Error Estimation and Reliability in Process Calculations Subject to Uncertainties on Physical Properties and Thermodynamic Models
Estimation of physical properties
Cubic equations of state
Binary interaction parameter
Thermodynamic consistency test
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AbstractThe issues related to error propagation from uncertainties in physical properties and thermodynamic models involved in process modelling and simulation are examined. Traditionally, the effect of these basic parameters are ignored in chemical and process engineering and designers make the final decision on determining equipment parameters such as sizing and residence time in an ad-hoc manner based on their prior experience with similar problems. The objective of this dissertation is to develop a self-contained and consistent mathematical procedure to quantify the effect of uncertainties related to thermodynamic models on process design calculations for flow sheets of any complexity. The methodology is based on the Monte Carlo technique along with Latin Hypercube Sampling (LHS) method. The development of such an error propagation algorithm requires that the uncertainty information of physical properties of pure compounds and vapour-liquid equilibrium (VLE) data of binary mixtures be readily available. A pure component database was developed for 176 pure hydrocarbons in the range of C5 to C36 based on NIST’s ThermoData Engine (TDE) system. Two generalized correlations for the calculation of critical properties and acentric factors parameterized by the normal boiling point and specific gravity were re-parameterized. The Peng–Robinson (PR) equation of state was re-parameterized against the pure component database using a weighted nonlinear least squares method for the determination of its dependency on acentric factors and the definition of the uncertainty of its generalized parameters. The variance-covariance matrices for error propagation calculations were also determined for each model. Binary mixture database was also developed containing experimental VLE data and their uncertainties taken from TDE for 87 binary mixtures present in natural gas processing. The quality of each isothermal VLE dataset was investigated using a thermodynamic consistency test. The binary interaction parameters associated with their uncertainties for the re-parameterized PR equation of state along with the van der Waals quadratic mixing rules were evaluated against the consistent VLE data using nonlinear optimization coupled with the Monte Carlo method taking into account the uncertainties of input parameters. Using the databases developed in this study, a simple and general error propagation algorithm based on the Monte Carlo technique combined with the LHS sampling method was developed and coupled with the VMGSim™ process simulator to analyze the effect of uncertainties on chemical process design and simulation. The method was applied to simplified cases of industrial interest such as gasoline blending and injection of liquid hydrocarbon to the existing natural gas pipeline. The results show how the new approach can guide process engineers in revisiting process design decisions affected by uncertainties related to thermodynamics.
Schulich School of Engineering