Analysis of the regimes of controlling transient processes in pipelines

Abstract

This paper considers the problem of optimal control of the process of going from one stable regime to an- other in piping the hydrocarbon raw material. We have investigated the influence of the transient period on the dissipation factor of the system, the length of the part of the pipeline, and the difference between the pa- rameters of the initial and final stable regimes with account for the technological limitations set on the con- trol actions and phase variables. The dependence of the optimal transient period on the class and range of Introduction. We have solved the problem of optimal control of the transient processes arising in piping the hydrocarbon raw material in going from one stable regime to another. These processes take place both in the case of planned changes in the transfer regimes and in the case of emergency shut-down of the pipeline (1, 2). In the mathe- matical formulation, the given problem is described by a system of equations with distributed parameters, in which the optimized parameter is the transient period, and the control actions are the rates of fluid flow at the ends of the linear part of the pipeline; limitations are formed thereby with account for the technological characteristics of the pumping plants (pumps) and the strength characteristics of the pipeline. The proposed optimality criterion for the above proc- esses takes into account the fact that complete and exact stabilization of the regime of raw material piping cannot be achieved by controlling these processes because of instrumental errors. The problem under consideration is closely con- nected with the problem of controlling wave processes investigated in (3-8). In distinction to our previous investigations, in the present work we have investigated numerically the problem of optimal (as to the operation speed) control of the regimes of fluid (oil) piping in the presence of certain technologi- cal limitations set on the control actions and on the state of the object being controlled. We have performed a quali- tative analysis of the dependence of the minimum transient period on the dissipation factor of the fluid being piped (determined by the fluid viscosity and the hydraulic resistance coefficient of the pipe and its diameter), the length of the part of the pipeline, the difference between the parameters of the initial and final stable regimes, and the range of permissible control actions. Formulation of the Problem. We consider the isothermal process of single-phase oil transportation over a linear part of a horizontal pipeline having a length l, a diameter d, and a hydraulic resistance coefficient λ. It is as- sumed that the fluid flow is laminar and the oil is considered to be an incompressible fluid with kinematic viscosity ν. At either end of the pipeline there are pumping plants providing the given transfer conditions.