The pipeline state estimation problem is posed to considered by the example of the simplest pipeline is formulated. It contains the simplified Navie-Stokes equations for the interior points of the pipe, and two boundary conditions for the fluid flow through the pump and valve. The main principles of the difference scheme for solving these model equations are described. The iterative quasi-linearization is proposed. The state estimation procedure is build on the basis of quasi-linearized model. Some results of numerical experiments are given.
In the past few years the state estimation problem for pipeline systems has become one of current importance. These are different approaches to this problem, using the online models. Most of them are built on the correct statement of boundary conditions . This paper represents a new technique for online state estimation based on the pipeline model and a latesh history of date, obtained from pressure sensors and flowmeters installed on the pipeline. The point is that in spite of the fact the modern oil pipelines are equipped with high tech equipments the accidents and oil spills keep happen, damaging the environment. To prevent these accidents one should have clear understanding about what is going on inside the pipeline. That is why mathematical models are attracted. They are generally accepted as the cheapest way of the investigation using mathematical modeling once can model almost all dangerous situation that take place in the real pipeline. But this is not enough. The pipeline when is use is the complex dynamical system, with many input and output signals. The input signals are the operator's commands, such as valve shutting, pump start, tank changeover, etc. output signals are the measurements of pressure and flow in situ, using special pressure sensors and flowmeters. As the case may be the pipeline can reach different states, depending on what command the operator has input. The wrong command can entail serious consequences. For example, the wrong stop of the pump can entail pipeline breakdown and therefore oil spill. But if it was possible for operator to control the flow process in the pipeline using its' online model one would avoid the accident. Mathematical model of a pipeline as a system with distributed parameters is represented with the hyperbolic system of partial equations and boundary conditions. To solve this system means to obtain the system state in the future time moments. But solving the hyperbolic system of partial equations is impossible without known initial state and boundary conditions at the next time moments. To know the state of the pipeline means to know the flow velocity and pressure distributions along the pipe. Despite the boundary conditions the initial state cannot be measured directly. Hence, one has to use identification methods to obtain the current state and to make a prediction on the basis of one. Identification of the current state can be carried out on the basis of some measurements from the past, i.e. using the latest history of date, obtained from pressure sensors.