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CHAPTER 11 BALANCES ON TRANSIENT PROCESSES

CHAPTER 11 BALANCES ON TRANSIENT PROCESSES. By : Ms. Nor Helya Iman Bt Kamaludin Email: helya@unimap.edu.my. INTRODUCTION. Transient ( unsteady-state ): Conditions at which the value of any system variable changes with time. Process systems: Batch system (no input and output streams) –

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CHAPTER 11 BALANCES ON TRANSIENT PROCESSES

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  1. CHAPTER 11BALANCES ON TRANSIENT PROCESSES By : Ms. Nor Helya Iman Bt Kamaludin Email: helya@unimap.edu.my PTT 108: Mass and Energy Balances

  2. INTRODUCTION • Transient (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) PTT 108: Mass and Energy Balances

  3. General Balance Equation Accumulation = Input + Generation - Output - Consumption Two forms of general balance equation; • Differential balances • Relate instantaneous rates of change at a moment in time • Integral balances • Relate changes that occur over a finite time period PTT 108: Mass and Energy Balances

  4. Differential Balances • Step 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 PTT 108: Mass and Energy Balances

  5. 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. PTT 108: Mass and Energy Balances

  6. Differential Balances (cont’d) • Step 5: Divide by ∆t and let ∆t approach 0. The ratio ∆M/ ∆t becomes the derivative of the Mwrtt (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) = … PTT 108: Mass and Energy Balances

  7. Class Discussion • Example 11.1-1 PTT 108: Mass and Energy Balances

  8. Integral Balances • Remember 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. PTT 108: Mass and Energy Balances

  9. Integral Balances (cont’d) • For a closed (batch) system, , thus the integral balance equation becomes: Initial input + generation = final output + consumption PTT 108: Mass and Energy Balances

  10. Class Discussion • Example 11.1-2 PTT 108: Mass and Energy Balances

  11. Balances on Single Well-Mixed Process Units Procedure for writing and solving a transient material balance equation: • 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. • 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. PTT 108: Mass and Energy Balances

  12. Balances on Single Well-Mixed Process Units (Cont’d) • 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). • 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 = 0 can be expressed as : t = 0, y = y0 or simply : y(0) = y0 PTT 108: Mass and Energy Balances

  13. Balances on Single Well-Mixed Process Units (Cont’d) • Solve the equation by • analytically • numerically • 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. • Use your solution to generate a plot or table of y versus t PTT 108: Mass and Energy Balances

  14. Class Discussion • Example 11.2-2 PTT 108: Mass and Energy Balances

  15. Energy Balances on Single-Phase Nonreactive Processes Step 1: General energy balance form: accumulation = input – output where: accumulation = input = output = (1) (2) (3) PTT 108: Mass and Energy Balances

  16. 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) (4) (5) PTT 108: Mass and Energy Balances

  17. Energy Balances on Single-Phase Nonreactive Processes (cont’d) • Some consideration made to the systems: • The system has at most of the single input and output stream respectively where each has same mass flow rate. • Kinetic and potential energy changes in the system and between the inlet and outlet streams are negligible. (6) (7) PTT 108: Mass and Energy Balances

  18. Energy Balances on Single-Phase Nonreactive Processes (cont’d) • Under the 2nd condition, Eq. (4) simplifies to • 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 (8) (9) PTT 108: Mass and Energy Balances

  19. Energy Balances on Single-Phase Nonreactive Processes (cont’d) • 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, PTT 108: Mass and Energy Balances

  20. 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) PTT 108: Mass and Energy Balances

  21. Energy Balances on Single-Phase Nonreactive Processes (cont’d) • General Energy Balance for Open System: • General Energy Balance for Closed System: PTT 108: Mass and Energy Balances

  22. Class Discussion • Example 11.3-1 • Example 11.3-2 PTT 108: Mass and Energy Balances

  23. Thank You..Good Luck for Final Exam.. PTT 108: Mass and Energy Balances

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