GNG1106 – Fundamentals of Engineering Computation Course ProjectChemical Engineering Transient Response of a Chemical ReactorThe study of chemical reactors is an important part of Chemical Engineering. The transient response of a chemical reactor is the change in the concentration of a chemical substance in the reactor when the concentration of an input flow is changed.Most of the chemical engineering applications will focus on mass balances for reactors. The mass balance is derived from the conservation of mass and states that inputs into the system minus the outputs from a system gives the accumulation of the mass in the system.Accumulation = inputs − outputs (Equation 1)The mass balance can be used for engineering problem solving by expressing the inputs and outputs in terms of measurable variables and parameters. For example, to apply mass balance to a conservative substance (that is, one that does not increase or decrease due to chemical transformations) in a reactor (Figure 1), the rate at which mass flows into the reactor through the inflow pipe and out of the reactor through the outflow pipe must be quantified. This can be done by taking the product of the flow rate Q(in cubic meters per minute) and the substance concentration c(in milligrams per cubic meter) for each pipe. Thus the input to the system is Qcinand the output from the system is Qc.Figure 1 – Simple reactor with single input and single outputWe are interested in the transient response (how the concentration of a substance in a reactor changes with time) of a completely mixed reactor (that is the concentration of the substance is the same throughout the reactor). To do this, we first develop a mathematical expression for the accumulation of mass in the reactor. For a constant-volume reactor (where the volume of liquid does not change), it can be simply formulated as Accumulation0V dc dt(Equation 2) where V= constant volume and c= concentration in the reactor. Thus, a mathematical formulation for accumulation is volume times the derivative of cwith respect to t; the equation represents how the accumulation of the chemical substance changes with respect to the change in concentration.The accumulation expressed in Equation 2 can be incorporated into a general mass balance framework. It can then be used to simulate the dynamics of a single reactor and a system of reactors. Only the single reactor shown in Figure 1 is considered. When the input flow and output flow rates are the same the volume in the reactor remains constant. The concentration of the output flow, c, is the same as the concentration of the substance in the reactor, that is, when input equals output the masse is conserved in the reactor (no accumulation occurs).Equations (1) and (2) can be combined to represent the mass balance for a single reactor shown in Figure 1: V dc=Qc Qc (Equation 3) dt inEquation (3) can be used to determine transient or time-variable response for the reactor, that is, how the concentration of the substance in the reactor can change over time, for a given initial concentration, c0(at time t=0) and the given flow concentrations cin(in the input flow) and c(reactor concentration). Applying calculus to Equation (3), the analytical solution for the change in reactor concentration over time is: