In every pilot plant test the issue of “mass balance” comes up. In just about every case there is a vague notion that, “We need a good mass balance.” Unfortunately the concept is rarely well defined or well understood by managers, supervisors and operators. These are the folks who have to run the pilot plant so that a “good mass balance” can be achieved. Unfortunately, this often this leads to poor and even unusable test data. This blog discusses mass balance in pretty simple terms for those folks who are not engineers, but need know about mass balance.
In simple terms, a mass balance is a calculation. It is an accounting of what went into and came out of a process. This purpose of the mass balance is to serve as a check of the measurement system. Since mass is essentially conserved in any physical or chemical process, the amount of mass that goes into a process should equal the mass that comes out of a process. If this is not the case, then the measurement system may be flawed. Hence, a mass balance is not important in and of itself. It is a check on the measurement processes. It is not unlike a year-end retail store inventory. We will use that as an example.
A year-end inventory is a counting of the actual physical inventory in a store. During the year the store keeps track of merchandise that was received and merchandise that was sold. We would want the starting number of various items (NINT). This would be the inventory at the start of the year. We would also want the number of items received (as in purchased) in the year (NPUR) and the number of items sent out (as in sold) in the year (NSOLD). We would compare the final number of items that we counted in the physical inventory (NFINAL) with what we calculated should be the final count. If NFINAL = NINT + NPUR - NSOLD all would be well and we would be home early for New Years.
If the NFINAL count was off a little bit we might recheck our count and calculations but we would not do much about the difference. We would expect some amount of error, even when counting items. It would be important to define what we meant by being off a little.
If NFINAL was not at all what we expected, we would start worrying that something was really wrong. Perhaps the data were incorrect. Perhaps some inventory counters were counting individual shoes while others were counting pairs of shoes. Maybe there was returned merchandise that was being double counted. Perhaps we were being shorted on some of our purchases. Maybe some items were transferred to other stores and we didn’t get that information. Of course there could have been a certain amount of shoplifting and even employee theft.
When the inventory doesn’t balance as closely as we expect, we would start looking for problems. The more detail we have about the items the better our chance for figuring out what went wrong. This is something that we have to design into our inventory system long before doing our final inventory.
At first we might want to keep our inventory system very simple. As our store became larger and more complex we would want to collect more detailed information about our items. We might be able to learn about our customer buying habits or our store’s ability to control particular inventory items. We have to do this at the start of the year and collect the same data consistently throughout the year or we won’t be able to make any sense of what was going on.
A mass balance for a test run is very similar to an inventory. First and foremost we must set up our system before the test so that we collect all the needed information consistently through the test. A simple mass balance will tell us if everything was properly accounted for, but will not tell us much about what might have gone wrong if something does go wrong. In a chemical process our inventory items can be molecules or atoms. In most cases molecules change form and are not “conserved” through the process. Atoms are not destroyed, they just change their associations. For example, methane might react with oxygen to form water and carbon dioxide as shown below:
CH4 + 2O2 -> CO2 + 2H2O (1)
Notice that the molecules change, but that we have the same number of carbon, hydrogen and oxygen atoms at the beginning and the end of the reaction. This is typical of chemical processes. If we “inventory” all the atoms at the beginning of the process and again at the end, we should find the same number of atoms. If we express that inventory as mass then we are doing a “mass balance” by various elements. If we don’t get the same mass of carbon, hydrogen and oxygen going into and out of the process we know that something went wrong.
In a chemical process things are a bit more complicated than in our inventory example. There are at least three reasons:
- Physical measurements are being taken rather than things being counted,
- In many cases the physical measurements are not direct mass measurements but rather are several measurements that must be converted into a mass number (e.g. measuring concentration of a component and then multiplying by a measurement of flow to get the final estimate of mass) and
- Some measurements are easy and accurate while others may be difficult or even impossible.
The first item introduces measurement error. It is an inescapable fact that every physical measurement is subject to measurement error. The second item tends to multiply that error as multiple measurements are combined to get final answers. Hence, the numbers never work out exactly right. It is very important to think through what the measurement error will be and adjust expectations accordingly. This can be done using a procedure called “Propagation of Error." We need to know how close is “good enough” and this is never a black or white decision.
The third item will drive our thinking and our Sampling and Analysis Plan. It makes no sense to try to draw any conclusions from data that are highly suspect. We must design our testing around measurements that can be made with reasonable precision and accuracy. This has to be a big part of planning when setting up any kind of experiment or trial.
Let’s illustrate how a mass balance might be used in a relatively simple (imaginary) chemical process. Let’s suppose that we are mixing together chlorine gas (Cl2) and methane gas (CH4) to make liquid methylene chloride (CH2Cl2, a solvent used in paint stripper). Our purpose for the plant trial might be to try out some new operating conditions to see if we can improve yields. The reactions of interest might be:
Cl2 + CH4 -> HCL + CH3Cl (a gas we don’t want) (2)
CH3Cl + Cl2 -> HCl + CH2Cl2 (the liquid product we want) (3)
CH2Cl + Cl2 -> HCl + CHCl3 (a liquid product that is OK if in small amounts) (4)
CHCl3 + Cl2 -> HCl + CCl4 (a toxic liquid product we don’t want at all) (5)
Notice that the first reaction is just a first step in getting to our product. We really don’t want the intermediate, CH3Cl (called methyl chloride which happens to be a gas). What we might do is recycle the gas back through the reactor to get the CH3Cl to become our desired product, liquid CH2Cl2. Nevertheless, we would have to be careful that we don’t recycle things other than CH3Cl. If we do we will make too much CHCl3 (chloroform) or CCl4 (very toxic carbon tetrachloride). How and how much we recycle the CH3Cl might be a critical operating parameter that we would test.
Our simplified process might look like:
Since we are interested in improving the yield of CH2Cl2 relative to CH4 and Cl2 we would certainly want to measure the amount of CH2Cl2 produced and the amounts of CH4 and Cl2 used. Nevertheless, if we just measure these, we will never be sure of our data. Our measurements of one or more of these might be way off and we might be fooling ourselves into believing something that wasn’t true. If, for example, our measured yield was 80% based on measuring CH4 and CH2Cl2, but our CH4 number was actually 50% low, then our yield would be off by 50%. Our true yield would only be 40%. Sooner or later we would figure that out, but it might be a very costly error.
The best way to avoid these kinds of serious errors would be to account for all the carbon, hydrogen and chlorine going into and coming out of the process. In the case of the 40% instead of 80% yield, a good accounting of the amount of carbon going in and coming out of the system could be very helpful. Our calculation might show that we seemed to be getting twice as much carbon out as we were putting in. Since this is clearly impossible we would quickly be tipped off that something was wrong with our measuring system. If we had collected redundant data through the test (perhaps measuring methane flow by two independent means), we might be able to “salvage” the test by using the alternative measurement method.
If we can identify and measure all compounds we can make separate mass balance calculations based on the all the different types of atoms (i.e. elements). That can give us redundant data that might help “salvage” a test should something go wrong. If all of these independent mass balances work out well we would have high confidence in our data. Unfortunately, it is rarely the case that we can measure all inputs and outputs with good confidence. Our example helps illustrate this.
In our imaginary systems we would probably find it rather difficult to accurately measure the HCl (hydrochloric acid gas). It is a very reactive toxic gas that easily dissolves in water and reacts with metals. In our pilot plant we would be a lot more interested in removing the gas for safe disposal than collecting samples for accurate measurement. If we found it impractical to measure HCl, then we could not do mass balance calculations on hydrogen and chlorine. We would have to do our mass balance on carbon only. We would have to be especially careful in identifying and measuring all of the hydrocarbons going into and coming out of the process. Any mistakes with this would mean that we wouldn’t have a mass balance calculation of any kind. If that should happen we would have no check on the measurement system and all the data from the test would be suspect. The whole test might be ruined.
In doing a proper mass balance it is critical that we select sampling points for composition and flow very carefully. Figure 1 shows 7 possible points (yellow numbered boxes). Nevertheless, in a real pilot plant there are usually huge constraints on where samples may be taken and flows may be measured. Some points are physically inaccessible while others may be impractical because of temperature or pressure. In Figure 1 we would want to select Points 1, 2 and 7 for our mass balance sampling and flow measurements. We would certainly want to avoid Point 3 (the recycle loop) for a mass balance calculation. That point might give us very useful process information, but if we included that flow in a mass balance calculation it would be like double counting returned merchandise in our inventory example.
There is one other point to make that sometimes gets lost in all the complications. Just as in our store inventory example, the beginning and ending inventories of tanks, reactors, hoppers and etc. must be considered. If in our imaginary plant, reactants can build up in the reactor or products can accumulate in the separator, we must take into account how much reactant or product was part of building up or draining off those levels. In a surprising number of cases these inventory measurments turn out to be very difficult and can add tremendous error to overall calculations.
In this simple example we have illustrated some of strategies and concerns that need to be considered in any Sampling and Analysis Plan for a pilot plant trial. The concepts are pretty simple, but there are devils in the details. Flows in pilot plants are often complicated and subject to revision. Such plants are often designed for multiple uses and may not be optimal for the current trial. It is not uncommon to discover after the fact that vent, flare or recycle lines were left open unexpectedly or to find that measurement devices were improperly sized, were out of calibration or just were not of the proper type. It is also not uncommon to find that data of all types were not properly recorded during the trial. Whereas much time is often spent on evaluating laboratory methods and procedures, it is actually rare that the same kind of scrutiny and care is given to the much more important field and plant data collection and measurements.
So what is a “good” mass balance? Most measurement techniques can operate easily within an error bar of a few percent (1% or 2%). When these errors are combined, the resulting error is often around 5% relative. There are exceptions to this rule of thumb, but a “good” mass balance is usually around 95%. That is to say the mass out is within 95% of the mass in. Real pilot plants often fail to meet that 95% criteria due to an accumulation of constraints. Nevertheless, any mass balance less than about 90% probably indicates significant measurement failures. By the way, it is rare for accumulated error to overcome natural losses from leaks, adsorption, etc. Hence, if the mass out exceeds the mass in this is usually an indication of a serious measurement or data collection error.
In summary:
- Mass balances are crucial mathematical checks on the validity of all data collected during a pilot plant trial,
- Careful planning and exacting implementation are required to get good mass balances,
- Coordination with managers, supervisors and operators of the pilot plant is critical to achieving a good mass balance and
- Laboratory data are very important, but careful attention to plant measurements are usually more important – failures in the field are more often the cause of things going awry.