1.2.4 Energy Balance
• Flow system
Q- W + FiHi – FoHo ± ΔHRVrA = dE/dt
(neglecting KE and PE) kJ/s
• in a pipe where no accumulation term and possibly KE and
PE:
Qo – Ŵs+ mo ((ui2- uo2)/2 + g(zi-zo)+ (hi-ho)) = 0 kJ/ s or
Q-Ws+ m((ui2- uo2)/2 + g(zi-zo)+ (hi-ho)) = 0 kJ/
• get Bernoulli eqn if substitute ho-hi = Δh - Δ(Pv) = Q-W
• and W = PΔv – lw (friction loss)
Δh – vΔP - PΔv = Q-PΔv + lw
Δh = Q + vΔP + lw
Ws+ (uo2- ui2)/2+g(zo-zi) + vΔP + lw = 0
v = 1/ρ
Ws+ (uo2- ui2)/2+g(zo-zi) + ∫P/ρ + lw = 0
• Typically in process flow calcs perform
material balances followed by energy (as they
are coupled)
• Terms used in energy calcs:
Heat of reaction – ΔHr - enthalpy change
when stoichiometric quantities of reactants
at T and P are completely converted to
products at same T and P
ΔHr < 0 reaction is exothermic e.g most fossil fuel
combustion
ΔHr > 0 reaction endothermic e.g. most fossil fuel
pyrolysis
1.3 Heat Exchange Equipment
i. shell and tube
ii. Condensers
• heat transfer equip used to liquefy vapours where latent heat of
vap us absorbed w/ coolant
iii. Reboiler
• usually shell/tube ex used to boil liquid for recirculation
www.distillationgroup.com
iv. Cooling Towers
• used to lower temp of recirc water used in condensers and heat exchangers
• large diameter columns with special packing to give good contact with low P
drop
• water distributed thru tower via nozzles or troughs of pies and air passed thru
forced draft and induced draft fans
Closed Loop Cooling Tower System (www.cheresources.com)
1.4 Mass transfer Ops
• mass transfer processes can be modelled by diffusion rate processes (gas
absorption, l-l extraction, packed towers) and/or equilibrium stages
(distillation, leaching, extraction in distillation towers, diffusion batteries)
• regardless of model need to know equilibrium relationship between phases
and components because once 2 phases are in equilibrium there is no mass
transfer
• as said before equilibrium is set by T, P, n so use phase rule: F=C-P+2
determines degree of freedom for phase calcs
a)Eqm relationship
• in our applications focus on distillation columns which are series of eqm stages
• where two streams run counter-currently to each other, in each stage they are
brought into contact, mixed, and separated, to work must enter stage not in eqm
and leave very close to eqm
• distillation or fractionation is a method of separation of HC by relative volatility
ij=Ki/Kj
where K- K-values = yi/xi really a measure of separation between liquid (x)
and gas (y) fractions at a give T and P
i. fractionators
• are designed as a series of equilibrium flashes:
equilibrium flash – say have a pure component of vapour and liquid at specified T
and P, at equilibrium a certain fraction exists as vapour the rest as liquid, if change
temp and/or pressure and allow to equilibrate fractions will shift, if now add other
compounds to pure and allow to equilibrate the l and v fractions and composition
will again shift  how shift determined by thermo  f(comp, T, P)
v, y1
Tin, Pin, z1
TS
PS
TS
Tin
l, x1
x1
y1
 in series of flashes:
 vapour enters from stage below @ T1
 l enters from stage above @ T2 (T1>T2)
 heat and mass transfer occurs so exit streams from stage
@ bubble pt l and dew pt v at same T and P
dew pt v
Stage may be a tray
or part of packing
(discussed in detail
later)
l at T2
T
contact
v at T1
T2
bubble pt l
T1
yDP
xBP
composition of exit streams are related by equilibrium constant (K)
Ki = ydp/xbp where K=f(T,P) – calculate using thermodynamics
(del G or chem potential)
Condenser – may have total or
partial reflux
Reflux
Overhead
Rectifying
Section – v enriched w/
low boilers
Stripping section – l
enriched w/ high boilers
Reboiler
Bottom Product
Figure modified from Perry’s
• May have multiple feeds at low T as approach top to provide reflux
• Use top l feed w/ crude stabilizers and deethanizers
 purpose is usually meet specs for bottom product , OH composition
determined by upstream process units
• trayed
1. bubble cap – prevents l from weeping thru vapour passages
- turndown ratio 8:1-10:1
2. valve – lower cost
3. sieve or Perforated – lowest cost, high capacity but subject to weeping
• initial design calcs based in theoretical trays (eqm calcs) and then apply a tray
efficiency
Bubble
Sieve
Valve
• packed columns
 as opposed to tray columns, contact btw l and v maintained
throughout column (vs. specific pts)  more detail later
• number of trays function of separation factors
q
Hv  H F
Hv  H L
where Hv is the enthalpy of the feed at the
dew point, HF is the enthalpy of the feed at
the boiling point, and HL is the enthalpy of
the feed at its entrance condition
 numbers 1-6 represent
theoretical amount of trays
required to achieve
separation  never truly
reach eqm at trays therefore
apply “tray efficiency”
Typical McCabe-Thiele diagram for distillation of a binary feed (Perry’s)
• condenser – partially or totally condense the vapour to a
boiling liquid to return to column and enhance mass transfer
as it is transferred to rising vapour stream  called reflux
(increases purity of OH product)
• reboiler – liquid partially reboiled to vapour
temperature increases as move down column due
increase in pressure and concentration of higher boiling
components
in design mass and energy balances are done at each
stage or plate to determine final concentration, T and P
profiles.
i.
Liquid/Gas Absorption ops
•
includes absorption, stripping and desorption
• soluble vapour absorbed from mixture with a liquid
(solute), solute is then regenerated  can also have gas
absorption with reaction (discuss later)
absorber vs. fractionator
•Packings/packed tower design
usually use a tower with packings or
trays/valves to accomplish gas absorption
 cylindrical column (tower), with gas
inlet, and distributor at the bottom, liquid
inlet and distributor at top, gas and liquid
outlets at top and bottom, and supported
mass of inert packing or series of
trays/valves
can be a “physical” absorption  process
occurs due to solubility and vapour-pressure
relationships or,
chemical absorption  chemical reactions
between absorbed substance and the
absorbing medium
packing increase the area of contact
between gas and liquid this results in
increased mass transfer between phases
the solute in the RICH gas is absorbed by
the liquid and exits the tower as a LEAN
gas
3 types of packing:
1. dumped or random packing – units 6-75 mm in diameter, cheap
inert material (clay, porcelain, plastics)
- area/volume column = 65-625 m2/m3
2. stacked – 50-200 mm in size, not commonly used due to
channelling
3. structured – knitted type mesh packing (i.e. wire gauze)
high l loading possible
area/volume column = 200-250 m2/m3
stacked
structured
http://www.tower-packing.com/Dir_structured_packing.htm
random
• initial design calcs based on P drop and diameter (Eckert method)
• must minimize P drop across column (low gas mass velocity) which also
prevents flooding (high l or v rates when delPgas > net gravity head of l) but
if gas mass velocity too low then must have larger column to maximize
contact between l and v
e.g. del Pmax=5-15 mm H2O/ft packed depth (max of 25) or
del Pflood = 0.115Fp0.7
where Fp is packing factor (dimensionless, del P in H2O/ft pack)
(l/v)max
liquid
flowrate
operating
strippingrange
flooding
max delP
rectifying
channeling
min allowable eff
vapour flowrate
• other column problems that must be mitigated by operating properly:
foaming
entrainment
weeping (when trays rely on gas pressure to hold l start leaking l thru gas
orifices)
• the maximum amount of solute that can be absorbed by the liquid is defined
by equilibrium calcs, actual amount is less and called the operating line:
Operating line - absorption
Tower bottom
y
Equilibrium line
Operating line - stripping
Tower top
x
** reversed op and eqm line for distillation
• instead of efficiency have Height of Packing Equivalent to Theoretical Plates
(or trays) HETP inversely prop to eff
then HETP*theoretical stages = hPC ~ 300-900 mm (1500 max)
• critical to maintain l distribution (avoid channelling) so redistribute ~ every 6
m of packing or 10 column diameters
• regenerate liquid in adjacent column
iii.) solid/gas absorption or fixed bed absorbers and fluidized beds
• solid acts as absorbent to remove impurities
• as with gas-liquid contactors can have physical or chemical absorption
• adsorbent particles placed in bed 0.3-1.2 m deep supported on screen or
perf plate, feed gas flows down thru bed to prevent fluidization, usually
have 2nd bed regenerating
• fluidized beds solid particles are fluidized to enhance mass and heat transfer