Showing posts with label mass balance. Show all posts
Showing posts with label mass balance. Show all posts
Thursday, August 30, 2012
Fundamentals of Material Balances (Part 3)
Material Balances on Single - Unit Processes
General Procedure
Given a description of a process, the values of several process variables, and a list of quantities to be determined :
- Choose 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 unknown stream variables on the chart.
- Express what the problem statement asks you to determine in terms of the labeled variables.
- If you are given mixed mass and mole units for a stream, convert all quantities to one basis or the other.
- Do the degree - of - freedom analysis. Count the unknowns and identify equations that relate them. The equations may be any of the these six types : "material balances", "energy balances", "process specifications", "physical property relationships and laws", "physical constraints", and "stoichiometric relations". If you count more unknown variables than equations, figure out what's wrong (the flowchart is not completely labeled, or an additional relation exists that was not counted, or one or more of your equations are not independent of the others, or the problem is underspecified or overspecified). If the number of unknowns does not equal the number of equations, there is no point wasting time trying to solve the problem.
- If the number of unknowns equals the number of equations relating them, write the equations in an efficient order and circle the variables for which will solve.
- Solve the equations.
- Calculate the quantities requested in the problem statement if they have not already been calculated.
- If a stream quantity or flow rate "ng" was given in the problem statement and another value "nc" was either choses as a basis or calculated for this stream, scale the balanced process by the ratio "ng/nc" to obtain the final result.
Example
A liquid mixture containing 45% benzene (B) and 55% toluene (T) by mass is fed to a distillation column. A product stream leaving the top of the column (the overhead product) contains 95% mole B, and a bottom product steam contains 8% of the benzene fed to the column (meaning that 92% of the benzene leaves with the overhead product). The volumetric flow rate of the feed stream is 2000 L/h and the specific gravity of the feed mixture is 0.872. Determine the mass flow rate of the overhead product stream and the mass flow rate and composition (mass fractions) of the bottom product stream.
Step :
1. Choose a basis. Having no reason to do otherwise, we choose the given feed stream flow rate (2000 L/h) as the basis of calculation.2. Draw and label the flowchart.
3. Write expressions for the quantities requested in the problem statement. In terms of the quantities labeled on the flowchart, the quantities to be determined are "m2" (the overhead product mass flow rate), "m3 = mB3 + mT3" (the bottom product mass flow rate), "xB = mB3/m3" (the benzene mass fraction in the bottom product), and "xT = 1- xB" (the toluene mass fraction). Once we determine "m2", "mB3", and "mT3", the problem is essentially solved.
4. Convert mixed units in overhead product stream.
5. Perform degree - of - freedom analysis
The problem is therefore solvable
6. Write system equations and outline a solution procedure. The variables for which equations will be solved are circled.
- Volumetric flow rate conversion. From the given specific gravity, the density of the feed stream is 0.872 kg/L. Therefore :
- Benzene split fraction. The benzene in the bottom product stream is 8% of the benzene in the feed stream. This statement translates directly into the equation :
- Benzene balance.
- Toluene balance.
7. Do the Algebra. The four equations may be solved manually or with equation - solving software. The results are "m1 = 1744 kg/h", "mB3 = 62.8 kg/h", "m2 = 766 kg/h", and "mT3 = 915 kg/h". A total mass balance (which is the sum of the benzene and toluene balances) may be written as a check of this solution :
8. Calculate additional quantities requested in the problem statement
Tuesday, August 28, 2012
Fundamentals of Mass Balances (Part 2)
Balances
The General Balance Equation
Supposes methane is a component of both input and output streams of a continuous process unit, and that in an effort to determine whether the unit is performing as designed, the mass flow rates of methane in both streams are measured and found to be different (min
≠ mout).
There are several possible explanations for the observed difference between the measured flow rates :
- Methane is being consumed as a reactant or generated as a product within the unit
- Methane is accumulating in the unit, possibly adsorbing on the walls
- Methane is leaking from the unit
- The measurements are wrong
A balance on a conserved quantity (total mass, mass of a particular species, energy, momentum) in a system (a single process unit, a collection of units, or an entire process) may be written in the following general way :
There are 2 types of balances :
- Differential balances. A balance that indicates what is happening in a system at an instant in time. Each term of the balance equation is "rate" (rate of input, rate of generation, etc) and has units of the balanced quantity unit divided by a time unit (people/year, gr/s, barrels/day, etc). This is the type of balance usually applied to a "continuous process."
- Integral balances. A balance that describe what happens between two instants of time. Each term of the equation is an "amount" of the balanced quantity and has the corresponding unit (people, gr, barrels). This type of balance is usually applied to a "batch process", with the two instants of time being the moment after the input takes place and the moment before the product is withdrawn.
- If the balanced quantity is total mass, set generation = 0 and consumtion = 0. Except in nuclear reactions, mass can neither be created nor destroyed
- If the balanced substance is a nonreactive species (neither a reactant nor a product), set generation = 0 and consumption = 0
- If a system is at steady state, set accumulation = 0, regardless of what is being balanced. By definiton, in a steady-state system nothing can change with time, including the amount of the balanced quantity
Thursday, August 23, 2012
Fundamentals of Mass Balances (Part 1)
Fundamentals of Mass Balances
 |
| Basic Diagram of Mass Balance |
Introduction
Certain restriction imposed by nature must be taken into account when designing a new product or analyzing the existing one. You cannot, for example specify an input to a reactor of 1000 g of lead and an output of 2000 g of lead or gold or anything else.
Similarly, if you know that 1500 lbm of sulfur is contained in the coal burned each day in a power plant boiler, you do not have to analyze the ash and stack gases to know that on the average 1500 lbm of sulfur per day leaves the furnace in one form or another.
The basis for both of these observation is the "the law of conservation of mass", which states that mass can neither be created nor destroyed.
The statement based on "the law of conservation of mass" such as :
Total mass of input = Total mass of output
is called by mass balances or material balances.
The design of a new process or analysis of an existing one is not complete until it is established that the inputs and outputs of the entire process and of each individual unit satisfy balance equations.
Process Clasification
Chemical processes may be classified :
- Batch Process. The feed is charged (fed) into a vessel at the beginning of the process and the vessel contents are removed sometime later. No mass crosses the system boundaries between the time the feed is charged and the time the product is removed. Example : Rapidly add reactants to a tank and remove the products and unconsumed reactants sometime later when the system has come to equilibrium.
- Continuous Process. The inputs and outputs flow continuously throughout the duration of the process. Example, pump a mixture of liquids into a distillation column at a constant rate and steadily withdraw product streams from the top and bottom of the column.
- Semi-Batch Process. Any process that is neither batch nor continous. Example, allow the contents of a pressurized gas container to escape to the atmosphere; Slowly blend several liquids in a tank from which nothing is being withdrawn.
If the values of all the variables in a process (temperatures, pressures, volumes, flow rates) do not change with time, except possibly for minor fluctuations about constant mean values, the process is said to be operating at steady state. If any of the process variables change with time, transient or unsteady-state operation is said to exist. By their nature, batch and semi-batch processes are unsteady-state operations, whereas continuous processes may be either steady - state or transient.
Batch processing is commonly used when relatively small quantities of a product are to be produced on any single ocassion, while continuous processing is better suited to large production rates. Continuous processes are usually run as close to steady state as possible; unsteady-state (transient) conditions exist during the start-up of a process and following changes in process operation conditions.
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