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Non-iterative design of multiple effect evaporators using Excel add-ins Abstract

All undergraduate engineering texts that cover multiple effect evaporation present the solution procedure as necessarily trial-and-error. We present a solution method for multiple effect evaporators that directly solves the nonlinear equations. We do this in Excel by using the solver function and a free add-in that automates steam table look-ups. The solution procedure draws heavily from the degree of freedom analysis taught in the introductory material and energy balances course.

Introduction

Multiple effect evaporation is an industrially important unit operation. It is the foundation of several industries, including, for example, the production of sugar, which had over $6.9 billion in revenues in the United States alone in 20081. Teaching multiple effect evaporation in the junior year of the chemical engineering curriculum reinforces and integrates key topics from the sophomore year such as mass and energy balances, structured problem solving, and steam table calculations. As a side benefit, teaching multiple effect evaporation allows the opportunity to discuss the work of Norbert Rillieux2, and his role as an inventor, entrepreneur, and engineer of color. However, in spite of multiple effect evaporation being industrially relevant and pedagogically useful, it remains relatively little taught.

Multiple effect evaporation is included in a few unit operations texts3,4, but it is not covered in chemical engineering heat transfer, separations (with one exception5), design, or transport textbooks. However, every text that covers multiple effect evaporation presents the solution procedure as necessarily iterative (a.k.a. trial-and-error). Textbooks published as recently as 2006 continue to perpetuate this trend, despite the fact that with modern tools iterative solutions are no longer necessary.

In our program evaporation is covered in the sixth semester fluid flow and heat transfer class; concurrent with thermodynamics. In this paper, we present a non-iterative method students can use to solve multiple effect evaporator problems using a free add-in for Microsoft Excel.

In a typical multiple effect evaporator homework problem (Figure 1) the feed conditions and flow rate (F) are given. The overall heat transfer coefficients (Ui) are assumed to be known. The desired final concentration (x1) is specified as well as the pressure (or equivalently, the temperature) of the saturated steam used as the heat source (Ps). Additionally, the pressure in one effect (usually the last) is specified (P3). The task of the students is to find the amount of steam that must be fed to the first effect (S), the unknown liquid and vapor flow rates (V1, V2, V3, L1, L2, L3), the pressures in the other effects (P1, P2), and heat transfer area of each effect (A). Generally the heat transfer areas for all effects are assumed equal. H (h) is the enthalpy of the vapor (liquid) phase with corresponding temperature Ti and latent heat λi.

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VanAntwerp, J., & Sykes, A., & si, X. (2009, June), Noniterative Design Of Multiple Effect Evaporators Using Excel Add Ins Paper presented at 2009 Annual Conference & Exposition, Austin, Texas. 10.18260/1-2--5709