Numerical Method of Solution of the Coefficient-Inverse Problem for Unsteady Motion in an Oil Pipeline

Abstract

Consideration is given to the approach to identifi cation of the coeffi cient of hydraulic resistance of a linear portion of a main pipeline in transporting raw hydrocarbons. The problem of identifi cation is reduced to a class of fi nitedimensional-optimization problems. To solve them, the author proposes effi cient numerical methods of fi nitedimensional optimization of fi rst order. For this purpose, in the work, the author derives formulas for the components of the gradient of the target functional in the space of identifi ed parameters. The obtained values of the optimized vector can be used for construction of the identifi ed function from any class of functions with interpolation and approximation methods. Results of the conducted numerical experiments are given. Keywords: distributed system, coeffi cient of hydraulic resistance, inverse problem, identifi cation problem, conjugate problem, functional gradient.Introduction. In recent years, pipeline transport systems have become the basic and most signifi cant means of transportation of raw hydrocarbons. One recognizes two sources of energy loss in the case of liquid motion in a pipeline: loss along the pipeline length and loss in local resistances. By local resistances are meant all kinds of devices of a small length (compared to the pipe length) and various locking devices, bends, valves, etc. The loss in local resistances is caused by the enhanced mixing of the liquid, which is accompanied by vortex formation, and by large velocity gradients. The loss along the pipe length or by friction is due to the friction in the fl ow and is dependent on the pipeline length and on the coeffi cient of hydraulic resistance [1,2]. The values of resistances of the pipeline′s portions exert a substantial infl uence on the motion of oil (gas) in the pipeline. It is well known [3] that the resistance of the pipeline′s portion depends not only on such geometric dimensions of the pipe as the portion length and the pipe diameter, but also on the roughness of the interior pipe surface infl uencing the value of the coeffi cient of hydraulic resistance. In the process of long-term operation of pipelines, the coeffi cients of hydraulic resistances of portions change, namely, increase as a result of the processes of hydrate formation on the interior surface of the pipelines. These processes are the most intense when technological regimes of operation of the pipelines are violated and on installations for preparation of oil products for transporting. The development of networks of main pipelines (mains) for transportation of raw hydrocarbons is accompanied by the wide and active use of modern instrumentation and computer aids in them, and also of remote-control systems. Therefore, of practical importance is to employ mathematical methods of identifi cation of the coeffi cients of resistance for tracking of the state of potions of a pipeline network. This makes it possible to detect suspicious portions on which intense hydrate-formation processes have begun, which has a substantial ...