Further Reading: The Concept of Balances Let’s explore this general concept in more detail as it underlies so much of fundamental chemical engineering analysis, thinking, and problem solving. Assuming that we have the appropriate understanding of the fundamentals of our reaction and the physical properties of our materials, we can begin to think about the design of a process to manufacture the materials of interest. There are two fundamental concepts that must be understood and taken into account into the design and operation of any process: mass or material balance and system boundary. 1) Mass (material) Balance Concepts First, (material) mass must be conserved. Put another way, what comes out of a process must be what we put into it plus whatever mass is accumulating within a system. Chemical Engineering Progress and the Beacon publication from AIChE’s Centre for Chemical Process Safety have reported many cases of major fire and environmental disasters via the simple mechanism of overflowing tanks. The most significant of these was the Flixborough disaster (Figure 1), summarized in a Chemical Engineering Progress “Beacon” article (9/2006, p. 17). Faulty instrumentation, an inadequate number of layers of protection, and insufficient communication have all been causes of major environmental and fire disasters.
Figure 1: Incident Summary: Flixborough Case History, AIChE, 2013. All of the process control instrumentation we use in actual product processes are designed to calculate balances but a number of things can happen that can cause surprises: 1) A reaction, with a very slow kinetic rate constant (more later), may be forming a material in the process that was unanticipated. Depending upon the downstream processing and how the anticipated products are handled (distillation, filtration, crystallization, etc.), this material may “bleed” out of the system after building up to a certain level. So eventually the mass balance will close, but in a short or intermediate time frame, it may not. 2) An unanticipated liquid reaction product, with a boiling point, which inter- feres with a distillation separation downstream, can cause a temporary build-up of material.
3) An unanticipated solid reaction product that precipitates out of solution and builds up in process equipment, possibly blocking process piping. We can consider a very simple example of a material balance for boiling a salt solution to increase its concentration, as shown in Figure 2. Let’s assume that we have 100 kg of a 10% salt solution entering an evaporator, and we want to increase its concentration to 50%. How much water has to be evaporated?
Figure 2: Salt evaporator material balance. Let’s first start with the feed stream. We have 100 total kg with 10% salt, so 0.10 Ă— 100 means there are 10 kg of salt in the feed stream. That also means there must be 100 − 10 or 90 kg of water in the feed. How much salt is in the concentrated product coming out of the evaporator? Since we know that salt does not have a vapor pressure and will not boil, we know that all of the salt must be coming out of the evaporator, meaning there is also 10 kg salt leaving the evaporator. How much water (x) was evaporated? We can calculate this with a simple mass balance calculation. If there is 10 kg of salt leaving the evaporator (the same as entered) and the solution is 20%, then the amount of water leaving the evaporator can be calculated as follows: 10 = 0.20(y) where y is the total solution amount: đ?‘Śđ?‘Ś =
10 = 50 đ?‘˜đ?‘˜đ?‘˜đ?‘˜ đ?‘œđ?‘œđ?‘œđ?‘œ đ?‘Ąđ?‘Ąđ?‘Ąđ?‘Ąđ?‘Ąđ?‘Ąđ?‘Ąđ?‘Ąđ?‘Ąđ?‘Ą đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ đ?‘ 0.20
Since we know that the solution leaving contains 10 kg of salt, the remainder must be water, so the water leaving the bottom of the evaporator is 50 − 10 or 40 kg. How much water is evaporated? The material balance on the water shows us that this must be 90 − 40 or 50 kg of water. This calculation is shown in Figure 2.
If we were measuring one or more of these variables and the balance did not “close,” then that indicates a problem that could be any one of these: 1)
The steam supply is inadequate to evaporate as much water as desired.
2)
The concentration of the incoming salt solution is less than designed.
3)
The rate of product leaving the evaporator is not what it is expected to be.
4)
The concentration of the salt solution leaving the evaporator is not as desired.
Just the simple concepts of mass balances can generate serious troubleshooting questions to be explored by the people running the evaporator. This may be made easier with any number of online instrumentation systems, but the simple concepts of material balance (“what comes in will come out eventually”) can focus the analysis. The accuracy and calibration of instrumentation such as weigh cells, flow meters, and concentration measurements can be critical in determining accurate material balances. 2) System Boundary Another important aspect of balances is where we draw the boundaries. Let’s take a look at a system where a slurry (a liquid containing suspended solids) is being pumped into a settling tank where solids settle out and the settled solids are drawn off in parallel with the clarified water (see Figure 3).
Figure 3: Slurry settling and concentration process. If we draw a box around the entire operation, we would expect that, over time, the amount of slurry entering the tank would equal the amount of water and the amount of enriched or concentrated solids to be equal.
However, we could draw the box at the point shown in Figure 4.
Figure 4: Mass balance around feed pipe. In this case, the amount of slurry entering the feed line must equal what actually enters the settling tank. If it did not, there is a leak in the pipe, or some of the solids are accumulating in the pipe, potentially plugging it if left unchecked. We could also draw the system boundary for a mass balance around the tank itself as shown in Figure 5.
Figure 5: Mass balance around the tank alone. In this case, we are measuring the input slurry mass and the mass in the tank. In its initial start�up, we would not expect this mass balance to “close� as the tank will fill up to some predetermined level prior to water overflowing and possibly solids building up to a point where they can be lifted out of the tank. In Figure 6, we see the total system mass balance. If, after some operating time, the sum of the mass of slurry in the tank did not equal the sum of the mass of solids and clarified water leaving the tank, it could indicate: 1) There is a leak in the system in the entering pipe (prior to its entry into the tank), the tank itself, or the clarified water outflow pipe. 2)
The solids are filling the tank and not being removed.
3) An unanticipated chemical reaction generating a gas, which is leaving the system through a vent pipe or building up pressure within the tank. You might think of other possibilities as well. These kinds of consequences, none of them desirable, are the key reasons that an online material balance in a manufacturing process is critical and usually incorporated into its process control and measurement systems.
Figure 6: Mass balance versus time and boundary—accumulation.