# Industrial Application of Material Balances Causes of Inconsistencies in Process Models and Industrial Processes

Process simulators, which initially were used for material and energy balances, are now used by process engineers for a number of important activities, including process design, process analysis, and process optimization. Process design involves selecting suitable processing units such as reactors, heat exchangers, distillation columns etc. and sizing them so that the feed to the process can be efficiently converted into the desired products. Process analysis involves comparing predictions of process variables using models of the process units with the measurements made in the operating process.

By comparing corresponding values of variables, you can determine if a particular process unit is functioning properly. If discrepancies exist, the predictions from the model can provide insight into the root causes of any problems.

In addition, process models can be used to carry out studies that evaluate alternate processing approaches and studies of debottlenecking, that is, methods designed to increase the production rate of the overall process. Process optimization is directed at determining the most profitable way to operate the process. For process optimization, models of the major processing units are used to determine the operating conditions, such as product compositions and reactor temperatures, that yield the maximum profit for the process.

Models of the processing units are based on material balances. For simple equipment, just a few material balances for each component in the system are sufficient to model the equipment. For more complex equipment such as distillation columns, you will find the models involve material balance equations for each component on each tray in a column, and some industrial columns have over 200 trays. For process design and most of process analysis, each processing unit can be analyzed and solved separately. Modern computer codes make it possible to solve extensive sets of simultaneous equations.

For example, the optimization model for an ethylene plant usually has over 150,000 equations with material balances comprising over 90% of the equations.

## Issues in the Solution of Equations in Models

The simultaneous solution of the large number of equations in process models presents a major challenge for commercial software vendors who develop and maintain the process models used for process design, process analysis, and process optimization.

Computational efficiency and solution reliability, including stability and convergence of algorithms, are two important factors affecting the use of commercial process simulators. If an excessive amount of computer time is required to solve the model equations, the utility of the simulators can be seriously undermined, particularly for process optimization applications, because they involve a large number of equations and naturally require considerable computer time for their solution. Also, optimization applications are applied continuously to many processes so that a long time to achieve a solution, or failure of the algorithm used to solve the equations, seriously degrades the performance of the software, and can make it impossible to obtain any expected benefits. You should be aware that the computational efficiency and reliability of software are affected by the way in which you formulate the process model equations and the order in which you enter them into the computer. In general, the more linear is a set of model equations, the faster the set can be solved, and the more reliable the solution.

## Material Balance Closure for Industrial Processes

One important way in which individual material balances are applied industrially is to check that "in = out", that is, to determine how well the material balances balance using process measurements in the equations. You look for what is called closure, namely that the error between "in" and "out" is acceptable. The flow rates and measured compositions for all the streams entering and exiting a process unit are substituted into the appropriate material balance equations. Ideally, the amount (mass) of each component entering the system should equal the amount of that component leaving the system.

Unfortunately, the amount of a component entering a process rarely equals the amount leaving the process when you make such calculations.

The lack of closure for material balances on industrial process occurs for several reasons:

- The process is rarely operating in the steady state. Industrial processes are almost always in a state of flux, and rarely reach precise steady-state behavior.
- The flow and composition measurements have a variety of errors associated with them. First, sensor readings have noise (variations in the measurement due to more or less random variations in the readings that do not correspond to changes in the process). The sensor readings can also be inaccurate for a wide variety of other reasons. For example, a sensor may require recalibration because it degrades, or it may be used for a measurement for which it was not designed.
- A component of interest may be generated or consumed inside the process by reactions that the process engineer has not considered.

As a result, material balance closure to within 5% for material balances for most industrial processes is considered reasonable.

Closure is defined as the calculated difference between the amount of a particular material entering and exiting the process divided by the amount entering multiplied by 100. If special attention is paid to calibrating sensors, material balance closure of 2 to 3% can be attained.

If special high accuracy sensors are used, smaller closure of the material balances can be attained, but if faulty sensor readings are used, much greater errors in material balances are observed. In fact, **material balances can be used to determine when faulty sensor readings exist.**