Initial value problems chemical reactor

Engineers develop mathematical models to describe processes of interest to them. For example, the process of converting a reactant A to a product B in a batch chemical reactor can be described by a first order, ordinary differential equation with a known initial condition. This type of model is often referred to as an initial value problem (IVP), because the initial conditions of the dependent variables must be known to determine how the dependent variables change with time. In this chapter, we will describe how one can obtain analytical and numerical solutions for linear IVPs and numerical solutions for nonlinear IVPs. 

In section 3.2.7, boundary value problems were solved as initial value problems. This methodology is especially useful for predicting the performances in chemical reactors. Maple s stop condition was used in this section to obtain t] vs. O curves. This is very useful because, it is generally easier to solve an initial value problem than a boundary value problem. This technique was then used in section 3.2.8 to predict multiple steady states in a catalyst pellet in section 3.2.8. This methodology is extremely useful for predicting the hysteresis curves in multiple steady state problems. 

Chapters 8-11 treat problems that are governed by differential equations. Chapter 8 provides methods to model chemical reactors. These are usually initial value problems, which are illustrated in Eq. (1.1). 

When it is necessary to include these effects - slow reaction rates, catalysts, heat transfer, and mass transfer - it can make an engineering problem extremely difficult to solve. Numerical methods are a must, but even numerical methods may stumble at times. This chapter considers only relatively simple chemical reactors, but to work with these you must leam to solve ordinary differential equations as initial value problems. 

Modeling of process equipment often requires a careful inspection of start-up problems that lead to differential equations of initial value type, for example, modeling of chemical kinetics in a batch reactor and modeling of a plug flow reactor. For the first example with two reactions in series... 

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