To overcome the mentioned problem,

To overcome the mentioned problem, the well scheme with a sucker rod pump is replaced by a simpler one that isessentially equivalent to the real scheme. It is illustrated in Fig. 1b. In the “equivalent” scheme, the well consists of a single pipe(i.e., there is no annular space), where the fluid is raised by container 9 having volume 10 that is equal to the volume of the fluidraised by a real pump in full cycle (double stroke) of the plunger. As one can see, the pump under consideration and the wellscheme are equivalent to real pump in terms of all parameters, but much simpler than it. The proposed scheme greatly simplifiessolving the problem in question.The processes described above can be presented using two functions: l t( )and h t( )in the coordinate system of x t, , whichare shown in Fig. 2, where the sinusoid l t( ) illustrates the reciprocating motion of the container for a full pumping cycle (T),while the curve h t( )shows an increase in the level of the fluid in the rising pipe during the same time. It should be noted that thereference point of the coordinate system is located in the downhole.