The discrete-imitation modeling concept of the “sucker-rod pump-well-reservoir” system and the optimization of the pumping process

A new approach to dynamic modeling based on a discrete-imitation concept has been developed. The fundamentals, including terms and principles of the concept, have been explained. The presented concept has been applied to the integrated modeling of the development of a volatile oil reservoir operated by a sucker-rod pumping well within a pump-well-reservoir system. The discrete-imitation model of the “pump-well-reservoir” system, developed based on the principles of the new concept, takes into account fluid flow between the annulus and the lifting bore. It was employed to investigate the operation of the sucker-rod pumping well. The correlation between pumping rate, pump fillage, and stroke speed has been investigated. It was observed that, as the stroke speed increases, both pump performance and pump fillage increase up to a certain point. Beyond this threshold, the pumping rate stabilizes, and the pump fillage experiences a sharp decline. Notably, the maximum pump fillage does not always align with the peak pumping rate. In such instances, achieving an optimal regime is possible only through intermittent pumping. An expression has been derived to determine the optimal pump idle time in intermittent mode.