1. Considering Physical Property Uncertainties in Process Design Abstract A systematic procedure has been developed for process unit design based on the “worst case” combination of physical property values and other process variables that are bounded within uncertainty limits. This procedure has been implemented using Polymath™ and MATLAB® for the design of a heat exchanger and a tubular reactor. It is shown that in some cases relatively small uncertainties in the property data may lead to disproportionally large increase in the key design parameter value ; thus the use of this systematic procedure is recommended. Mordechai Shacham, Dept. of Chem. Engng, Ben Gurion University of the Negev, Beer-Sheva, Israel Neima Brauner, School of Engineering, Tel-Aviv University, Tel-Aviv, Israel Michael B. Cutlip, Chem. Engng, University of Connecticut, Storrs, CT, USA MATLAB functions for finding the “worst case” cooler length  Parameter uncertainties may have a great effect in process unit design, and the design should often consider the “worst case” scenario so that the process unit will be able to carry out its task properly for the full range of possible parameter values.  An important class of parameter values used in the design of most process units is represented by the collection of physical properties of the chemical compounds involved.  Parameter uncertainty is usually considered in the context of process optimization as the following minimax problem s. t. h ( d, z, θ ) = 0; g ( d, z, θ ) ≤ 0 and θ L ≤ θ ≤ θ U where C is a scalar cost function, d is a vector of design variables, s is a vector of state variables, θ is a vector of parameters with θ L as lower and θ U as upper bounds, h, g are vectors of equality and inequality constraint functions respectively.  For determining the “worst case” scenario no design parameter optimization need to be carried out and only the maximum in θ of C ( d, z, θ ) is sought.  The cost function C usually represents a key dimension of the process unit that has the greatest effect on its cost (length of a heat exchanger or a reactor volume).  The constraint functions h utilize the mathematical model of the process unit, and the parameters θ are physical, thermodynamic and additional properties for which the uncertainties are known.  The use of the proposed technique is demonstrated using the DIPPR 1 database as source of the property data and uncertainty values, POLYMATH 2 is used for constructing and solving the process unit models and the MATLAB3 fmincon.m function is used for maximizing the objective function subject to constraints and uncertainty limits. 1 http://www.aiche.org/dippr/ 2 http://www.polymath-software.com 3 http://www.mathworks.com Partial MATLAB formatted model of the cooler (generated in part by POLYMATH POLYMATH results for nominal physical property values Conclusions Design of Co-current Flow Double Pipe Cooler Find heat exchanger length that yields hot fluid exit temperature of 80 ºF Co-current flow, double pipe cooler representation in POLYMATH format Use of the fmincon library function for maximizing the cooler’s length subject to the physical property uncertainties % property uncertainties  A simple, systematic, fully numerical procedure for process unit design with some of the parameters subject to uncertainties has been developed.  The examples presented in the poster and the associated extended abstract demonstrate that the use of this procedure for “worst case” is absolutely essential as in some cases relatively small uncertainties in the property data may lead to disproportionally large increase in the key design parameter value Functions for iterating on exchanger length to reach 80 ºF exit temp. of benzene. Solution for the case when physical properties are subject to the most extreme uncertainty values