[en] To increase the precision and reliability of process control, random uncertainty factors affecting the control system must be accounted for. We propose a novel approach based on the operational matrix technique for robust PI controller design for dead-time processes with stochastic uncertainties in both process parameters and inputs. The use of the operational matrix drastically reduces computational time in controller design and statistical analysis with a desired accuracy over that of the traditional Monte-Carlo method. Examples with deterministic and stochastic inputs were considered to demonstrate the validity of the proposed method. The computational effectiveness of the proposed method was shown by comparison with the Monte-Carlo method. The proposed approach was mainly derived based on the integrator plus dead-time process, but can be easily extended to other types of more complex stochastic systems with dead-time, such as a first-order plus dead-time or a second-order plus dead-time system

[en] Highlights: • Reliability of the SMR liquefaction process is effectively measured. • A gPC based surrogate modeling approach is applied for uncertainty quantification. • Sobol sensitivity indices are obtained directly from the surrogate model. • Computational time is significantly reduced compared to MC/qMC approaches. -- Abstract: To develop a safe and profitable process, uncertainty quantification is necessary for a reliability, availability, and maintainability (RAM) analysis. The uncertainties of 3% in each key decision variables are propagated which could bring the system into an unreliable/risk region. Hence, in this study, uncertainty quantification (UQ) with simultaneous determination of sensitivity indices (SI) is proposed using generalized polynomial chaos (gPC) modeling approach. This approach reduces about 90% of the total computational time when compared with the conventional simulation approaches required for a complex first principle based model. Subsequently, a knowledge inspired reliability analysis is carried out using the uncertainty analysis (UA). By using the statistical properties of the process, for example, mean/optimal value at 50% failure give the bound between [0.7174, 0.9496] for LNG product stream. Further, it was found that LNG with 10% end flash gas (or 90% liquefaction rate) can be obtained with a failure probability of 14.43%. This value of reliability is promising for a given specified deviation; hence, the process could be assumed to be near to its reliable optimal operational region.

[en] Highlights: • Uncertainty quantification was performed to measure the reliability of natural gas liquefaction process. • Surrogate model using polynomial chaos expansion approach was used for sensitivity analysis. • Sobol′ sensitivity indices can be obtained directly from the surrogated gPC model. • Study helps the robust design by evaluating the bounds and reliability based on confidence levels. The practical quantification of a model's ability to describe information is extremely important for the practical estimation of model parameters. Hence, in this study, a complex sweet natural gas refrigeration chemical process was selected for uncertainty quantification (UQ) and sensitivity analysis (SA). A computer code was generated to create a hybrid digital simulation system (HDSS) to connect two commercially important software programs, namely Matlab and Aspen Hysys. Monte Carlo (MC) and Halton based quasi-MC (QMC) methods were used for uncertainty propagation (UP) and uncertainty quantification (UQ). A surrogate model based on the polynomial chaos expansions (PCE) approach was applied for SA. Sobol′ sensitivity indices were evaluated to identify influential input parameters. The proposed PCE methodology was compared with a traditional MC based approach to illustrate its advantages in terms of computational efficiency and acceptable accuracy. The results indicated that UQ and SA help in an in-depth understanding of the chemical process determining the feasibility and improving the operation based on reliability and consumer demands. This study used in the robust design by evaluating the bounds and reliability based on confidence levels and thereby increasing the reliance of the process at hand.

[en] Highlights: • Uncertainty quantification and sensitivity analysis for LNG process. • Standard Monte Carlo (MC) method is utilized. • Relative percentage of the Sobol total effect indices for DMR LNG process. • Probability distribution of the approach temperature for DMR liquefaction process. • Global sensitivity analysis with less computational effort. -- Abstract: The dual mixed refrigerant (DMR) liquefaction process is complicated and sensitive compared to the competitive propane pre-cooled mixed refrigerant liquefied natural gas (LNG) process. When any uncertainty is introduced to the process operation conditions, it is necessary for the DMR process to be re-optimized to maintain efficient operation at a minimal cost. However, in actual operation, re-optimization is a challenging task when the process operational input variables are varied, typically owing to the lack of information regarding the nature, impact, and levels of uncertainty. Within this context, this study investigates the uncertainty levels in the overall energy consumption and minimum internal temperature approach (MITA) inside LNG heat exchangers with variations in the operational variables of the DMR processes. Moreover, a global sensitivity analysis is conducted to identify the influence of random inputs on the process performance parameters. The required energy is significantly influenced by the variations in the variables in the cold mixed refrigerant (approximately 63%), while changes in the warm mixed refrigerant (WMR) section only slightly affect the uncertainty of the required specific energy. Furthermore, the probability distribution of the approach temperature (MITA1) inside the WMR exchanger is mainly affected by changes in the compositions of methane, ethane, and propane, as well as the high pressure of the cold mixed refrigerant (approximately 97%). Conversely, the flow rate of ethane and low pressure of the WMR significantly affect the uncertainty of the approach temperature (MITA2) inside the cold mixed refrigerant exchanger.