TABLE OF CONTENTS Unstructured population balance models use a single variable, such as cell mass, to indicate the state of a cell in the culture. Unstructured models are the least complex PBMs, and will be explored in this and the following chapters. We will derive a general population balance model that uses cell mass or any other variable that is conserved in a cell division, together with associated substrate and product balances. The age population balance is also rederived together with the boundary conditions that are specific to cell age as the cell state parameter.
A state parameter such as cell mass is conserved in a cell division, in the sense that the sum of the mass of the two newly formed cells is equal to that of the cell that divided. All PBEs based on such a conserved cell state parameter share the same general form. Before deriving this model, we must define the physical setting of the cell population a little better. We will consider a culture inside a well-mixed vessel with one liquid feed stream and one liquid exit or product stream. The vessel may also be supplied with a gas feed for aeration and have an exit gas stream. However, as the gas streams do not contain any cells, they can be ignored for the moment. The two liquid streams are assumed to have the same volumetric flow rates and the feed stream is assumed sterile but will contain nutrients required for...
