Total mass balance is calculated by applying the fundamental principle that mass is neither created nor destroyed in a closed system. The general mass balance equation is: Input + generation – output – consumption = accumulation. This equation allows us to track the movement of mass within a system over time.
Understanding the Terms
Here's a breakdown of each term in the mass balance equation:
- Input: The mass entering the system. This can be in the form of raw materials, feed streams, or any other mass that adds to the system's total.
- Generation: The mass created within the system, specifically due to a chemical reaction where products are formed. For example, if a reaction makes a new chemical compound, the mass of this product is considered generation.
- Output: The mass exiting the system. This can be in the form of products, byproducts, waste streams, or any other mass leaving the system.
- Consumption: The mass used within the system, typically due to a chemical reaction. This refers to the mass of reactants used up during a reaction.
- Accumulation: The change in mass within the system over a period of time. A positive accumulation means the system is gaining mass, while a negative accumulation means the system is losing mass.
Steps to Calculate Total Mass Balance
To perform a mass balance calculation, you can follow these general steps:
- Define the System: Clearly identify the boundaries of your system. What is included, and what is not? This is critical for understanding what constitutes an input and output.
- Identify Inputs and Outputs: Determine all the streams of mass entering and exiting the system. Note these down, ensuring you account for every source and sink of mass.
- Account for Generation and Consumption: If chemical reactions are present, identify which substances are being generated and which are being consumed in reactions. Be sure to only count the changes in mass due to chemical transformations here, not simply the presence of a substance.
- Collect Data: Quantify the mass of each input, output, generation, and consumption stream. Data may be available as mass flow rate (e.g. kg/min or lb/hr) or total mass (e.g. kg or lb) over a given time period. Ensure consistency in measurement units.
- Apply the Mass Balance Equation: Plug the quantified values into the general mass balance equation.
- Solve for the Unknown: Typically, you will be trying to calculate one unknown quantity by substituting the known quantities into the mass balance equation. The unknown might be the amount of a product formed, the loss of a reactant, the accumulation, or any other mass quantity.
- Verify Results: Check if the final answer is consistent and meets the physical limits of the system.
Example
Let's say you have a reactor where A reacts to form B.
- Input: 100 kg of A is fed into the reactor.
- Generation: 60 kg of B is produced by the reaction.
- Output: Some mass of unreacted A and the 60 kg of B exit the system. The mass of unreacted A is 20kg.
- Consumption: 80kg of A reacted to produce 60kg of B.
- Accumulation: In this scenario, assuming no accumulation of mass within the reactor.
So the mass balance would look like this:
100kg + 60kg - 20kg - 80kg = 60kg
The equation holds true and there is no accumulation or loss in the system. All of the input mass can be accounted for through the reaction and exiting the system.
Practical Insights
- Steady-State Systems: If the accumulation is zero, the system is in a steady state where the input equals the output plus the net generation and consumption.
- Batch Processes: If the system is closed, such as a batch process, and nothing enters or leaves, then all accumulation can be accounted for by generation and consumption within the system.
- Complex Systems: For complex systems, it can be helpful to create a flow diagram to visualize all the mass flows.
- Mass Balance Error: Some error is expected in experimental data, however, the closure of mass balance calculations is important. If there is a significant discrepancy, this indicates a potential error in measurements, unaccounted streams, or system assumptions.
By using the principle of mass balance, engineers and scientists can analyze various systems such as chemical reactors, biological systems, and environmental processes. This principle is a cornerstone of many engineering disciplines.
