This paper studies the convective heat transfer of a hybrid nanofluid in the inclined channel, whose walls are both heated by the uniform heat flux. The governing ordinary differential equations are made nondimensional and solved analytically, in which explicit distributions of velocity, temperature and pressure are obtained. The effects of flow reversal, wall skin friction and Nusselt number with the hybrid nanofluid depend on the nanoparticle volume fractions and pressure parameters. The obtained results indicate that the nanoparticle volume fractions play a key role in delaying the occurrence of the flow reversal. The hybrid nanofluids hold more delayed range than conventional nanofluids, which is about 2.5 times that of nanofluids. The calculations have been compared with the base fluid, nanofluid and two kinds of hybrid models (type II and type III). The hybrid model of type III is useful and simplified in that it omits the nonlinear terms due to the interaction of different nanoparticle volumetric fractions, with the relative error less than 3%. More results are discussed in the results section below.

A non-Darcy flow with moving boundary conditions in a low-permeability reservoir was solved using the homotopy analysis method (HAM), which was converted into a fixed-boundary mathematical model via similarity transformation. Approximate analytical solutions based on the HAM are guaranteed to be more accurate than exact analytical solutions, with relative errors between 0.0089% and 2.64%. When λ = 0, the pressure drop of the Darcy seepage model could be instantaneously transmitted to infinity. When λ > 0, the pressure drop curve of the non-Darcy seepage model exhibited the characteristics of tight support, which was clearly different from the Darcy seepage model’s formation pressure distribution curve. According to the results of the HAM, a moving boundary is more influenced by threshold pressure gradients with a longer time. When the threshold pressure gradients were smaller, the moving boundaries move more quickly and are more sensitive to external influences. One-dimensional, low-permeability porous media with a non-Darcy flow with moving boundary conditions can be reduced to a Darcy seepage model if the threshold pressure gradient values tend to zero.

This paper studies the impact of shape factor on a mass-based hybrid nanofluid model for Homann stagnation-point flow in porous media. The HAM-based Mathematica package BVPh 2.0 is suitable for determining approximate solutions of coupled nonlinear ordinary differential equations with boundary conditions. This analysis involves discussions of the impact of the many physical parameters generated in the proposed model. The results show that skin friction coefficients of Cf_x and Cf_y increase with the mass of the first and second nanoparticles of the hybrid nanofluids w₁ and w₂ and with the coefficient of permeability in porous media. For the axisymmetric case of γ = 0, when w₁ = w₂ = 10 gr, w_f = 100 gr and Cf_x = Cf_y = 2.03443, 2.27994, 2.50681, and 3.10222 for σ = 0, 1, 2, and 5. Compared with w₁ = w₂ = 10 gr, w_f = 100 gr, and σ = 0, it can be found that the wall shear stress values increase by 12.06%, 23.21%, and 52.48%, respectively. As the mass of the first and second nanoparticles of the mass-based hybrid nanofluid model increases, the local Nusselt number Nu_x increases. Values of Nu_x obviously decrease and change with an increase in the coefficient of permeability in the range of γ < 0; otherwise, Nu_x is less affected in the range of γ > 0. According to the calculation results, the platelet-shaped nanoparticles in the mass-based hybrid nanofluid model can achieve maximum heat transfer rates and minimum surface friction.

The wetting and nonwetting fluid saturations in porous reservoirs always change during long-term injection and production. The fracture process zone (FPZ) is a prominent feature in the rock fracture process. If the FPZ properties are influenced by pore fluids, the process of hydraulic fracturing will change greatly. The existing models do not consider the role of pore fluid when characterizing the FPZ. In this paper, a modified Dugdale–Barenblatt (D–B) model with capillary pressure is proposed. The model reflects the fact that the FPZ length decreases nonlinearly with the increase in capillary pressure, and it reveals the mechanism of capillary pressure on the equivalent fracture cohesion in the FPZ, which affects the FPZ length. Three-point bending tests were carried out on sandstone under various fluid saturations through digital image correlation (DIC), acoustic emission (AE), and scanning electron microscope (SEM). It was found that the FPZ length of the water–oil-saturated samples was 30–50% smaller than that of water-saturated/oil-saturated samples due to the capillary pressure effect, and the modified D–B model was well consistent with the experiments. The AE behaviors of different saturated samples were not the same: The cumulative AE signals changed abruptly at 90% of the peak load for the water–oil-saturated samples and at 50% of the peak load for water-saturated samples. This demonstrated that the effect of capillary pressure was more obvious than the weakening effect of microstructural damages. The significant influence of capillary pressure on FPZ requires continuous recognition in hydraulic fracturing design.

Rich in valuable reserves, conglomerate reservoirs in China have gradually emerged as a fundamental development source. Currently, research pertaining to the macromechanical properties of crack propagation in conglomerates is conducted either by directly employing various physical tests or by formulating a simplified numerical model for simulation, while disregarding the influence of the conglomerate mesostructure. In this paper, the analysis is performed by adopting techniques such as CT scanning and Particle Flow Code (PFC) numerical simulation. CT scanning is used to identify the mesoscopic structure of the conglomerate, and then, a numerical model is devised in accordance with the CT scanned digital image. Three-point bending simulation experiments are conducted for 3 sets of semicircular conglomerate specimens possessing prefabricated cracks, to analyze the influence of the initiation and evolution of mesostructure on the fracture failure behavior. Research suggests: ① The mesostructure within the conglomerate is complexified due to the presence of gravel. Conglomerate specimens exhibiting different mesostructures tend to diversify the possible modes of destruction of the conglomerate. ② A fluctuation is noticed at peak load under the fracture toughness test. The numerical simulation of the fracture toughness undertaken via the PFC method revealed the reason for the peak load fluctuation during the fracture propagation to be the constant penetration of the cracks into or out of gravel particles. ③ The fracture toughness simulation tests ascertain the existence of certain fracture characteristic units during the fracture propagation process, wherein the evolution of the internal mesostructure considerably influences the macroscopic failure mode of the conglomerate.

Salt diapirs are commonly seen in the North Sea. Below the Zechstein Group exist possibly overpressured salt-anhydrite formations. One explanation as to the salt precipitation in areas with salt diapirs is that salt cementation is thermally driven and occurs strongly in places adjacent to salt diapirs. This paper assumes that the sealing effect of the cap rock above the salt formations is compromised and overpressured fluids, carrying dissolved minerals such as anhydrite (CaSO₄) and salt mineral components (NaCl of halite), flow into the porous sedimentary layers above the salt formations. Additionally, a salt-diapir-like structure is assumed to be at one side of the model. The numerical flow and heat transport simulator SHEMAT-Suite was developed and applied to calculating the concentrations of species, and dissolution and precipitation amounts. Results show that the overpressured salt-anhydrite formations have higher pressure heads and the species elements sodium and chlorite are transported into porous sediment rocks through water influx (saturated brine). Halite can precipitate as brine with sodium and chlorite ions flows to the cooler environment. Salt cementation of reservoir rocks leads to decreasing porosity and permeability near salt domes, and cementation of reservoir formations decreases with growing distance to the salt diapir. The proposed approach in this paper can also be used to evaluate precipitation relevant to scaling problems in geothermal engineering.