olymers. It has been found that the most economical and efficient way to produce such chemicals on a large scale is via the continuous process operating in the steady-state. This is the reason for the emphasis on this type of material balance problem Another class of material balance problems is those involving blending and mixing. A sub stantial number of the products produced by the chemical processing industries are blends or mix- tures of various constituents or ingredients. Examples of blends are gasoline and animal feeds of precise mixtures, prescription drugs and polymeric resins Dynamic material balance problems arise in the operation and control of continuous processes. Also, batch processes, by their very nature, are dynamic. In either case we must consider how the state of the process varies as a function of time. In addition to determining the flow rates and compositions of the interconnecting streams, we must also follow the changes in inventory within the process itself. In the three types of problems just discussed, we are interested in predicting the performance of the process or equipment. Our models start by assuming that the law of conservation of mass is obeyed. A fourth type of problem, which encountered by engineers in the plant, starts with actual operating data, generally flow rates and compositions of various streams The problem is to determine the actual performance of the plant from the available data This, in many ways, is a much more difficult problem than the first three. Why? Simple The data may in error for one reason or another. A flow meter may be out of calibration or broken entirely. A composition measurement is not only subject to calibration errors but sampling errors as well. Thus the first thing one must do when dealing with plant data is to determine, if possible, whether or not it is accurate. If it is, then we can proceed to use it to analyze it to determine process performance. If not, we must try to determine what measurements are in error, by how much, and make the appropriate corrections to the data. This is known as data reconciliation and is possible only if we have redundant measurements B. Historical Perspective The solution of material balance problems for continuous steady-state processes of any complexity used to be very difficult. By its nature, the problem is one of solving a large number of simultaneous algebraic equations, many of which are highly nonlinear. Before the availability of computers and the appropriate software, the solution of the material balance model for a chemical process typically took a team of chemical engineers using slide rules and adding machines days or weeks, if not months. And given the complexity of the problem, errors were ommon The methods used in those days to solve material balance problems days are best described as ad hoc. Typically an engineer started with the process specifications such as the production-2- polymers. It has been found that the most economical and efficient way to produce such chemicals on a large scale is via the continuous process operating in the steady-state. This is the reason for the emphasis on this type of material balance problem. Another class of material balance problems is those involving blending and mixing. A sub￾stantial number of the products produced by the chemical processing industries are blends or mix￾tures of various constituents or ingredients. Examples of blends are gasoline and animal feeds; of precise mixtures, prescription drugs and polymeric resins. Dynamic material balance problems arise in the operation and control of continuous processes. Also, batch processes, by their very nature, are dynamic. In either case we must consider how the state of the process varies as a function of time. In addition to determining the flow rates and compositions of the interconnecting streams, we must also follow the changes in inventory within the process itself. In the three types of problems just discussed, we are interested in predicting the performance of the process or equipment. Our models start by assuming that the law of conservation of mass is obeyed. A fourth type of problem, which encountered by engineers in the plant, starts with actual operating data, generally flow rates and compositions of various streams. The problem is to determine the actual performance of the plant from the available data. This, in many ways, is a much more difficult problem than the first three. Why? Simple. The data may in error for one reason or another. A flow meter may be out of calibration or broken entirely. A composition measurement is not only subject to calibration errors but sampling errors as well. Thus the first thing one must do when dealing with plant data is to determine, if possible, whether or not it is accurate. If it is, then we can proceed to use it to analyze it to determine process performance. If not, we must try to determine what measurements are in error, by how much, and make the appropriate corrections to the data. This is known as data reconciliation and is possible only if we have redundant measurements. B. Historical Perspective The solution of material balance problems for continuous steady-state processes of any complexity used to be very difficult. By its nature, the problem is one of solving a large number of simultaneous algebraic equations, many of which are highly nonlinear. Before the availability of computers and the appropriate software, the solution of the material balance model for a chemical process typically took a team of chemical engineers using slide rules and adding machines days or weeks, if not months. And given the complexity of the problem, errors were common. The methods used in those days to solve material balance problems days are best described as ad hoc. Typically an engineer started with the process specifications such as the production