Identification and research of factors affecting the optimal distribution of well flow rates in space

The paper discusses and research the factors affecting the filtration rate to reduce stagnant zones in the domain and spreading outside the block under consideration. The main hydrodynamic factors in production by In-Situ Leaching are the distribution of permeability in the reservoir and well flow rates. The study of the factors was carried out on the basis of mathematical models using Darcy Law and Law of Conservation of Mass. Calculation was accomplished on a two-dimensional area with an isotropic and non-uniform permeability distribution to determine the effect of permeability on the leached area. The permeability coefficient was distributed respectively over three zones, in the southern part the permeability was low, in the central transition from low to high, respectively, in the northern part there was a highly permeable zone. Three wells were located in the domain, with the production well in the center of the domain. Injection wells are located symmetrically with respect to a horizontal line passing through the center of the area under consideration. The calculation was carried out for three modes of well flow rates with the ratio of the flow rates of the injection wells 0.5 / 0.5, 0.2 / 0.8, 0.8 / 0.2 relative to the flow rate of the production well. On the basis of comparative analyzes of the obtained results, it is concluded that: at the same flow rates, regardless of the permeability of the zones, the results obtained show that the leaching area in the low-permeability zone is larger in comparison with the high-permeability zone; with an increase in permeability, the shape of the leaching zone tends from round to drop-shaped; with an increase in the flow rate of wells in the radius of the leaching zone, it increases if the flow rate of solutions is much higher than the filtration rate.

Catalytic Functionalized Structured Monolithic Micro-/Mesoreactors: Engineering, Properties, and Performance in Flow Synthesis: An Overview and Guidelines

In this review article, we first discussed the development of silica monoliths with hierarchical macro-/mesopore structure and their potential figures of merit as continuous-flow micro-/mesoreactors of up to 30 ml working volume. Making use of the flow hindrance of different pore structures seen from the Darcy law perspective, we discriminated four structures of the monoliths (M1–M4). We then summarized the most important results, mainly from our studies of continuous-flow structured monolithic reactors and rotating bed reactors (RBRs) filled with structured pellets, activated with various catalytic entities and enzymes. The results show that an increase in the flow rate and thus velocity in reactors activated with more conventional catalytic sites has no or a minor positive effect on the apparent reaction rate. On the contrary, in those with the most open structure (M1) and functionalized with enzymes, it could increase by more than two orders of magnitude even at low overpressures. The production systems worked stably for at least 200 h. To conclude, the synthetic system made of the hierarchically structured monoliths, or RBRs filled with structured catalytic pellets, lay the foundation for a new platform for the high-yield production of a wide variety of specialty chemicals, even on a multikilogram scale, in a safe and sustained manner.

Effect of inclination angle on bioconvection in porous square cavity containing gyrotactic microorganisms and nanofluid

The current article investigates the effect of inclination angle on thermo-bioconvection within the porous-square shaped cavity filled with gyrotactic type microorganisms and nanofluid. The Darcy law with Boussinesq estimation is used for the momentum equation in porous media. The transformed governing equations are solved by Galerkin’s method of finite elements. The effect of inclination angle in the square cavity is interpreted by varying the angle from [Formula: see text] to [Formula: see text]. The effect of inclination on different quantities, for instance, Rayleigh number, bioconvective Rayleigh number, Peclet number, Brownian motion, heat source/sink, and ratio of buoyancy, is discussed. Further, the mean quantities of Nusselt number [Formula: see text], Sherwood number [Formula: see text], and density number [Formula: see text] are analyzed at vertical walls. A quantitative outcome of the study is that the maximum values of [Formula: see text], [Formula: see text], and [Formula: see text] are found for the angle [Formula: see text] and [Formula: see text].

Study on Non-Darcian Flow in Interlayer Shear Weakness Zones in the Basalt by High-Pressure Packer Tests

The interlayer shear weakness zone (ISWZ) is a special structural plane with different widths and spacing in stratified rock masses, it has higher permeability compared with surrounding rocks which is a risk factor for the safety of the hydropower station project. The high-pressure packer test (HPPT) by step injection is always applied to characterize the permeability of ISWZ. However, the non-Darcian flow is easy to appear under high pressure, which makes the Darcy law model no longer applicable. In this study, two non-Darcian flow analytical methods for confined aquifer were proposed to investigate the non-Darcian flow permeability parameters. The equivalent permeability coefficients of different non-Darcian models were derived as well. The in situ tests were conducted on the ISWZs at the Baihetan hydropower station to verify the proposed methods. The results indicate that the flow is non-Darcian flow in the test section from integrity to destruction during the whole HPPT process. Izbash’s law has a better fit than Forchheimer’s law in this complicated test situation. The equivalent permeability coefficients after destruction are one or two orders of magnitude larger than those before. Meanwhile, it is necessary to pay attention to the increased difference of two expressions of the equivalent permeability coefficients under higher gradient (i) or velocity (v). In general, these methods can be used to evaluate the characteristic of ISWZ to analyze the impact on engineering stability.

The Mixed Virtual Element Method for Grids with Curved Interfaces in Single-Phase Flow Problems

In many applications the accurate representation of the computational domain is a key factor to obtain reliable and effective numerical solutions. Curved interfaces, which might be internal, related to physical data, or portions of the physical boundary, are often met in real applications. However, they are often approximated leading to a geometrical error that might become dominant and deteriorate the quality of the results. Underground problems often involve the motion of fluids where the fundamental governing equation is the Darcy law. High quality velocity fields are of paramount importance for the successful subsequent coupling with other physical phenomena such as transport. The virtual element method, as solution scheme, is known to be applicable in problems whose discretizations requires cells of general shape, and the mixed formulation is here preferred to obtain accurate velocity fields. To overcome the issues associated to the complex geometries and, at the same time, retaining the quality of the solutions, we present here the virtual element method to solve the Darcy problem, in mixed form, in presence of curved interfaces in two and three dimensions. The numerical scheme is presented in detail explaining the discrete setting with a focus on the treatment of curved interfaces. Examples, inspired from industrial applications, are presented showing the validity of the proposed approach.

Optimization Approach for Determination of the Dosage of Diversion Agents in Temporarily Plugging Fracturing of Shale Using 3D Printing Fractures

Application of diversion agents in temporarily plugging fracturing of horizontal wells of shale has becoming more and more popular. Nevertheless, the studies on determining the diverter dosage are below adequacy. A novel approach based on laboratory experiments, logging data, rock mechanics tests and fracture simulation was proposed to optimizing the dosage of diversion agents. The optimization model is based on the classic Darcy Law. A pair of 3D-printed rock plates with rugged faces was combined to simulate the coarse hydraulic fractures with the width of 2.0 ~ 7.0 mm. The mixture of the diversion agents and slickwater was dynamically injected to the simulated fracture in Temco fracture conductivity system to mimic the practical treatment of temporarily plugging fracturing. The permeability of the temporary plugging zone in the 3D-printed fractures was measured in order to optimize the dosage of the selected diversion agents. The value of Pnet (also the value of ΔP in Darcy Formula) required for creation of new branched fractures was determined using the Warpinski-Teufel Failure Rules. The hydraulic fractures of target stages were simulated to obtain the widths and heights. The experimental results proved that the selected suite of the diversion agents can temporarily plug the 3D-printed fractures of 2.0 ~ 7.0 mm with blocking pressure up to 15 MPa. The measured permeability of the resulting plugging zones was 0.724 ~ 0.933 D (averaging 0.837 D). The value of Pnet required for creation of branched fractures in shale of WY area (main shale gas payzone of China) was determined as 0.4 ~ 15.6 MPa (averaging 7.9 MPa) which means the natural fractures and/or weak planes with approaching angle less than 70o could be opened to increase the SRV. The typical dosage of the diversion agents used for one stage of the horizontal wells was calculated as 232 ~ 310 kg. The optimization method was applied to the design job of temporarily plugging fracturing of two shale gas wells. The observed surface pressure rise after injection of diversion agents was 0.6 ~ 11.7 MPa (averaging 4.7 MPa) and the monitored microseismic events of the test stages were 37% more than those of the offset stages.

Transport Behavior of Liquid Hydrocarbon in Shale Matrix with Mixed Wettability Nanopores

Shale oil is an unconventional petroleum resource which has high total organic carbon (TOC) content and abundant nanopores. The transport behavior of oil through organic rich shales cannot be described by the classical Darcy law due to its complex pore structure and the complicated distribution of organic matter, which results in nanoconfined effects. In this work, on the basis of the boundary slip phenomenon and the fractal scaling theory, a model for oil transport in shale matrix is established considering nanoconfined effects and adsorbed organic matter. The results show that it is necessary to make correction of viscosity and the boundary slip length in order to accurately describe the flow behavior of oil in shale matrix with mixed wettability nanopores. Long chain molecules are more sensitive to nanoconfined effects, especially when adsorbed organic matter is considered. Also, the oil transport capacity in organic shale matrix is greatly enhanced compared to the classical no-slip permeability model. Meanwhile is the oil transport capacity is significantly reduced in inorganic shale matrix. This work shows that the identification of higher TOC region and considering the nanoconfined effects are necessary from the concept of oil transport in shale matrix.

A Novel Design Method for Optimizing the Diverter Dosage in Hydraulic Fracturing Using Three-Dimensionally Printed Fractures

Application of diversion agents in temporarily plugging fracturing of horizontal wells of shale has becoming more and more popular. Nevertheless, the studies on determining the diverter dosage are below adequacy. A novel approach based on laboratory experiments, logging data, rock mechanics tests and fracture simulation was proposed to optimizing the dosage of diversion agents. The optimization model is based on the classic Darcy Law. A pair of 3D-printed rock plates with rugged faces was combined to simulate the coarse hydraulic fractures with the width of 2.0 ~ 7.0 mm. The mixture of the diversion agents and slickwater was dynamically injected to simulate the fracture in Temco fracture conductivity system to mimic the practical treatment to temporarily plugging the fracture. The permeability of the temporary plugging zone in the 3D-printed fractures was measured in order to optimize the dosage of the selected diversion agents. The value of Pnet (also the value of ΔP in Darcy Formula) required for creation of new branched fractures was determined using the Warpinski-Teufel Failure Rules. The hydraulic fractures of target stages were simulated to obtain the widths and heights. The experimental results proved that the selected suite of the diversion agents can temporarily plug the 3D-printed fractures of 2.0 ~ 7.0 mm with blocking pressure up to 15 MPa. The measured permeability of the resulting plugging zones was 0.724 ~ 0.933 D (averaging 0.837 D). The value of Pnet required for creation of branched fractures in shale of WY area (main shale gas payzone of China) was determined as 0.4 ~ 15.6 MPa (averaging 7.9 MPa) which means the natural fractures and/or weak planes with approaching angle less than 70° could be opened to increase the SRV. The typical dosage of the diversion agents used for one stage of the horizontal wells (averaging TVD 3600 m) was calculated as 232 ~ 310 kg. The optimization method was applied to the design job of temporarily plugging fracturing of two shale gas wells. The observed surface pressure rise after injection of diversion agents was 0.6 ~ 11.7 MPa (averaging 4.7 MPa) and the monitored microseismic events of the test stages were 37% more than those of the offset stages.

Nanomechanical Concepts in Magnetically Guided Systems to Investigate the Magnetic Dipole Effect on Ferromagnetic Flow Past a Vertical Cone Surface

Because of the floating magnetic nanomaterial, ferrofluids have magneto-viscous properties, enabling controllable temperature changes as well as nano-structured fluid characteristics. The study’s purpose is to evolve and solve a theoretical model of bioconvection nanofluid flow with a magnetic dipole effect in the presence of Curie temperature and using the Forchheimer-extended Darcy law subjected to a vertical cone surface. The model also includes the nonlinear thermal radiation, heat suction/injection, viscous dissipation, and chemical reaction effects. The developed model problem is transformed into nonlinear ordinary differentials, which have been solved using the homotopy analysis technique. In this problem, the behavior of function profiles are graphically depicted and explained for a variety of key parameters. For a given set of parameters, tables representthe expected numerical values and behaviors of physical quantities. The nanofluid velocity decreases as the ferrohydrodynamic, local inertia, and porosity parameters increase and decrease when the bioconvection Rayleigh number increases. Many key parameters improved the thermal boundary layer and temperature. The concentration is low when the chemical reaction parameter and Schmidt number rises. Furthermore, as the bioconvection constant, Peclet and Lewis numbers rise, so does the density of motile microorganisms.