAB), which involve spontaneous imbibition(SI) experiments, interfacial tension (IFT), and contact angle (CA)measurements, are presented in the current work. The SI measurementsare used to probe the potential of the individual LNS fluids to producebeyond the synthetic brine, while the IFT and CA results indicatethe mechanisms involved during the interaction between the fluids.The cumulative oil recovered from the LNS injection cycles into thefractured core plug at 70 & DEG;C temperature, 3000 psi confiningpressure, and 2100 psi back pressure is herein reported. The outcomeof these experiments divulged that the injection of the cationic surfactantsin the first LNS cycle aided the recovery of oil in the second cycleduring the injection of the & gamma;-alumina NPs. The introductionof the surfactant and NPs after the LSW injection in the first cycleassisted in recovering more oil from LSW injection in the second andthird sequences. Overall, the cumulative oil recovery from the threecycles of the LNS sequential injection is approx. 18% of the originaloil in place (OOIP) in addition to oil recovery from waterflooding,which shows the promising potential of this technique in oil productionfrom FCRs.

In this study, adsorption capacity of Berea sandstones varying wettability states with respect to hydrogen (H2) and hydrogen-methane (H2-CH4) mixture are examined to assess the viability of depleted oil and gas reservoirs for large scale hydrogen storage. We investigate pure hydrogen and hydrogen-methane mixture adsorptions as a function of pressure, temperature, and rock surface wettability. The obtained results indicate that as the CH4 fraction increases from 0 to 20 %, the gas uptake exhibits a more significant rise, going from 0.98 to 1.68 cm3/g for oil-wet sandstone and from 1.04 to 1.2 cm3/g for untreated samples, both at 25 degrees C. This suggests a pronounced affinity of CH4 for the aged rock. The adsorption capacity of the H2-CH4 mixture increases from 1.2 to 1.68 cm3/g at 80 bar and 25 degrees C when rock samples are exposed to crude oil compared with the untreated rock samples. Investigating the impact of temperature on adsorption capacity reveals a decrease in gas uptake as the measurement temperature rises from 25 to 60 degrees C across all pressure levels. All rock samples exhibit a positive hysteresis in adsorption and desorption isotherms at various temperatures. The Freundlich, Redlich-Peterson, and Sips models are found to be more representative in describing the adsorption characteristics, suggesting multilayer adsorption on the rock surface. Our findings provide insights into the impact of natural gas adsorption and desorption on overall hydrogen production. This study can improve the accuracy and efficacy of reservoir simulations and flow models that depict the movement of hydrogen and natural gas through porous media within sandstone reservoirs.

Capillary phase transitions (evaporation, melting, and sublimation) and the pore triple point of CO2 confined in MCM-41 mesoporous media with a pore diameter of 3.5 nm have been studied by using an isochoric heating procedure in a high-pressure low-temperature differential scanning calorimeter over a pressure range of 0.5-40.5 bar. The procedure is validated by the agreement between the measured conditions of bulk evaporation/sublimation and literature data. The main finding in this work is that the solid-to-fluid phase transitions of CO2 in MCM-41 shift to temperatures higher than those of the corresponding bulk phase transitions. It is also found that the formation of a solid phase of CO2 in MCM-41 does not require the presence of a liquid or solid in the bulk. The capillary-melting and capillary-evaporation curves approach each other as temperature decreases until they meet at the pore triple point. The effect of pressure on capillary melting temperature is significant at pressures close to the pore triple point. Furthermore, the capillary-melting curve approaches the bulk saturated vapor-pressure curve as temperature increases, thus hinting an agreement with the prediction by molecular dynamics simulation in the literature that the curves eventually intersect each other at a high temperature and pressure. Based on the measured capillary phase transitions, the pore triple-point temperature and pressure of nanoconfined CO2 are bracketed and found to be much lower than those of the bulk triple point.

We studied thermal dispersion in a fracture walled by a porous and permeable rock matrix, where the fluid flow and heat transport are coupled across the interface between these media. The reduced order model of the advective‐dispersive heat transport in the fracture‐matrix system is resulted from the Reynolds decomposition. The model allows the calculations of the upscaled dispersion and advection terms. A simple scaling relation is developed to estimate heat extraction from geothermal fracture‐matrix systems. It was shown that the extracted heat is inversely proportional to the height of the matrix squared. Our finding also revealed that the dimensionless extracted heat is weakly dependent on fracture Peclet number and matrix Darcy number and is threefold the matrix dimensionless thermal diffusion time. In the analysis presented, we assumed a homogenous system. The heterogeneity caused by a variation in fracture and rock matrix properties (such as porosity, permeability, thickness, and aperture) adds more complexity. Including these complexities in the determination of the thermal dispersion with the coupled fracture‐matrix approach needs further investigation. However, the developed model, along with the findings of this study, provides valuable insight into the physics of thermal energy extraction from fractured geothermal reservoirs and can be used for testing the underlying hypotheses in real‐field applications.

A number of microfluidic systems of interest essentially consist of micro-scaled channels/tubes, whose walls are inherently rough. The novelty of the current study lies in exploring the impact of the wall roughness on mass transfer in the case of flow through a microtube with porous wall. The current investigation is possibly the first attempt at exploring the effect of mass transfer for a porous-walled, rough microtube, as earlier studies were limited to the analysis of hydrodynamic and thermal effects only in an impervious microtube. In particular, the effects of the corrugation amplitude and the wavenumber on the mass transport have been assessed in detail in this work, via a combination of perturbation approximations and numerical analysis. Several interesting revelations are elicited regarding the effects of these pertinent parameters on the mass transfer coefficient, permeation flux, wall surface concentration, and delivery flux of the neutral solute. It has been unveiled that it is possible to enhance the solute mass flux by 10% via appropriate tuning of corrugation amplitude. The findings of the study can help in better understanding of mass transport for a porous-walled, rough microtube, which has critical relevance in several important applications such as micromixers, targeted drug delivery, and so on.

We extend the Taylor-Aris dispersion theory to upscale the gas absorption into a viscous incompressible liquid flowing along an inclined surface. A reduced-order model of advection-dispersion-reaction is developed with the aid of Reynolds decomposition and cross-sectional averaging techniques. The upscaled model allowed evaluation of the dispersion, advection, and absorption kinetics as a function of the Peclet number (Pe) and the Damköhler number (Da). The transport and kinetics parameters for the limiting cases of nonabsorption and absorption dominant are also evaluated. The upscaled model is solved analytically, and the obtained solution is used to evaluate the upscaled mass transfer between the gas and liquid. The results for the overall Sherwood number identify three regions: (i) advection dominant, (ii) transition where both advection and absorption play a role, and (iii) absorption dominant. The scaling relation between the Sherwood number (Sh) and the Da for the last region was determined to follow Sh∼Da^{1/2}. It is also revealed that in the first two regions, the Sherwood number versus the Peclet number exhibits a bell-shaped (or Gaussian) behavior, suggesting an optimal Pe that maximizes mass transfer between gas and liquid in these regions. The model and insights presented have the potential to be applied in a wide range of industrial separation processes involving the interaction of a gas exposed to a liquid flowing downward on an inclined surface under gravity.

We report novel transport phenomena arising from an interface between two immiscible liquids in a laminar flow. In the context of the Taylor–Aris dispersion theory, we provide a quantitative description and demonstrate that the planar interface between two liquids in a laminar flow can lead to uphill advection and dispersion, dispersion barrier, as well as osmotic dispersion. The developed understanding of the newly identified transport phenomena paves the way for further research in this area and enables the insightful elucidation of mixing and separation processes in multiphase systems.