The Optimal Sine Pulse Frequency of Pulse Hydraulic Fracturing for Reservoir Stimulation

Pulse hydraulic fracturing (PHF) is a key technique for reservoir stimulation. PHF can well accelerate the rupture of rock. However, the supercharging mechanism of PHF is not fully understood. The main reason is that the pressure distribution and its variation, especially the peak pressure characteristics, are unclear inside the pipe and fissure. The present research focuses on the sine pulse applied at the inlet of a pipe or fracture to reveal the variation regularity of peak pressure with the pulse frequency, amplitude, pipe length, diameter and wave speed. First, the weakly compressible Navier–Stokes equations were developed to simulate the variation of fluid pressure. The computation codes were developed using the MacCormack method validated by the existing experimental data. Then, the sine pulse effect was studied inside the pipe and fissure. Last, a new frequency model was built to describe the relationship between the optimal pulse frequency, wave speed and pipe length. The results show that there is a family of frequencies at which the peak pressure of the endpoint can be significantly enhanced and that these frequencies are the optimal pulse frequency. It is found that the optimal pulse frequency depends on the pipe or fissure length and wave speed. At the optimal pulse frequency, the peak pressure at the endpoint can be increased by 100% or more, and the cavitation phenomenon occurs. However, the peak pressure decreases when with the decrease in the pipe diameter and fissure departure due to the friction drag effect of the wall. These new landmark findings are very important for the PHF technique. In addition, a new universal frequency model is built to predict the optimal sine pulse frequency. The present research shows the variation regularity of the fluid pressure inside the pipe and develops a sine frequency-controlled method, providing a potential guide for reservoir stimulation

The Optimal Sine Pulse Frequency of Pulse Hydraulic Fracturing for Reservoir Stimulation

Pulse hydraulic fracturing (PHF) is a key technique for reservoir stimulation. PHF can well accelerate the rupture of rock. However, the supercharging mechanism of PHF is not fully understood. The main reason is that the pressure distribution and its variation, especially the peak pressure characteristics, are unclear inside the pipe and fissure. The present research focuses on the sine pulse applied at the inlet of a pipe or fracture to reveal the variation regularity of peak pressure with the pulse frequency, amplitude, pipe length, diameter and wave speed. First, the weakly compressible Navier–Stokes equations were developed to simulate the variation of fluid pressure. The computation codes were developed using the MacCormack method validated by the existing experimental data. Then, the sine pulse effect was studied inside the pipe and fissure. Last, a new frequency model was built to describe the relationship between the optimal pulse frequency, wave speed and pipe length. The results show that there is a family of frequencies at which the peak pressure of the endpoint can be significantly enhanced and that these frequencies are the optimal pulse frequency. It is found that the optimal pulse frequency depends on the pipe or fissure length and wave speed. At the optimal pulse frequency, the peak pressure at the endpoint can be increased by 100% or more, and the cavitation phenomenon occurs. However, the peak pressure decreases when with the decrease in the pipe diameter and fissure departure due to the friction drag effect of the wall. These new landmark findings are very important for the PHF technique. In addition, a new universal frequency model is built to predict the optimal sine pulse frequency. The present research shows the variation regularity of the fluid pressure inside the pipe and develops a sine frequency-controlled method, providing a potential guide for reservoir stimulation

Chaos Adaptive Improved Particle Swarm Algorithm for Solving Multi-Objective Optimization

To overcome the problem of premature convergence on Particle Swarm Optimization (PSO), this paper proposes both the improved particle swarm optimization methods (IPSO) based on self-adaptive regulation strategy and the Chaos Theory. Given the effective balance of particles’ searching and development ability, the self-adaptive regulation strategy is employed to optimize the inertia weight. To improve efficiency and quality of searching, the learning factor is optimized by generating Chaotic Sequences by Chaos Theory. The improved method proposed in this paper achieves better convergence performance and increases the searching speed. Simulation results of some typical optimization problems and comparisons with typical multi-objective optimization algorithms show that IPSO has a fast convergence speed, the diversity of non-dominated and the ideal convergence. The algorithm meets the requirements of multi-objective optimization problem. DOI : http://dx.doi.org/10.11591/telkomnika.v12i1.318

Numerical Simulation and Sensitivity Analysis of Hydraulic Fracturing in Multilayered Thin Tight Sandstone Gas Reservoir

Hydraulic fracturing is a necessary measurement to realize the commercial exploitation of oil and gas, but its application in multilayered thin tight sandstone gas reservoirs is still not perfect, which usually have thin gas layers mixed with complex intervals, and shows a dramatic variation in geological and geomechanical properties in the vertical direction. When conventional hydraulic fracturing methods are applied to this kind of reservoir, it is hard to get proper fracture propagation, especially for fracture height control. Facing this situation, this paper proposes a numerical study of the hydraulic fracturing mechanism and analyzes its influencing factors in the multilayered thin tight sandstone gas reservoir. Relying on a real reservoir in the Ordos Basin in China, relevant geological and geomechanical parameters of major gas layers and interlayers are obtained. According to these parameters, the hydraulic fracturing simulation in the multilayered thin tight gas reservoir model is carried out, based on which, the sensitivity analysis of different geological and fracturing parameters which affect the fracture propagation is performed. Furthermore, a real low-production well after fracturing in this kind of reservoir is selected as an example, and based on the analysis, an optimized fracturing scheme is proposed to adapt to the characteristics of the reservoir. According to the comparison of fracturing and production simulations, the optimized fracturing scheme can prevent hydraulic fractures from breaking through thin interlayers, control the fracture height, and prevent fractures from communicating strata with a high water-bearing layer. At the same time, with the same amount of proppant and fracturing fluid, longer fracture length and better fracture conductivity are created, so that the productivity of the optimized fracture has been greatly improved

A Semianalytical Model for Simulating Fluid Flow in Tight Sandstone Reservoirs with a Bottom Aquifer

Water breaks through along fractures is a major concern in tight sandstone reservoirs with a bottom aquifer. Analytical models fail to handle the three-dimensional two-phase flow problem for partially penetrating inclined fractures, so time-consuming numerical simulation are often used for this problem. This paper presents an efficient semianalytical model for this problem considering three-dimensional fractures and two-phase flow. In the model, the hydraulic fracture is handled discretely with a numerical discrete method. The three-dimensional volumetric source function in real space and superposition principle are employed to solve the model analytically for fluid flow in the reservoir. The transient flow equations for flow in three-dimensional inclined fractures are solved by the finite difference method numerically, in which two-phase flow and stress-dependent properties are considered. The eventual solution of the model and transient responses are obtained by coupling the model for flow in the reservoir and discrete fracture dynamically. The validation of the semianalytical model is demonstrated in comparison to the solution of the commercial reservoir simulator Eclipse. Based on the proposed model, the effects of some critical parameters on the characteristics of water and oil flow performances are analyzed. The results show that the fracture conductivity, fracture permeability modulus, inclination angle of fractures, aquifer size, perforation location, and wellbore pressure drop significantly affect production rate and water breakthrough time. Lower fracture conductivity and larger inclination angle can delay the water breakthrough time and enhance the production rate, but the increment tends to decline gradually. Furthermore, water breakthrough will occur earlier if the wellbore pressure drop and aquifer size are larger. Besides, the stress sensitivity and perforation location can delay the water breakthrough time

Deformation Law of Tunnels Using Double-Sidewall Guide Pit Method under Different Excavation Sequences

The double-sidewall guide pit method finds extensive application in the construction of large cross-section tunnels in soft rock strata due to its minimal disruption to the surrounding rock, thereby enhancing tunnel stability. To investigate the loading and deformation patterns of the surrounding rock and tunnel support using the double-sidewall guide pit method, this study compares the impacts of various construction sequences on surface settlement, surrounding rock stress, and lining stress using indoor model tests. The experimental results show that after excavating the upper guide hole on one side, the excavation of the lower guide hole on the same side is carried out. The upper and lower support structures form a closed loop, and the structure can better constrain the surrounding rock and control the deformation of the surrounding rock, whereas the lower structure can share the stresses suffered by the upper structure. Therefore, compared with the upper and lower excavation methods, the surface settlement caused by the left and right excavation methods is smaller, the disturbance to the surrounding rock is smaller, and the supporting structure is more evenly and stably stressed in the excavation process

Significant Increase of Erectile Dysfunction in Men With Post-stroke: A Comprehensive Review

Men with erectile dysfunction (ED) are considered to be at risk from stroke events. Conversely, post-stroke patients are also at high risk of ED, whereas a quantitative result from all the relevant studies has not been previously addressed. Therefore, we have performed a comprehensive review and meta-analysis on this issue. This study was registered on PROSPERO (ID No. CRD42021226618). Twenty studies with a total of 3,382 stroke events were included, of which six studies were included for quantitative analysis, and the remaining 14 studies were calculated for the ratio of ED. Synthetic results from four eligible studies providing the ED cases showed that stroke patients were associated with a significantly higher risk of ED than the general population [pooled relative risk (RR) = 3.32, 95% confidence interval (CI): 1.25-8.82