(669c) Robust Process Modelling and Optimization Under Uncertainty

Authors: 
Abubakar, U., University of Aberdeen
Sriramula, S., University of Aberdeen, Aberdeen
Renton, N. C., University of Aberdeen, Aberdeen, United Kingdom



ROBUST PROCESS MODELLING AND
OPTIMIZATION UNDER UNCERTAINTY

Usman Abubakar, Srinivas Sriramula and
Neill C. Renton

Lloyd's
Register Foundation (LRF) Centre for Safety & Reliability Engineering,
University of Aberdeen, UK.

This paper
presents a new stochastic module that can be integrated into traditional
deterministic simulators to facilitate chemical process modelling, design, and
operations under uncertainty. The paper shows how the proposed stochastic
module could be employed to obtain a wide range of probabilistic process
performance measures to support decisions allowing improvements in process
robustness, cost efficiency, safety and reliability. The module can be applied
to model performance behaviour of processes with implicit or unknown
performance functions, linear or nonlinear responses, governed by Gaussian or
non-Gaussian random variables. There is also a provision for both random and
systematic sampling in the framework. Sample case studies have been performed
to highlight the applicability of the new module, including the one described
in Fig.1. It depicts a synthesis gas (syngas) production process, which is
subject to input noise.

Figure 1: Modelling
stochastic performance of syngas production process

Samples of sizes 1000,
2000, 10000 and 30000 were drawn from the assumed distributions of each of the
uncertain variables and the effects of the random inputs are propagated across
the process flow diagram using a traditional process simulation package. The sampling is automated so that a large number of
random outputs corresponding to the uncertain inputs can be obtained typically
in minutes.  The results are used to determine a limit state function, M = G(X),
where X is the vector of the random inputs, M ≤ 0 is
setup to split the process performance space into failure and success regions and
M = 0 defines the failure boundary. The properties of the random variables
are then used to determine the probability that P[M ≤ 0] , thus:

Equationnew.gif

Where fX(.)
is the joint probability density function. In addition, process
reliability/flexibility index, most probable design/operation condition,
performance space charts, global sensitivity indices, etc, can be obtained from
the module. Adding such capabilities to the traditional deterministic process
simulators provides a simple method of generating probabilistic performance
measures that can support chemical engineers as they seek to improve plant
safety, reliability and financial performance.