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1.6 Basic Methodology of Model Development

In this section, we discuss the basic procedure for developing mass transfer models. The starting point for model formulation is to choose a control volume and mark its boundary surface (i.e., the control surface). A system or control volume can be defined as any part of the equipment, as the entire equipment, or even as the large-scale system as a whole. The basic conservation laws are then applied to the system. Conservation law is discussed in Section 1.7.

Control volume can be of any size and shape. Typically, models at three levels are developed based on the size of the control volume: differential models, macroscopic (or macroscale) models, and mesoscopic (or mesoscale) models. These three types of models are explained sequentially in the following sections. On the topmost level is the differential control volume and the differential models. This type of model contains the local information at each point in the continuum. However, for design of process equipment, macro or meso levels may also be used. Although models at these levels are not as detailed as the differential models, they are easier to solve and to apply in practical designs. Hence modeling at all three levels is covered in this book.

For modeling very large or complex systems, such as transport of a pollutant in the environment or drug metabolism in the human body, the system is divided into a number of interconnected compartments and a macroscale model is applied to each compartment. Applications of these so-called compartment models are provided in Chapter 13.

Conservation laws alone are not sufficient to complete the model, since the model will contain terms for the mass crossing into a control surface. Hence additional closure relations are needed. For example, a differential model using the conservation principle alone will contain the flux vector as a parameter. This system has to be closed and a flux versus concentration relation has to be applied using a constitutive model. Similarly, the macro- and meso-level models may contain terms such as the mass crossing a larger-size control surface or from one phase to another. Suitable transport laws must be applied to close these terms, thereby completing the model. Hence coupling the conservation laws together with suitable transport law is the basic methodolgoy in developing mass transfer models.

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