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1 1 by the shaded area. Mass accumulates within the system at a rate dM/dt, owing to the competing effects of a convective flow input (mass flow rate in) and an output stream (mass flow rate out). 11. Balancing the total mass of an arbitrary system. 2 Formulation of Dynamic Models dV dt -= Fo-Fl The steady-state condition of constant volume in the tank (dV/dt = 0) occurs when the volumetric flow in, Fo, is exactly balanced by the volumetric flow out, F1. Total material balances therefore are mostly important for those modelling situations in which volumes are subject to change, as in simulation examples CONFLO, TANKBLD, TANKDIS and TANKHYD.

The above procedure is best illustrated in the simulation examples (BATCHD, TANKD, HOMPOLY, KLADYN, TUBED, TUBDYN, DISRE, DISRET, ENZSPLIT, ENZDYN, and BEAD). 1 39 Case A. Continuous Stirred-Tank Reactor (CSTR) The material balance for a continuous-flow , stirred-tank reactor with first-order reaction is and this is treated in more detail in Chapter 3. The dimensions for each term in the above equation are those of mass per unit time and the units would normally be kmol/s or kg/s. Dividing the balance equation by the volume of reactor, V, leads to the equation in the form This equation has two parameters z, the mean residence time (z = V/F) with dimensions of time and k , the reaction rate constant with dimensions of reciprocal time, applying for a first-order reaction.

Flow Term At moderate temperature changes cpi is again assumed constant and therefore the flow term is with the units 32 1 Basic Concepts energy This term actually describes the heating of the stream entering the system with temperature To to the reaction temperature T I , and is therefore only needed if streams are entering the system. Heat Transfer Term The important quantities in this term are the heat transfer area A, the temperature driving force or difference (Ta-Tl), where Ta is the temperature of the heating or cooling source, and the overall heat transfer coefficient U.

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