CHAPTER 11 BALANCES ON TRANSIENT PROCESSES By : Ms. Nor Helya Iman Bt Kamaludin Email:...

PTT 108: Mass and Energy Balances

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CHAPTER 11BALANCES ON

TRANSIENT PROCESSES

By : Ms. Nor Helya Iman Bt Kamaludin

Email: [email protected]


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INTRODUCTIONTransient (unsteady-state):

Conditions at which the value of any system variable changes with time.

• Process systems: Batch system (no input and output streams) –

always transient Semibatch system (has input stream but no

output stream or vice versa) – always transient Continuous system (have input and output streams) – always transient when they are start up, shut down or become transient at other times due to planned or unexpected changes in operating conditions)


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General Balance Equation

Accumulation = Input + Generation -

Output - Consumption

Two forms of general balance equation;1) Differential balances

Relate instantaneous rates of change at a moment in time

2) Integral balances Relate changes that occur over a finite time

period


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Differential BalancesStep 1: Write general balance equation

Step 2: Let consider the following terms of species A

(kg/s) : inlet mass flow rate (kg/s) : outlet mass flow rate (kg/s) : rate of generation (kg/s) : rate of consumption


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Differential Balances (cont’d)

Step 3: Write a balance on A for a period of time from t to t + ∆t (suppose ∆t is

small enough), we get

Step 4: Suppose the mass of A in the system changes by an amount ∆M (kg) during

the small time interval. ∆M is the

accumulation of A.


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Differential Balances (cont’d)Step 5: Divide by ∆t and let ∆t approach 0.

The ratio ∆M/ ∆t becomes the derivative of the

M wrt t (dM/ dt). The differential balance

equation become:

where M is the amount of balanced quantity in

the system and four terms on the right side are

the rates that may vary with time.Step 6: Write the complete balance equation

in expression for M(t)

t = 0 (initial condition) , M = … or simply M(0) = …


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Class Discussion

Example 11.1-1


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Integral BalancesRemember differential balance equation:

Step 1: Write the equation in form of

Step 2: Integrate from an t0 to tf to form integral

balance equation:

where left side is the accumulation and right side is

the amount of balanced quantity in the system

respectively.


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Integral Balances (cont’d)

For a closed (batch) system, , thus the integral balance equation becomes:

Initial input + generation = final output + consumption


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Class Discussion

Example 11.1-2


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Balances on Single Well-Mixed Process Units

Procedure for writing and solving a transient material balance equation:

1. Eliminate terms in the general balance equation that equal zero Exp: input and output for batch systems, generation

and consumption for balances on total mass and nonreactive species.

2. Write an expression for the total amount of the balanced species in the system. Exp: [V(m3)p(kg/m3) for total mass, V(m3)CA (mol A/m3)

or ntotal (mol)xA (mol A/mol) for species A]

Differentiate the expression wrt time to obtain the

accumulation term in the balance equation.


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Balances on Single Well-Mixed Process Units (Cont’d)

3. Substitute system variables into the remaining terms (input, generation, output, consumption) in the balance equation. Make sure that all the terms have the same units (kg/s. lb-mole/h, etc).

4. If y(t) is the dependent variable to be determined (e.g., the mass of the system contents, the conc of the species A, the mole fraction of the methane), rewrite the equation to obtain the explicit expression for dy/dt.

Boundary condition:for specified time : t = 0can be expressed as : t = 0, y = y0

or simply : y(0) = y0


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Balances on Single Well-Mixed Process Units (Cont’d)

5. Solve the equation by analytically numerically

6. Check the solution using:(a) Substitute t = 0 and verify that the known

initial condition [y(0) = y0] is obtained.

(b) Find the long-time asymptotic (steady-state) value of the dependent variable, solving the resulting algebraic equation and verify.

(c) Differentiate solution to obtain an expression dy/dt, substitute and verify.

7. Use your solution to generate a plot or table of y versus t


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Class Discussion

Example 11.2-2


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Energy Balances on Single-Phase Nonreactive Processes

Step 1: General energy balance form: accumulation = input – output

where:accumulation =

input =

output =

(1)

(2)

(3)


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Energy Balances on Single-Phase Nonreactive Processes (cont’d)Step 2: Substitute (1), (2) and (3) into general energy

balance and then divide by ∆t and let ∆t approach to

0. We obtain the general differential energy

balance:

*If there are several input and output streams, a term below

must be included in Eq. (4)(5)

(4)


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Energy Balances on Single-Phase Nonreactive Processes (cont’d)Some consideration made to the systems:

1. The system has at most of the single input and output stream respectively where each has same mass flow rate.

2. Kinetic and potential energy changes in the system and between the inlet and outlet streams are negligible.

(7)

(6)


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Energy Balances on Single-Phase Nonreactive Processes (cont’d)

Under the 2nd condition, Eq. (4) simplifies to

3. The temperature and the composition of the system contents do not vary with position within the system (the system is perfectly mixed). Thus, the outlet stream and the system contents must be at the same temperature

(9)

(8)


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Energy Balances on Single-Phase Nonreactive Processes (cont’d)4. Consider the following conditions:

No phase changes or chemical reactions take place

within the system and are independent of pressure mean and of the system contents (and

the inlet

and outlet streams) are independent of composition

and temperature unchanging with time if Tr is a ref temp at which and M = mass (or

number of moles) of the system contents,


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Energy Balances on Single-Phase Nonreactive Processes (cont’d)

Then, we get

Finally substitute the expressions of (6) through (10) into (4) to obtain

(10)


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Energy Balances on Single-Phase Nonreactive Processes (cont’d)General Energy Balance for Open

System:

General Energy Balance for Closed System:


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Class Discussion

Example 11.3-1Example 11.3-2


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Thank You..Good Luck for Final Exam..

CHAPTER 11 BALANCES ON TRANSIENT PROCESSES By : Ms. Nor Helya Iman Bt Kamaludin Email:...

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