Optimization of chemical plant simulation using double collocation

A method has been constructed for the solution of a wide range of chemical plant simulation models including differential equations and optimization. Double orthogonal collocation on finite elements is applied to convert the model into an NLP problem that is solved either by the VF 13AD package based on successive quadratic programming, or by the GRG2 package, based on the generalized reduced gradient method. This approach is termed simultaneous optimization and solution strategy. The objective functional can contain integral terms. The state and control variables can have time delays. Equalities and inequalities containing state and control variables can be included into the model as well as algebraic equations and inequalities. The maximum number of independent variables is 2. Problems containing 3 independent variables can be transformed into problems having 2 independent variables using finite differencing. The maximum number of NLP variables and constraints is 1500. The method is also suitable for solving ordinary and partial differential equations. The state functions are approximated by a linear combination of Lagrange interpolation polynomials. The control function can either be approximated by a linear combination of Lagrange interpolation polynomials or by a piecewise constant function over finite elements. The number of internal collocation points can vary by finite elements. The residual error is evaluated at arbitrarily chosen equidistant grid-points, thus enabling the user to check the accuracy of the solution between collocation points, where the solution is exact. The solution functions can be tabulated. There is an option to use control vector parameterization to solve optimization problems containing initial value ordinary differential equations. When there are many differential equations or the upper integration limit should be selected optimally then this approach should be used. The portability of the package has been addressed converting the package from V AX FORTRAN 77 into IBM PC FORTRAN 77 and into SUN SPARC 2000 FORTRAN 77. Computer runs have shown that the method can reproduce optimization problems published in the literature. The GRG2 and the VF I 3AD packages, integrated into the optimization package, proved to be robust and reliable. The package contains an executive module, a module performing control vector parameterization and 2 nonlinear problem solver modules, GRG2 and VF I 3AD. There is a stand-alone module that converts the differential-algebraic optimization problem into a nonlinear programming problem.

Chemical reactions at nuclear fuel-clad interfaces

This thesis presents a study of the chemical reactions that may occur at the fuel- clad interfaces of fuel elements used in advanced gas-coooled reactors (A.G.R.) The initial investigation involved a study of the inner surfaces of irradiated stainless steel clad and evidence was obtained to show that fission products, in particular tellerium, were associated with reaction products on these surfaces. An accelerated rate of oxidation was observed on the inner surfaces of a failed A.G.R. fuel pin. It is believed that fission product caesium was responsible for this enhancement. A fundamental study of the reaction between 20%Cr/25%Ni/niobium stabilised stainless steel and tellerium was then undertaken over the range 350 - 850 degrees C. Reaction occurred with increasing rapidity over this range and long term exposure at ≤ 750 degrees resulted in intergranular attack of the stainless steel and chromium depletion. The reaction on unoxidised steel surfaces involved the formation of an initial iron-nickel-tellerium layer which subsequently transformed to a chromium telluride product during continued exposure. The thermodynamic stabilities of the steel tellurides were determined to be chromium telluride > nickel telluride > iron telluride. Oxidation of the stainless steel surface prior to tellerium exposure inhibited the reaction. However reaction did occur in regions where the oxide layer had either cracked or spalled.