Pipeline Heating Method Based on Optimal Control and State Estimation
Heat Transfer Engineering
In production of oil and gas wells in deepwaters the flowing of hydrocarbon through pipeline is a challenging problem. This environment presents high hydrostatic pressures and low sea bed temperatures, which can favor the formation of solid deposits that in critical operating conditions, as unplanned shutdown conditions, may result in a pipeline blockage and consequently incur in large financial losses. There are different methods to protect the system, but nowadays thermal insulation and
... nsulation and chemical injection are the standard solutions normally used. An alternative method of flow assurance is to heat the pipeline. This concept, which is known as active heating system, aims at heating the produced fluid temperature above a safe reference level in order to avoid the formation of solid deposits. The objective of this paper is to introduce a Bayesian statistical approach for the state estimation problem, in which the state variables are considered as the transient temperatures within a pipeline cross-section, and to use the optimal control theory as a design tool for a typical heating system during a simulated shutdown condition. An application example is presented to illustrate how Bayesian filters can be used to reconstruct the temperature field from temperature measurements supposedly available on the external surface of the pipeline. The temperatures predicted with the Bayesian filter are then utilized in a control approach for a heating system used to maintain the temperature within the pipeline above the critical temperature of formation of solid deposits. The physical problem consists of a pipeline cross section represented by a circular domain with four points over the pipe wall representing heating cables. The fluid is considered stagnant, homogeneous, isotropic and with constant thermo-physical properties. The mathematical formulation governing the direct problem was solved with the finite volume method and for the solution of the state estimation problem considered here, we used the Particle Filter. The optimal control was based on a linear quadratic controller and an associated quadratic cost functional, which was minimized through the solution of Riccati's equation.