Oilfield Sewage System Scheduling is a complicated, large-scale, nonlinear system problem with multiple variables. The complexity of the sewage system pipeline network connection grows along with the ongoing building of oilfield stations, and the shortcomings of the sewage system water quantity scheduling program based on human experience decision-making become increasingly apparent. The key to solving this problem is to realize the digital and intelligent scheduling of sewage systems. Taking the sewage system of an oil production plant in Daqing oilfield as the research object, the water scheduling model of the sewage system is established in this paper. Aiming at the complex nonlinear characteristics of the model, the Levy flight speed updating operator, the adaptive stochastic offset operator, and the Brownian motion selection optimization operator are established by taking advantage of the particle swarm optimization (PSO) and the cuckoo search (CS) algorithm. Based on these operators, a hybrid PSO-CS algorithm is proposed, which jumps out of the local optimum and has a strong global search capability. Comparing PSO-CS with other algorithms on the CEC2022 test set, it was found that the PSO-CS algorithm ranked first in all 12 test functions, proving the excellent solving performance of the PSO-CS algorithm. Finally, the PSO-CS is applied to solve a water scheduling model for the sewage system of an oil production plant in Daqing Oilfield. It is found that the scheduling plan optimized by PSO-CS has a 100% water supply rate to the downstream water injection station, and the total energy consumption of the scheduling plan on the same day is reduced from 879.95 × 10⁶ m⁵/d to 712.84 × 10⁶ m⁵/d, which is a 19% reduction in energy consumption. The number of water balance stations in the sewage station increased by 7, which effectively improved the water resource utilization rate of the sewage station.

The energy consumption issue of water injection systems has always been a key focus of energy conservation and consumption reduction in oilfield production. Optimizing the operational schemes of the water injection system is of great significance for achieving energy conservation and consumption reduction goals in oilfields. This article establishes a mathematical model for optimizing the operating parameters of oilfield water injection systems, with the operating parameters of water injection pumps as design variables and the objective function of minimizing water injection energy consumption. In the model, multiple constraints such as the balance of supply and demand of water within the station, pump flow rate, and injection well pressure are considered. Using the four defensive behaviors of the Crested Porcupine Optimizer (CPO) to optimize the Particle Swarm Optimization (PSO) Algorithm, a Multi-Mechanism Threat Response Strategy for Dynamic Parameter Adjustment is proposed to form a Hybrid Particle Swarm–Crested Porcupine Algorithm (PSCPA). Compared with the other nine algorithms, the PSCPA has better solving efficiency. Applying this method to a practical case of an old oilfield, the optimized water injection system scheme reduced power consumption by 11,719.23 KWh/d, increased the average pump efficiency of the system by 9.3%, and reduced system unit consumption by 0.37 KWh/d. Therefore, this algorithm has good practicality for optimizing the operation of large-scale and highly sensitive water injection systems.

The problems of uneven load and low operating efficiency in the oil-gathering system of old oilfields lead to higher operating costs. In order to reduce operating costs, the layout-reconfiguration optimization model is established, and the minimum comprehensive investment is taken as the objective function. The multi-constraint conditions, such as the current situation of the oil-gathering system, the processing capacity, the possibility of pipeline failure, and the obstacles, are considered. The hybrid arithmetic–fireworks optimization algorithm (AFOA) is proposed to solve the model. Combined with the experience of the hybrid metaheuristic algorithm, using hybrid metaheuristics, the hybrid of the arithmetic optimization algorithm (AOA) and the operator of the fireworks algorithm (FWA) is considered, and some improved operators of FWA are integrated into AOA to form a new algorithm (AFOA) to achieve a better solution effect. Compared with the 11 other algorithms, AFOA has better solution efficiency. This method is applied to the actual case of an old oilfield. The optimized scheme increases the average load rate of the station by 15.9% and reduces the operating costs by 38.1% per year. Overall, the reconstruction costs will be recovered in a short period.

In this study, we employ the homotopy renormalization (HTR) method to analytically investigate Rasmussen’s problem, which characterizes the viscous fluid motion between a pair of infinitely large, coaxially rotating disks. The original set of nonlinear ordinary differential equations is reformulated within a homotopy-based framework, allowing us to construct global asymptotic approximations with closed-form expressions. The HTR method overcomes the limitations of traditional perturbation and renormalization techniques, and avoids the need for asymptotic matching. In addition, the analytic expressions allow for direct estimation of flow parameters such as boundary layer thickness. These results demonstrate the effectiveness of the HTR method in asymptotic analysis and highlight its potential for broader applications in nonlinear fluid dynamics.