3. Material Balance Calculations
All material balance calculations have one single theme that is the given values from output and input stream variables must be used to derive and solve the equations of others. To solve these equations is usually simple algebra, but by using a description of a process and a collection of process data can complicate solving the equations. The following can be used to approach the difficulties presented by a mass balance problem.
1. Flowcharts
It is important to organize the information in a way that is suitable for equations, because most of the mass balance problems are given in an essay-like form of information and then asked to determine something in the process. The best way to organize this information is to draw a flowchart of the process. This can be done by using boxes or other symbols to represent process units, like reactors, mixers, separation units, etc., and lines with arrows to represent inputs and outputs.
The chart should be fully labelled when it is drawn, with values of known process variables and symbols for unknown variables being written for each input and output stream.
2. Flowchart Scaling and Basis of Calculation
Scaling the flowchart is the procedure where the values of all stream amounts or flow rates is changed by a proportional amount while leaving the stream compositions unchanged. Scaling up: if the final stream quantities are larger than the original quantities. Scaling down: if the final stream quantities are smaller than the original quantities. Furthermore, it must be noted that you cannot scale masses or mass flow rates to molar quantities or vice versa by simple multiplication.
A basis of calculation is an amount or flow rate of one stream or stream component in a process. By choosing a balance of calculation the first step in balancing an equation is done; all unknown variables are determined to be consistent with the basis.
Choose the quantity that is given, for example the stream amount or the flow rate, if it is given. Assume the stream amount or flow rates is one if no stream amounts and flow rates is known. Choose a total mass or mass flow rate of that stream as a basis (100kg) if the mass fractions are known; choose a total number of moles or molar flow rate if the mole fractions are known.
3. Balancing a Process
The following rules apply to nonreactive processes:
The maximum number of independent equations can be derived by writing balances on a nonreactive system equals the number of chemical species in the input and output streams.
Write balances that involves the fewest unknown variables.
4. Degree-of-Freedom Analysis
By drawing a properly labelled flowchart you can determine whether you have enough information to solve the given problem, is called a degree-of-freedom analysis.
The following steps should be done to perform a degree-of-freedom analysis:
- Draw a complete labelled flowchart
- Count the unknown variables on the chart
- Count the independent equations relating them
- Subtract the second number (independent) from the first number (unknown)
n_df= n_(unknowns )- n_(indep eqns)
There are three possible results:
* If n_df = 0, there are n independent equations in n unknowns and the problem can be solved.
* If n_df > 0, there are more unknowns than independent equations relating them, and additional variable values must be specified before all remaining values can be determined.
* If n_df < 0, there are more independent equations than unknown variables. The flowchart is either incomplete labelled or over specified.
5. General Procedure for Single-Unit Process Material Balance Calculations
-Choose as a basis of calculation an amount or flow rate of one of the process streams.
-Draw a flowchart and fill in all known variable values, including the basis of calculation. Then label all unknown stream variables on the chart.
-Express what the problem statement asks you to determine in terms of the labelled variables.
-Convert all quantities to one basis if you are given mixed mass and mole units for a stream.
-Do a degree-of-freedom analysis.
-Write the equations in an efficient order (minimizing simultaneous -calculations) and circle the variables you will solve, if the number of --equations relating the unknowns equals the number of unknown variables.
-Solve the equations.
-If the quantities requested have not been calculated, calculate them.
-Scale the balanced process by the ratio n_g⁄n_c to obtain the result, if a stream quantity or flow rate n_g was given in the problem statement and another value was either chosen as basis of calculation or calculated for this stream.
All material balance calculations have one single theme that is the given values from output and input stream variables must be used to derive and solve the equations of others. To solve these equations is usually simple algebra, but by using a description of a process and a collection of process data can complicate solving the equations. The following can be used to approach the difficulties presented by a mass balance problem.
1. Flowcharts
It is important to organize the information in a way that is suitable for equations, because most of the mass balance problems are given in an essay-like form of information and then asked to determine something in the process. The best way to organize this information is to draw a flowchart of the process. This can be done by using boxes or other symbols to represent process units, like reactors, mixers, separation units, etc., and lines with arrows to represent inputs and outputs.
The chart should be fully labelled when it is drawn, with values of known process variables and symbols for unknown variables being written for each input and output stream.
2. Flowchart Scaling and Basis of Calculation
Scaling the flowchart is the procedure where the values of all stream amounts or flow rates is changed by a proportional amount while leaving the stream compositions unchanged. Scaling up: if the final stream quantities are larger than the original quantities. Scaling down: if the final stream quantities are smaller than the original quantities. Furthermore, it must be noted that you cannot scale masses or mass flow rates to molar quantities or vice versa by simple multiplication.
A basis of calculation is an amount or flow rate of one stream or stream component in a process. By choosing a balance of calculation the first step in balancing an equation is done; all unknown variables are determined to be consistent with the basis.
Choose the quantity that is given, for example the stream amount or the flow rate, if it is given. Assume the stream amount or flow rates is one if no stream amounts and flow rates is known. Choose a total mass or mass flow rate of that stream as a basis (100kg) if the mass fractions are known; choose a total number of moles or molar flow rate if the mole fractions are known.
3. Balancing a Process
The following rules apply to nonreactive processes:
The maximum number of independent equations can be derived by writing balances on a nonreactive system equals the number of chemical species in the input and output streams.
Write balances that involves the fewest unknown variables.
4. Degree-of-Freedom Analysis
By drawing a properly labelled flowchart you can determine whether you have enough information to solve the given problem, is called a degree-of-freedom analysis.
The following steps should be done to perform a degree-of-freedom analysis:
- Draw a complete labelled flowchart
- Count the unknown variables on the chart
- Count the independent equations relating them
- Subtract the second number (independent) from the first number (unknown)
n_df= n_(unknowns )- n_(indep eqns)
There are three possible results:
* If n_df = 0, there are n independent equations in n unknowns and the problem can be solved.
* If n_df > 0, there are more unknowns than independent equations relating them, and additional variable values must be specified before all remaining values can be determined.
* If n_df < 0, there are more independent equations than unknown variables. The flowchart is either incomplete labelled or over specified.
5. General Procedure for Single-Unit Process Material Balance Calculations
-Choose as a basis of calculation an amount or flow rate of one of the process streams.
-Draw a flowchart and fill in all known variable values, including the basis of calculation. Then label all unknown stream variables on the chart.
-Express what the problem statement asks you to determine in terms of the labelled variables.
-Convert all quantities to one basis if you are given mixed mass and mole units for a stream.
-Do a degree-of-freedom analysis.
-Write the equations in an efficient order (minimizing simultaneous -calculations) and circle the variables you will solve, if the number of --equations relating the unknowns equals the number of unknown variables.
-Solve the equations.
-If the quantities requested have not been calculated, calculate them.
-Scale the balanced process by the ratio n_g⁄n_c to obtain the result, if a stream quantity or flow rate n_g was given in the problem statement and another value was either chosen as basis of calculation or calculated for this stream.
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