Improved grey Verhulst model with complex order reverse accumulation and its application in oil well production prediction

Purpose Reverse accumulation is adopted to give grey Verhulst modeling an explicit preference for the most recent information. By extending the accumulation order from the real domain to the complex domain, the model enhances the prediction accuracy and adaptability to data with saturation characteristics. Design/methodology/approach Guided by the principle of new information priority, the latest data point (last observation) was treated as the most critical information source. First, complex-order reverse accumulation and reverse reduction generation operators were constructed to expand the solution space of accumulation orders to the complex field. Second, a complex-coded Particle Swarm Optimization (PSO) algorithm was adopted to dynamically search the objective function, enabling the efficient acquisition of the optimal complex order that minimizes the prediction error. Findings A reverse accumulation method was introduced to process the original sequence, effectively addressing the issue of weighing new and old information. Meanwhile, complex-order accumulation overcomes the limitation of integer- and fractional-order grey models in achieving high fitting accuracy for diverse data patterns. In addition, the complex-coded PSO algorithm accelerates the search for the optimal complex order, improving computational efficiency while ensuring solution precision. Research limitations/implications This study theoretically and empirically confirms the effectiveness of the complex order reverse accumulation grey Verhulst model in predicting oil well production through multiple case studies, providing a new approach for oil well data prediction. Practical implications Three petroleum-related case studies (long-term oil well production, startup liquid level of low-permeability intermittent wells, and national crude oil consumption) demonstrate that the Mean Absolute Percentage Error (MAPE) of the proposed model is consistently less than 1.5%, meeting the high-precision standard of MAPE <5% in engineering practice. Social implications This study enhances oil well production forecasting accuracy, enabling oilfield enterprises to optimize extraction strategies, reduce operational costs, and extend stable production periods. Simultaneously, it supports national energy strategic reserve planning and energy security decision-making. Originality/value This study established a complex-order reverse accumulation grey prediction model by extending the accumulation order to the complex domain. The empirical results demonstrated superior performance.