CHEE 221: Chemical Processes and Systems
Module 4. Energy Balances without Reaction
Part b: Energy Balances using Steam Tables
(Felder & Rousseau Ch 7.5‐7.6) Energy Balances: Accumulation = In –Out
Batch (Closed) System: EEUQWKP Continuous (Open) System at Steady‐State: EEHQWKP s
• Changes in kinetic and potential energy can be calculated (usually small for chemical systems) • Heat and work input is given in the problem (or is often what you must solve for) • The major task is calculating changes in U or H –Ch7: Using tabulated values (steam tables) –Ch8: Calculate as function of phase and T –Ch9: Energy balances with Rxn Thermodynamic Data
It is not possible to know the absolute value of Uˆ or Hˆ for a pure substance, but you can determine the change in Uˆ( Uˆ) or H ˆ ( Hˆ ) corresponding to a specified change of state (temperature, pressure, and phase). The change is actually often what we want to know.
A common practice is to arbitrarily designate a reference state for a substance at which Uˆ and Hˆ are arbitrarily set to be equal to zero, and then tabulate Uˆ and/or Hˆ for the substance relative to the reference state. For example,
CO (g, 0C, 1 atm) CO (g,100C, 1 atm):
ˆ ˆ reference state HCO HCO 0 2919 J/mol
We say: “The specific enthalpy of CO at 100C and 1 atm relative to CO at 0C and 1 atm is 2919 J/mol”. CHEE 221 F&R Ch 7.5a 3 Reference States and State Properties
Most (all?) enthalpy tables report the reference states (T, P and State) on which the values ofHˆ are based; however, it is not necessary to know the reference state to calculateH (change in enthalpy) for the transition from one state to another. ˆ ˆ –fromH state 1 to state 2 equals H 2 H1 regardless of the reference ˆ ˆ state upon which H1 and H2 were based –Caution: If you use different tables, you must make sure they have the same reference state
This result is a consequence of the fact thatHˆ (andUˆ ) are state properties, that is, their values depend only on the state of the species (temperature, pressure, state) and not on how the species reached its state. When a species passes from one state to another, both Uˆ and Hˆ for the process are independent of the path taken from the first state to the second one. CHEE 221 F&R Ch 7.5a 4 F&R Example 7.5‐1
The following entries are taken from a data table for saturated methyl chloride:
ˆ 3 ˆ State T(F) P (psia) V (ft /lbm ) H (Btu/lbm )
Liquid -40 6.878 0.01553 0.000
Vapour 0 18.90 4.969 196.23
Vapour 50 51.99 1.920 202.28
1. What reference state was used to generate the given enthalpies? 2. Calculate Hˆ and Uˆ for the transition of saturated methyl chloride vapour from 50F to 0F.
CHEE 221 F&R Ch 7.5a 5 Steam Tables
Tables located in the back of F&R can be used to estimate Uˆ , Hˆ , and Vˆ for liquid water and steam (water vapour) at any specified temperature and pressure.
Recall the phase diagram for water:
Vapour‐liquid equilibrium (VLE) curve or saturation line –water may exist Subcooled liquid as saturated water, saturated steam (vapour) or mixture of both. superheated steam
CHEE 221 F&R Ch 7.5b 6 Steam Tables
Saturated Steam Tables: Data taken along the VLE curve or saturation line.
Table B.5 Saturated Steam: Properties of saturated water and saturated steam as a function of temperature from 0.01C (triple point) to 102C. Note boiling points at various P values and vapour pressures at T values.
Table B.6 Saturated Steam: Properties of saturated water and saturated steam as a function of pressure (same data as Table B.5 but over a much larger range of temperatures and pressures).
Superheated Steam Table: Data taken from points below the VLE curve or saturation line –vapourheated above its saturation temperature.
Table B.7 Superheated Steam: Properties of superheated steam at any temperature and pressure – includes data for liquid water (data in the enclosed region), and saturated water and saturated steam.
CHEE 221 F&R Ch 7.5a 7 Notes on the Steam Tables
Reference state for the tabulated thermodynamic data in the steam tables is liquid water at the triple point (0.01C and 0.00611 bar) [triple point is where all three phases of water can coexist] kJ kJ Units are on a mass basis: Uˆ and Hˆ kg kg Heat of vapourization (evaporation) is the difference between vapour and liquid enthalpies
Properties of liquid water are not a strong function of pressure at constant temperature, therefore Hˆ Uˆ since volume change is small
Volumetric properties of steam are extensively tabulated: when steam tables are available, don’t use the ideal gas law.
Remember: Hˆ (P,T ) Uˆ PVˆ
CHEE 221 F&R Ch 7.5a 8 Steam Tables – Interpolation
Sometimes you need to an estimate of specific enthalpy, specific internal energy or specific volume at a temperature and pressure that is between tabulated values (Usually B7) Use linear interpolation:
use this equation to estimate y
for an x between x0 and x1
E.g.; superheated steam at 20 bar, with enthalpy of 3065 kJ/kg. What T is the steam at?
Steam at 400 ºC and 25 bar. What is the specific enthalpy?
CHEE 221 9 F&R Example 7.5‐2
1. Determine the vapour pressure, specific internal energy, and specific enthalpy of saturated steam at 133.5C. 2. Show that water at 400C and 10 bar is superheated steam and determine its specific volume, specific internal energy, and specific enthalpy relative to liquid water at the triple point. 3. Show Uˆ and Hˆ for superheated steam depend strongly on temperature and relatively slightly on pressure.
For another perspective on Steam Tables, see the “Steam Table Tutorial” posted on the “Useful Links” tab of the course web page.
CHEE 221 F&R Ch 7.5a 10 Week 8 Pre-tutorial exercise: Steam
Part 1. At the F&R Encyclopedia of Chemical Engineering Equipment (textbook website), read the section on steam turbines (2nd part of Turbine Section)
Part 2. Use the steam tables to determine the state (liquid, vapour or mixture of the two; saturated or supersaturated) and approximate temperature (no need to use extrapolate) of 1 kg of water at 1 bar with the following enthalpies (relative to liquid water at the triple point)
a) 100 kJ b) 419 kJ c) 1500 kJ d) 2676 kJ e) 3000 kJ
CHEE 221 Energy Balance Procedures
• Pretty much the same as for Material Balances! • Draw and completely label a flow diagram – Include Temperatures, Pressures, and Phases (gas, liquid, …) • Perform (if possible) all material balances • Write the appropriate form of Energy Balance (closed or open), and eliminate terms that are negligible (with proper justification) • Determine the enthalpies (internal energies) of each stream
–H2O, steam Look them up in the steam tables! –Other components Calculate them (Ch. 8 –9) • Solve the problem! CHEE 221 F&R Ch 7.6 12 Example
Steam at 80 bar absolute with 155C of superheat is fed to a turbine at a rate of 2000 kg/h. The turbine operation is adiabatic, and the effluent is saturated steam at 1 bar. Calculate the work output of the turbine in kilowatts, neglecting kinetic and potential energy changes.
Definition:
“Degrees of Superheat” is the difference between the actual temperature and the temperature of saturated steam at the same pressure.
CHEE 221 13 Example 7.6‐3
Saturated steam at 1 atm is discharged from a turbine at a rate of 1150 kg/h. Superheated steam at 300Cand1atmisneededas a feed to a heat exchanger; to produce it, the turbine discharge stream is mixed with superheated steam available from a second source at 400C and 1 atm. The mixing unit operates adiabatically. Calculate the amount of superheated steam at 300C produced and the required volumetric flow rate of the 400C steam.
CHEE 221 14 Problem 7.26 F&R
Liquid water is fed to a boiler at 24C at 10 bar and is converted at constant pressure to saturated steam. Use the steam tables to calculateHˆ(kJ / kg) for this process, and then calculate the heat input required to produce 15,000 m3/h of steam at the exiting conditions. Assume that the kinetic energy of the entering liquid is negligible and that the steam is discharged through a 15 cm ID (inner diameter) pipe.
CHEE 221 15