Stochastic kriging (SK) methodology has been known as an effective metamodeling tool for approximating a mean response surface implied by a stochastic simulation. In this paper we provide some theoretical results on the predictive performance of SK, in light of which novel integrated mean squared error-based sequential design strategies are proposed to apply SIC for mean response surface metamodeling with a fixed simulation budget. Through numerical examples of different features, we show that SIC with the proposed strategies applied holds great promise for achieving high predictive accuracy by striking a good balance between exploration and exploitation. Published by Elsevier B.V.

Fischer-Tropsch Synthesis (FTS) is a promising technology for the production of ultra-clean fuels and chemical feedstocks from biomass, coal, or natural gas. Iron catalysts are ideal for conversion of coal and biomass. However, precipitated iron catalysts used in slurry-bubble column reactors suffer from high attrition resulting in difficulty separating catalysts from product and increased slurry viscosity. Thus, development of an active and selective-supported iron catalyst to manage attrition is needed. This thesis focuses on the development of a supported iron catalyst and kinetic models of FTS on the catalyst using advanced statistical methods for experimental design and analysis. A high surface area alumina, modified by the addition of approximately 2 wt% lanthanum, was impregnated with approximately 20 wt% Fe and 1% Pt in a two step procedure. Approximately 10 wt% Fe and 0.5 wt% Pt was added in each step. The catalyst had a CO uptake of 702 μmol/g, extent of reduction of 69%, and was reduced at 450°C. The catalyst was stable over H2 partial pressures of 4-10 atm, CO partial pressures of 1-4 atm, and temperatures of 220-260°C. Weisz modulus values were less than 0.15. A Langmuir-Hinshelwood type rate expression, derived from a proposed FTS mechanism, was used with D-optimal criterion to develop experiments sequentially at 220°C and 239°C. Joint likelihood confidence regions for the rate expression parameters with respect to run number indicate rapid convergence to precise-parameter estimates. Difficulty controlling the process at the designed conditions and steep gradients around the D-optimal criterion resulted in consecutive runs having the same optimal condition. In these situations another process condition was chosen to avoid consecutive replication of the same process condition. A kinetic model which incorporated temperature effects was also regressed. Likelihood and bootstrap confidence intervals suggested that the model parameters were precise. Histograms and skewness statistics calculated from Bootstrap resampling show parameter-effect nonlinearities were small.