CHE 321 Lecture Notes - Lecture 10: Invertible Matrix, Detailed Balance, Reaction Rate Constant

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4 Oct 2017

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Consider n species 1,2, , that are involved in a set of first-order reversible reactions. , = 1,2, , is a rate constant of reaction producing from . , =, (1) is the concentration of . The rate of reaction can be written as: Consider an isothermal constant volume, well stirred batch reactor. Define = 12 (3) can be written as: = 0 has solutions, but one of them will satisfy, = 0 = 0 = 0 . Eigenvalues are 0,1,2, , 1 1,2, ,. ,0 = 0. This means not only system is in equilibrium, but also every reaction is independently in equilibrium. 2017 meenesh r. singh (mrsingh@uic. edu) k ij k a ji k is a symmetric matrix. K has real eigenvalues has real eigenvalues. k. 8eq x j x i k j i k ij k. Theorem: let a be a symmetric matrix (with real eigenvalues) and x be any vector in n d .

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Learning objectives To gain an understanding of how to derive mathematical models to describe the operation of batch, semi-batch and continuous flow reactors. To gain an understanding of how to use mathematical models, by employing a numerical method, to find the performance characteristics of chemical reactors such as the product distribution. Skills outcomes Ability to analyse modes of process operation of chemical reactors. Ability to solve problems related to reactor design and employ appropriate numerical techniques to perform quantitative analysis of reactor performance. Assignment Description Consider the batch process shown in Figure 1: a stirred tank (CSTR-100) is connected in series with a reactor (CRV 100) containing a mass per unit volume, W, of solid catalyst. The reactants and products of the reaction process are all liquids which are circulated via a pump (P-100), There is no feed to this closed-loop system and no product is withdrawn. No chemical reaction process occurs in the absence of catalyst hence none occurs in the stirred tank. Assume that initially the tank and reactor contain only reagent A You may also assume: the tank and the reactor are instantaneously well mixed, there is no change in fluid density accompanying the reaction process. the volume of the liquid in the connecting pipe work may be neglected, there is no resistance to mass transfer in the reactor (at the interface between the solid-catalyst particles and the liquid), Figure 1 schematic diagram of units in the batch process The reaction scheme is A notequalto B rightarrow C The first reaction is first order with respect to A in the forward direction, with rate constant, k_u and first order with respect to B in the reverse direction with rate constant, k_lb The second reaction is irreversible and first order with respect to B with rate constant k_a For a solid-catalysed process an appropriate batch-reactor performance equation for reagent A is I/C_A0 = V/W integral_0^XA dX_A/-r_A^r Here, t is elapsed time, C_sa is the initial concentration of reagent A V is the volume of liquid in the reactor, X_a is the fractional conversion of reagent A and r_A^r is the rate of appearance by chemical reaction of reagent A in moles per unit mass of solid-catalyst per unit time. What are the units of the rate constants The volume of the stirred tank is V_1 and the volume of the void-space in the reactor is V_2. By performing a material balance derive performance equations describing the time dependence of the concentration of reagent A and products Band C in the stirred tank. Explain the meaning of any terms you introduce Similarly derive performance equations describing the time dependence of the concentration of reagent A and products Band C in the reactor. Explain the meaning of any terms you introduce Using the performance equations you have derived in parts and investigate how the distribution of products the tank and in the reactor varies with time depending on la the ratio where q is the volumetric flow rate, the ratio the ratio and the ratio Assume that is constant, 1 mole/litre, and that v_2 and w are constant. In your assignment report you must provide the evidence on which you have based your investigation and hence your conclusions. This includes output from any numerical approach you use to solve the performance equations such as the Euler method implemented in an Excel spreadsheet, You must decide on an appropriate range of ratio values to use for (d and then justify the values you have selected in your write-up. You should mot write more than 2500 words for part excluding table captions and figure captions. Provide a brief summary to your report

CHE 321 Lecture Notes - Lecture 10: Invertible Matrix, Detailed Balance, Reaction Rate Constant

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