Flow Solution Research Articles

Weak solutions of anisotropic (and crystalline) inverse mean curvature flow as limits of p-capacitary potentials

We construct weak solutions of the anisotropic inverse mean curvature flow (A-IMCF) under very mild assumptions both on the anisotropy (which is simply a norm in RN with no ellipticity nor smoothness requirements, in order to include the crystalline case) and on the initial data. By means of an approximation procedure introduced by Moser, our solutions are limits of anisotropic p-harmonic functions or p-capacitary functions (after a change of variable), and we get uniqueness both for the approximating solutions (i.e., uniqueness of p-capacitary functions) and the limiting ones. Our notion of weak solution still recovers variational and geometric definitions similar to those introduced by Huisken-Ilmanen, but requires to work within the broader setting of BV-functions. Despite of this, we still reach classical results like the continuity and exponential growth of perimeter, as well as outward minimizing properties of the sublevel sets. Moreover, by assuming the extra regularity given by an interior rolling ball condition (where a sliding Wulff shape plays the role of a ball), the solutions are shown to be continuous and satisfy Harnack inequalities. Finally, examples of explicit solutions are built.

Approximate Analytic Solution of a Potential Flow Around an Obstacle

Approximate Analytic Solution of a Potential Flow Around an Obstacle

A model of cement grout flow in a fracture network system

Understanding the mechanism of cement grout flow in fractured rocks is essential for controlling seepage in the construction of hydraulic projects. However, simulating grouting in fractured rocks is complex due to random fracture distribution and non-Newtonian grout flow. This study proposes a numerical model for simulating cement grout flow, considering the hydro-mechanical coupled process in a three-dimensional fracture network system based on the unified pipe-network method. A pipe-network equivalence method is used to derive equivalent pipes for the process of grouting displacement, and the flow field can be solved in unified pipe networks. The hydro-mechanical coupled process is achieved by incorporating an analytical solution for the stress distribution of the center borehole model on an infinitely large plane and a constitutive model for the estimation of the fracture aperture. The time-varying property of the cement grout flow is also considered in the simulation of grouting. The reliability of the numerical model is verified by comparing with analytical solutions for grout flow in a water-saturated fracture. Grouting experiments in fracture networks are also performed to demonstrate the applicability of the proposed method. The influence of various factors on the propagation of cement grout is further investigated in three-dimensional fracture network models.

Existence and multiplicity of solutions for a new p(x)-Kirchhoff equation

Abstract This article is devoted to study a class of new p ( x ) p\left(x) -Kirchhoff equation. By means of perturbation technique, variational method, and the method invariant sets for the descending flow, the existence and multiplicity of solutions to this problem are obtained.

Parametric analysis of reverse electrodialysis process for improved power generation: Influence of spacer thickness, feed solution flow rate, membrane, and concentration

Reverse electrodialysis (RED) technology produces electrical energy from a salinity gradient by transporting ions through ion-exchange membranes (IEM). Although research into this technology has recently seen considerable growth, there is still interest in improving its efficiency. As a result, a mathematical model to study the RED process was developed using Aspen Custom Modeler software, focusing on three membranes (Fumasep (FAD/FKD), Fujifilm Type 10, and Selemion (AMV/CMV)). A parametric analysis was conducted, considering spacer thickness, salinity gradient, and feed-solution flow rates. Evaluation of internal resistance, gross power density, and net power density was also performed. Results showed that using a thicker spacer (270 μm) in the high compartment and a thinner spacer (150 μm) with a high Reynolds number in the low compartment led to higher net power densities of 2.17 W·mcp−2 and 6.74 W·mcp−2 for Fumasep (FAD/FKD) membrane with (brackish/seawater) and (brackish/brine), respectively. Among the membranes tested, Fumasep (FAD/FKD) and Fujifilm Type 10 had similar results, with the former slightly exceeding the latter. However, the Selemion membrane (AMV/CMV) performed poorly in all tests.

Triple solutions for unsteady stagnation flow of tri-hybrid nanofluid with heat generation/absorption in a porous medium

The present theoretical study focuses on enhancing the performance and efficiency of casting and extrusion processes. Thus, this work examines the flow characteristics and heat transfer of unsteady tri-hybrid nanofluid flow in porous media while also considering the heat source/sink effect. The governing boundary layer equations are solved via a built-in collocation method available in MATLAB software. Three distinct numerical solutions which convey the fluid flow characteristics have been identified. Notably, nanofluid composition influences boundary layer separation, with tri-hybrid nanofluid showing enhanced heat transfer when the stretching/shrinking parameter exceeds −10.53. When the sheet shrunk at −10.8, ternary and hybrid nanofluids improved thermal efficiency by 15.22 % and 20.38 %, respectively, compared to mono nanofluids.

Electrospinning of polyetherketoneketone fibers: The effect of fabrication regime on the morphology, physico-chemical and biological characteristics

Electrospinning is a unique technology based on the fabrication of polymer fibers from the solution under an applied electric field. Electrospun membranes are applied in various fields, starting from filter technologies to tissue engineering. Polyalyletherketones (PAEK) is a family of synthetic bioinert polymers characterized by outstanding mechanical performance, high chemical stability, and biocompatibility. In the present study, the effect of electrospinning parameters (collector-to-tip distance, applied voltage, spinning solution flow rate and polymer concentration in the spinning solution) on the morphology of the fabricated polyetherketoneketone (PEKK) membranes as well as their crystal structure, chemical stability and biocompatibility was investigated. Based on 108 combinations of the electrospinning parameters, it was found that minimum concentration of PEKK in the spinning solution in 1,1,1,3,3,3-hexafluoropropan-2-ol (HFP) required for the fibers’ formation is 4 wt %, while the applied voltage providing fibers without defects was found at 20 kV. It was demonstrated that the tested electrospinning regimes allow to fabricate the membranes with average fiber diameter from 0.76 ± 0.29 to 1.46 ± 0.60 μm and porosity from 87 ± 1 to 92 ± 1 %. It was found that electrospinning process has no effect on the chemical structure of PEKK macromolecules. Electrospinning parameters had no effect on crystal structure of PEKK in the fabricated membranes, which was found to be amorphous. The fabricated membranes demonstrated high Young modulus (above 150 MPa) and elongation over 170 %, were stable in strong alkali and acid solutions and biocompatible towards mouse embryonic fibroblasts.

Chromium removal from concentrated ammonium-nitrate solution: Electrocoagulation with iron in a plug-flow reactor

Highly concentrated ammonium nitrate (AN) solutions are characteristic of explosives manufacturing wastewaters and liquid fertilizer commodities, but chromium (Cr) contamination from corroding metal infrastructure or source impurities can pose problems. Technologies are needed to decontaminate AN from Cr without chemical alterations if AN is to be recovered as a resource. Iron-based electrocoagulation is a proven way to produce Fe(II) for reducing dissolved Cr(VI) to the less soluble and less toxic form of Cr(III), but is an untested technology for AN brines. This work examined Cr removal from synthetic wastewater with high concentrations of AN (400 g/L) by electrocoagulation in a flow-through reactor, where the effects of time, solution flow rate, applied current, and coexisting ions were analyzed. This method not only reduces Cr(VI) to Cr(III) using the produced Fe(II), but also promotes complete Cr removal from solution with the formation of insoluble Fe-Cr precipitates. A slower flow rate and higher applied current increased the removal efficiency of the reactor; furthermore, the reactor took up to one hour to reach steady state conditions, depending on the flow rate. Cr concentrations along the anode length were modeled using a simplified advection–dispersion-reaction model, providing reaction rate coefficients for various flow rates and currents. Overall, the results of this work showed that electrocoagulation with iron can be used for treatment of AN solution contaminated with Cr(VI). This work also provides design guidelines with a corresponding model for field applications in future work.

A Semi-Analytical Solution of Two-Dimensional Unsteady Groundwater Flow Outside a Long-Strip Excavation Pit with a Cut-Off Wall

In deep excavation engineering, the implementation of cut-off walls stands as a crucial measure to ensure structural support stability. However, the existing theories for dewatering design often overlook the variations in cut-off wall penetration depths, potentially compromising the efficacy of groundwater control strategies. Addressing this gap, this study conducts a comprehensive investigation into the dynamics of groundwater levels within confined aquifers during the dewatering process of strip excavation pits with cut-off walls. Central to this inquiry is the conceptualization of the entire excavation pit as a singular large-diameter well, with the open part beneath the cut-off wall in the confined aquifer serving as a constant-flux boundary. Employing an advanced analytical modeling approach, the study formulates a robust framework to describe the intricate interplay of unsteady groundwater flow phenomena. Leveraging the techniques of the Laplace and finite cosine transform methods, a semi-analytical solution is derived to elucidate groundwater drawdown patterns over time. The validation of the proposed solution against finite element method results underscores its fidelity and applicability. The parametric analysis reveals a dynamic evolution in drawdown characteristics within the confined aquifer, transitioning from initially cone-shaped distributions to more linear profiles that eventually stabilize with prolonged dewatering. This evolution is governed by the aquifer’s inherent anisotropy and the barrier effect exerted by the depth of cut-off wall penetration. The parametric research also underscores the critical role of lateral boundary distance in influencing groundwater drawdown patterns. The presented solutions can be used to identify optimal penetration depth ratios tailored to specific parameters, thereby offering insights for optimizing dewatering strategies for deep excavation groundwater control. Moreover, a case study was included in this study using the proposed analytical solution, and a comparison was made with field data to validate the practical applicability of the approach.

Characterization of Wormhole Growth and Propagation Dynamics during CHOPS Processes by Integrating Rate Transient Analysis and a Pressure-Gradient-Based Sand Failure Criterion in the Presence of Foamy Oil Behavior

Summary Characterization of wormhole growth and propagation dynamics has been made possible with the semi-analytical models developed in this work by integrating both rate transient analysis (RTA) and a pressure-gradient-based (PGB) sand failure criterion in the presence of foamy oil behavior. The nonlinearity caused by the foamy oil properties is linearized using pseudofunctions, while the source function and finite difference methods are applied to obtain the solutions for the linearized models in the matrix and wormhole subsystems, respectively. A sequential method is adopted to solve the coupling fluid-solid problem, where new wormhole segments can be generated once the PGB sand failure criterion has been achieved, while their updated petrophysical properties can be sent back to obtain the solutions for the fluid flow in the next time interval. Furthermore, the influence of sand failure/fluidizing and foamy oil properties on the dynamic wormhole network can be investigated with the generated type curves. Both wormhole growth and foamy oil flow dictate an upward fluid production at the early times, while the production-induced pressure depletion dominates the declining production at the late times. The fractal wormhole networks can be dynamically characterized by history matching the field fluid and sand production profiles. Both the sand failure degree and foamy oil properties dictate the effective wormhole coverage and intensity. Sand production is found to be influenced by both the breakdown pressure gradient and wormhole conductivities, while oil production rate can be dominated by the wormhole coverage and intensity. Foamy oil flow can increase the oil production rate and increase the wormhole coverage compared with the conventional oil. The newly developed method in this work has been validated and then applied at field scale to dynamically characterize the wormhole growth and propagation by considering both the sand failure phenomenon and foamy oil properties within a unified, consistent, and accurate framework. Compared to the conventional numerical simulations, the novelty of such a semi-analytical method can not only allow us to characterize the growth and propagation dynamics of the fractal-like wormholes without the need for grid refinement near the wormhole grids but also take the complex sand failure and foamy oil behavior into account. In addition, it can minimize the impact of grid orientation effects in numerical simulations, enabling the growth and propagation of the wormholes in arbitrary directions rather than orthogonal directions conditioned to the largest pressure gradient.

The Infusion of Piperacillin/Tazobactam with an Elastomeric Device: A Combined 24-H Stability Study and Drug Solution Flow Rate Analysis.

Bacterial respiratory tract infections (e.g., in patients with cystic fibrosis) may be treated with the intravenous infusion of a piperacillin/tazobactam (P/T) solution through an elastomeric device. In the present work, we combined a 24-h drug stability study with an assessment of the drug solution flow rate during an in vitro simulated infusion. Experiments were performed in triplicate with two excipient-free generic P/T solutions and an excipient-containing proprietary P/T solution in saline (all 50/6.25 mg/mL) released from an elastomeric infusion device at 32 °C. The P/T solutions' stability was assessed by an HPLC-UV assay, pH and osmolality measurements, a visual assessment, and particle counting. Before these analyses, a forced degradation study was performed. To assess the flow rate, a precision scale was used to weigh the solution collected at the infusion line outlet. The stability criteria were <10% degradation and a flow rate within ± 15% of the nominal value over the 24-h infusion period: all three P/T solutions were found to be stable. The actual flow rate was lower than the expected flow rate; this difference was probably due to the drug solution's high viscosity and must be taken into account in clinical use.

EVA NEXUS-Phaco performance study.

To investigate a novel phacoemulsification system "EVA NEXUS" (D.O.R.C., Dutch Opthalmic Research Center) in comparison to the existing system "EVA" in clinical use. And to compare both phacoemulsification systems in terms of efficiency, safety and postoperative inflammatory activity. In this study standardized cataract surgery was performed on both eyes of the study participant, using the "EVA system" (control group, n=20) on one eye and the "EVA NEXUS system" (intervention group, n=20) on the other eye. Only patients with cataract LOCS Grading 1-3 and no accompanying eye diseases were included in this study. A total of 20 patients were included in this study, with each treatment arm including 20 eyes. During surgery a 0.1 mL aqueous humor sample was collected 1min after phacoemulsification to measure the total prostaglanin E2 concentrations using an enzyme-linked immunosorbent assay. The endothelial cell count, visual and refractive outcomes, and anterior chamber flare were evaluated preoperatively, and 1d, 1wk, and 3mo postoperatively. There were no statistically significant differences between both groups regarding intraoperative safety parameters including effective phacoemulsification time (P=0.904), balanced saline solution flow (P=0.701) and total surgery time (P=0.565). Postoperative prostaglandin E2 levels, anterior chamber flare as well as endothelial cell loss tended to be lower in the NEXUS-Group, however not being statistically significant (P=0.718; 0.164; 0.486). Both systems provided similar clinical outcomes, regarding best corrected visual acuity and refractive parameters, showing no statistically significant differences between both groups. Both systems show a high level of safety and efficency with similar results in terms of safety parameters including postoperative inflammatory activity and endothelial cell loss as well as visual and refractive outcomes. Although statistically not significant, the EVA NEXUS system tends to cause less postoperative inflammation with lower prostaglandin E2 levels and lower anterior chamber flare values.

Synthesis of a Hybrid Membrane of Polysulfone with Zinc Oxide for Cleaning Textile Effluents.

This study aimed to investigate the influence of the ZnO concentration on the structure of a membrane for effluent filtration, varying this concentration from 0% to 3%. To analyze the results, X-ray diffraction tests, Fourier-transform infrared spectroscopy, apparent porosity, atomic force microscopy, and scanning electron microscopy were used, all of which were employed for the characterization of the produced membranes. The solution simulating the effluent was analyzed before and after the filtration process to assess the filtration results. The conducted tests reported results for filtered solution flow, turbidity, pH, dissolved oxygen, and electrical conductivity. All these results indicated that the membrane with the best performance in terms of cleanliness and the amount of filtered effluent was the one produced with a 13% hybrid polysulfone loaded with 1% ZnO in its structure.

Offline constrained reinforcement learning for batch-to-batch optimization of cobalt oxalate synthesis process

The cobalt oxalate synthesis, a batch process, plays a crucial role in the refinement of cobalt metal. The mean particle size of cobalt oxalate is a critical indicator that reflects product quality. However, excessive ammonium oxalate solution flow can heighten waste disposal costs in the production process. To address these issues, we propose a novel offline reinforcement learning (RL) algorithm that guarantees compliance with constraints in the cobalt oxalate synthesis process, utilizing exclusively static datasets. This method employs cost critic networks to assess costs, transforming the constrained optimization problem into an unconstrained one by introducing Lagrangian multipliers. We use exponential moving average (EMA) to optimize the update of proportional integral derivative (PID) control multipliers, reduce overshoot and oscillation in the control process, and thus improve the overall stability of the system. Furthermore, to optimize algorithm performance, a deep residual network (DResNet) is integrated into the policy network. Experimental results indicate that the algorithm’s optimization policy performs significantly better under constraints.

Transport Properties of Aqueous Methane Solutions and Blocking Behavior of Intelligent-Responsive Temporary Plugging Agent in a Switchable Nano-channel: A Dissipative Particle Dynamics Simulation Study.

Intelligent-responsive temporary plugging agents (TPAs) have great potential in the field of oil and gas resource extraction due to their self-adaptability to the environment. However, the transport mechanism of oil and gas molecules, such as aqueous methane solution in intelligent-responsive TPA-modified nano-channels and the blocking behavior of TPA, have not been verified yet. In this work, dissipative particle dynamics simulations (DPD) are conducted to investigate the velocity distribution and the force characteristics of aqueous methane solutions under different driving velocities, as well as the blocking effect of TPA to the flow of solution. Simulation results indicate that aqueous methane solution primarily concentrates in theuncovered area of the TPA and diffuses into the TPA-covered area when the nano-channel is closed. The velocity distribution of the flowing solution in the open nano-channel follows a subparabolic pattern. Methane molecules in the closed nano-channel show sharp oscillations in velocity and force profiles, which can be mitigated by increasing the methane concentration. The designed TPA effectively blocks fluid flow but its head and tail are vulnerable to the shear forces from the fluid. This study enhances the understanding of the nanoflows in the wellbores during the extraction of oil and natural gas resources.

An in-depth examination of artificial intelligence-based methods for optimal power flow solutions

An in-depth examination of artificial intelligence-based methods for optimal power flow solutions

All Organic Quinone Solid State Batteries for Environmentally Friendly and Chemical Robust Alternatives Beyond Lithium-Ion Batteries

Introduction: Organic solid-state quinone batteries have unparalleled properties that can meet the most urgent challenges the industry faces. It can create an energy system that is environmentally friendly and electrochemically robust, while being cost efficient enough for industry to adopt and invest in. The inspiration for fully organic solid-state batteries came from extended studies on our all-organic aqueous redox flow batteries, where much of the science of organic redox coupling molecules were understood. Like redox flow batteries, organic solid state quinone batteries utilizes the breaking and reforming of bonds to generate electrical energy. However, it doesn’t require the constant flow of charge carrier solution like the flow batteries. Consequently, this avoids the cost of an extra pumping system and significantly reduce the size of the batteries compared to flow battery systems. Furthermore, the downsized battery system allows for the cell to be implemented into applications such as EV and portable devices. The redox species are directly deposited onto the electrodes. This deposition of active material on carbon paper enables higher surface area for charge transfer, which increases the capacity for fast charge and discharge compared to flow batteries. Additionally, the active materials are of organic quinone nature providing great robustness that other battery systems like lithium-ion batteries don’t allow. The redox chemistry of these quinones still happens in aqueous system, which allows us to use very small amount of aqueous electrolyte instead of the combustible organic solvent used in lithium batteries. Results and discussion: The appropriate quinone species for this solid-state battery must be electrochemically stable and dissolution free in the aqueous system. Various quinones with different substituents were tested. One of the promising redox couples discovered is 2-methylanthraquinone (MAQ) and duroquinone (DQ). The couple displayed a cell voltage of 400 mV (0.4 V) as shown in Figure 1. This value was found to correspond to the redox potential difference between DQ and MAQ. New methods of deposition of active materials onto the electrodes were developed. High conductivity was achieved by introducing CNT with appropriate binder, which resulted in improvements to the cell’s charge and discharge performance (Figure 2). Figure 1. Cyclic voltammetry study of 10 mM 2-Methylanthraquinone (MAQ) and 10 mM Duroquinone (DQ) in 1 M sulfuric acid with 20% ethanol, MSE reference electrode, glassy carbon, 50 mV/s. (Refer to image file) Figure 2: Charge and discharge of solid-state batteries of 2-Methylanthraquinone (MAQ) and Duroquinone (DQ) at 10 mA. (Refer to image file)For the positive side, 0.164 g of duroquinone was deposited on 25 cm2 carbon paper with 0.05 g of CNT. Correspondingly, 0.222 g of 2-Methylantroquinone was deposited for the negative side. The cell was assembled with Nafion 117 as separator and small amount of 1 M sulfuric acid as the supporting electrolyte. The initial charge and discharge curve of this cell showed 97% columbic efficiency. Long-term cycling to test the stability was performed and other redox couples also showed higher cell voltage with high efficiency.The next step for this study is to explore different redox couples that might have better compatibility and higher cell voltage compared to the current redox couple. This will be done through studying the large library of organic compounds including quinones and other redox active organic compounds. Figure 1

Modeling and Experimental Validation on a Bipolar Membrane Electrodialysis Stack for Lithium Sulfate Separation

Recycling lithium-ion battery materials is a crucial step to achieving a circular economy. Among a few methods for recycling spent battery materials, a novel hydrometallurgical recycling process with leaching by acids and precipitation by bases was proposed [1]. Lithium sulfate (Li2SO4) leachate solution is generated at the end of the closed-loop recycling process. Such Li2SO4 solution can be separated by electrodialysis (ED) to form H2SO4 and LiOH solutions, which are reused for leaching and precipitation of the recycling process. The present study attempts to model this ED process and validate the model with experimental data.An ED stack based on bipolar membranes (EDBM); see Fig. 1a, was built with repetitive unit cells, each consisting of a bipolar membrane, anion exchange membrane (AEM), and cation exchange membrane (CEM). Li2SO4 enters the dilute channel and splits into SO4 2- and Li+, which travel through the AEM and CEM, respectively. Water electrolysis occurs within the bipolar membrane to produce H+ and OH-, which react with SO4 2- and Li+ to form H2SO4 and LiOH, respectively; see Fig. 1b. A two-dimensional (2D) multiphysics model is developed to elucidate the coupled transport processes within the unit cell. Conservation equations for mass, momentum, and species are solved. The transport of ions is described by the Nernst-Planck equation. Electroneutrality equations are satisfied in these membranes and channels. Electro-osmotic water transport across the membranes is considered.The effective cross-sectional area of the stack was 121.8 cm2 (70mm×174mm). The flow channel between consecutive membranes was 0.8 mm, with a mesh inserted to facilitate mixing. Experiments were carried out with the EDBM stack over different conditions such as current density, number of cell pairs, and flow rates. All experiments were operated at constant current mode [2]. The feed, acid, and base solutions were recirculated through their tanks at initial concentrations of 1.1, 0.1, and 0.1 mol/L. The ion concentrations of the solutions were measured periodically with inductively coupled plasma (ICP) mass spectrometry. The weight and the pH value of the solution tanks were also recorded.The concentration of H2SO4 is found to increase with time linearly, whereas that of LiOH levels off due to a significant electro-osmosis that drags water through the CEM into the concentrate channel. This drag reduces the performance of EDBM due to the dilution of water into the concentrate compartment. However, electro-osmotic water transport also leads to a velocity increase in the concentrate channel, which is consistent with the simulation results in our previous ED model [3]. It is found that the voltage loss across the bipolar membrane ca. 1V accounts for a significant part of the unit cell of about 1.27V.The migration of ions in electrodialysis mainly relies on diffusion and electric drive. The streamlines and the concentration distribution of Li+ under different voltages indicate that increasing voltage accelerates ion migration, see Fig. 1(c). Furthermore, the effect of the potential and concentration variations on EDBM performance is also investigated. The effects of applied current density and inlet velocity are studied on species concentrations and fluxes. Increasing the stack current density accelerates the separation process, see Fig. 1(d). It is found that increasing the solution flow rate can increase LiOH solution concentration, ion recovery rate, and current efficiency. However, the impact of the flow rate is low.This work demonstrates that EDBM can be a simple and energy-saving alternative to the current chemical precipitation method to produce LiOH from Li2SO4. The present study provides new insights into optimal operation and design for Li2SO4 EDBM. The findings are helpful in determining how the stack can be scaled up for practical application.[1] A review of recycling spent lithium-ion battery cathode materials using hydrometallurgical treatments, JCY Jung, PC Sui, J Zhang, J. Energy Storage 35, 102217, 2021.[2] Electrodialysis of a Lithium Sulphate Solution: An Experimental Investigation. B Kang, D Kang, JCY Jung, A Asadi, PC Sui, J. Electrochem. Soc. 169 (6), 063515, 2022.[3] A Comprehensive Computational Fluid Dynamics Modeling of Lithium Sulphate Electrodialysis, A Asadi, HB Harandi, JCY Jung, PC Sui, J. Electrochem. Soc. 170(9), 093502, 2023. Figure 1

Novel analytical solution for solvent-solute flow: Application to pressure transmission testing of reactive shales

Coupled solvent-solute flow is a common phenomenon observed while drilling shale formations using water-based fluids, leading to unfavorable outcomes. Designing optimal fluid formulation requires laboratory tests, such as pressure transmission tests, to evaluate shale-fluid interactions. In this study, an analytical solution was derived for the coupled flow of solvent-solute under pressure transmission testing conditions. It was derived based on the semi-infinite domain solution employing the method of images. The solution was then verified against the semi-analytical solution from the literature. The analysis of the solution revealed that early time pressure response at the outer boundary is primarily governed by hydraulic diffusivity while late time response is by ion diffusion. It also showed that the coefficient of lambda, introduced during derivations, quantifies the chemical effects. In addition, sensitivity analysis was conducted to better understand how variations in key parameters impact the overall transport processes within reactive shales. Finally, a good agreement was obtained by comparing the analytical solution with experimental data from various published sources. The solution will help researchers in gaining new insights into the shale fluid interactions and designing optimal fluid formulations.

Experimental and Theoretical Studies of Nano-Silica Solutions in Narrow Flow Paths Applied to Sealing Cement Cracks

Summary A cement crack is a typical cause of oil and gas well failure. Cracks weaken cement, reducing zonal isolation and fluid leakage. Nanoparticle (NP) gels are being tested for fracture treatment. When crushed into cracks, the flow behavior of NP problem solutions should be predicted. The potential efficacy of utilizing NP gels as a remedial measure for fractures is currently under investigation. It would be advantageous to determine if the flow behavior of solutions for NP problems can be anticipated when they are compressed into crevices. This study aimed to analyze the behavior of nano-silica solutions as they flow through ducts with rectangular cross-sections and varying crack dimensions. The introduction of NP solutions into the core leads to a decrease in pressure, which suggests that the nano-silica has been effectively transported through the crack. As the size of the fracture decreases, there is a corresponding increase in pressure drops, while the flow rate experiences a concurrent increase. This study presents responses of a pressure gradient to fluid concentration for a range of fracture widths, heights, and flow rates. The prediction of laminar flow in ducts is based on the linear correlation between the flow rate and the pressure gradient. Furthermore, the reduced pressure gradient indicates enhanced fluid flow within the fracture because of the amplified slot width. The fluid flow model proposed by Guo et al. (2022) was utilized to conduct a comparative analysis with the experimental data. Compared with test data, the model differs by roughly 90%. The technical cause of the flow model-observed data discrepancies is unknown. The flow model did not account for friction between NPs-NPs and NPs-walls in rough ducts. An empirical correlation has been found that quantifies the ratio as a function of nonsilica solution flow rate, cross-sectional geometry parameters, and nano-silica concentration. The correlation was calculated using nonlinear regression. The empirical relation and actual ratio have a significant correlation, as shown by R2 = 0.8965. In practice, Guo et al.’s (2022) hydraulic model’s pressure drops should be multiplied by the empirical correlation’s ratio to reduce errors.