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Unformatted text preview: Chapter 3 : Mathematical Analysis of Material Balance Equations and Process Flow Sheets Department of Chemical and Biological Engineering The University of British Columbia 2006 1 Introduction Chemical process synthesis is evolutionary. We start with the basics: What product do we want to make? What raw materials are available? What reactions are feasible? We then move on to sketches of simple block flow diagrams, we identify the key process units required, and consider how to connect these units together. We make simplifying approximations, quickly complete process flow calculations, and make preliminary assessments for alternative arrangements. Once one or more preliminary block flow diagrams have been sketched, we use more detailed specifications of stream composition and system performance. To evaluate process performance we carry out a series of sensitivity analyses. We take a more rigorous, mathematical, and systematic look at process flow calculations. 2 Material BalanceAgain We already introduced the material balance equation as Input Output + Generation Consumption = Accumulation We learned the importance of clearly defining a system, identifying components, and defining stream and system variables. We will revisit these ideas with three goals in mind: 1. To reiterate the importance of mastering these concepts 2. To develop more complete and rigorous expressions for the material balance equation 3. To illustrate use of the material balance equation in solving more challenging process flow problems. 3 Conservation of Mass and the Material Balance Equation Recall the definition of system : It has a defined boundary (surface area) which encloses a volume. If material enters and leaves the system, it crosses the system boundary. Within the system, physical and chemical changes may take place. Recall the law of conservation of mass : Mass is neither created nor destroyed (we ignore Einstein and E = mc 2 ). We will apply this law to the system illustrated in the following figure. The system contains a mixture of compound A (molar mass M A ), and compound B (molar mass M B ). The mass of A and B inside the system is m A , sys and m B , sys , respectively. 4 Conservation of Mass ... (2) (Top) System contains a mixture of A (large spheres) and B (small spheres) with one inlet and one outlet stream. (Bottom) Block flow diagram If the total mass in the system is m sys , then m sys = m A , sys + m B , sys (1) 5 Conservation of Mass ... (3) Stream 1 flows into the system and stream 2 flows out, with compounds A and B present in both. The total mass flow rate of streams 1 and 2 are m 1 and m 2 . Then m A1 , m B1 , m A2 , and m B2 denote the mass flow rates of compounds A and B in streams 1 and 2, and m 1 = m A1 + m B1 (2a) m 2 = m A2 + m B2 (2b) If m 1 and m 2 are constant, then the total mass entering the system over a time interval t is m 1 t and the mass leaving the system is m 2 t...
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 Winter '08
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