Analysis of Different Sampling Methods for the Simulation-Based Optimization Approach to Model Feedstock Development for Chemical Process Industry

Analysis of Different Sampling Methods for the Simulation-based Optimization Approach to Model Feedstock Development for Chemical Process Industry

Ismail Fahmi, Selen Cremaschi

Department of Chemical Engineering, The University of Tulsa, 800 South Tucker Drive, Tulsa, Oklahoma 74104, USA

10C04: Energy and Sustainability in Operations

Abstract

Chemical Process Industry (CPI) has been highly dependent on the fossil-based materials as the feedstock. As the reserve for this non-renewable resource depletes, alternative resources need to be discovered. Among many options, biomass is considered very promising because it is renewable, locally available, and abundant. However, incorporating biomass as a feedstock for CPI requires significant amounts of investments for both research and development (R&D) and production capacity expansions. How these investments will shape the evolution of the biomass to commodity chemicals (BTCC) system should be investigated. Moreover, the uncertain decision-dependent endogenous technology evolutions of the BTCC system complicate the analysis. Fahmi and Cremaschi [1] have presented a prototype simulation-based optimization (SIMOPT) approach to study the feedstock development for CPI. The SIMOPT framework explained in [1] uses the concept of generating multiple unique timelines to represent various controlled evolution of the system under uncertainties. The SIMOPT framework [1] uses deterministic optimization with stochastic simulation in an integrated fashion to study the impact of uncertainties on the system performance. Deterministic optimization is used to produce the optimum decision set for the system at its current state. The optimization formulation for the BTCC investment planning used in the SIMOPT framework is explained in detail in [2]. Stochastic simulation is used to predict the system performance under uncertainties. In a single SIMOPT run, the simulation proceeds through the time steps based on the decision set determined by the deterministic optimization. Because of the accumulated differences between the expected and the realized behavior of the system, the system performance under the original decisions may no longer be applicable or feasible at one point in time. This condition is called a trigger event. In case of a trigger event, the simulation is halted and deterministic optimization is recalled to determine a new set of optimal decisions for the remainder of the timeline. The control is passed back to simulation along with the new set of decisions. The iteration between the deterministic optimization and stochastic simulation continues until the final time step. After the completion of the final step, a unique controlled evolution of the system performance under uncertainties (i.e., one unique timeline) is generated. Multiple unique timelines are produced because of different realizations of the uncertain parameters. To have a thorough analysis of the BTCC system performance accounting for different uncertainties, a statistically significant number of timelines are required, i.e. the quality of the results depends on the quality of the uncertain variables' space coverage. This can simply be done by gathering a virtually infinite number of timelines. However, such an approach would be prohibitively expensive in computational costs. Therefore, the minimum number of timelines that will achieve preset statistical significance in the results should be determined. In this work, a systematic analysis using different sampling methods to cover the uncertain parameters space of the BTCC investment planning problem is presented. The sampling methods considered in this work are Monte Carlo Sampling, Latin Hypercube Sampling, Univariate Dimension Reduction, Hammersley Sampling, and Halton Sampling. The performance metrics used for the comparison of these methods are the stabilization of four statistical moments (i.e., mean, variance, skewness, and kurtosis) of the objective and the overall objective distribution shape using the Smirnov test. A BTCC system of ethylene production is presented as the case study.

Keywords: BTCC investment planning, simulation-based optimization, sampling methods comparison

References:

[1]        I. Fahmi and S. Cremaschi, "A Prototype Simulation-based Optimization Approach to Model Feedstock Development for Chemical Process Industry," 22nd European Symposium on Computer Aided Process Engineering, 2012.

[2]        I. Fahmi and S. Cremaschi, "Stage-gate Representation of Feedstock Development for Chemical Process Industry," Foundations of Computer-Aided Process Operations 2012, vol. , 2011.