Exergy Analysis of STHE

1
Exergy Analysis of STHE

• P M V Subbarao
• Professor
• Mechanical Engineering Department
• I I T Delhi

Formalization of Thermo-economics..
2
Shell and Tube as a Thermal System

• In most cases, heat exchangers are designed for
  one of two cases

• fixed thermal duty or

• fixed heat exchanger area with specified flow
  rates.

3
Availability Exergy

• Availability at the original state The
  potential for achieving the maximum possible work
  by the mass.
• Exergy Flow Availability The maximum
  reversible work per unit mass flow without the
  additional heat transfers is the flow
  availability or exergy.
• e is the physical exergy.
• For liquids, the physical exergy can be obtained,
  when assuming a constant specific heat capacity,
  as

where v is the specific volume determined at
temperature T0.
4
The Exergy Destruction Rate A Measure of
Running Cost

• The entropy generation lowers the overall exergy
  level of a thermal system.
• Identify the regions in space where this occurs
  (the locations that have entropy generation).
• The exergy destruction is identical to the term,
  irreversibility.
• The exergy destruction rate for the control
  volume of an adiabatic heat exchanger in steady
  state is calculated from the difference between
  the incoming and outgoing exergy flows

5
Formulation of Objective Functions

• Type 1 Objective function Fixed Thermal Duty
• Type 2 Objective function Fixed Heat
  Transfer Area

6
Objective function Fixed Thermal Duty

• In the case of design with fixed thermal duty,
  consider the effect of varying the baffle
  spacing, baffle cut etc., while keeping the heat
  transfer rate constant at any prescribed value.
• At the fixed heat transfer rate, by reducing the
  baffle spacing, baffle cut etc., the heat
  transfer area, and also the capital cost, of the
  exchanger is decreased because the shell side
  heat transfer coefficient is increased.
• On the other hand, this generally means higher
  total exergy destruction, due to more pressure
  drop which leads to larger costs associated with
  the exergy destruction.

7

• Thus, there may exist an optimum baffle spacing,
  baffle cut etc., that minimizes the total annual
  cost.
• In this case, the objective function can be
  expressed as

Where top is the period of operation per year,
cex is the unit cost of the exergy, ED is the
rate of exergy destruction, a1 is the capital
recovery factor and CHEX is the capital cost of
the heat exchanger.

• Consider a heat exchanger without baffles as a
  reference case.

8
Objective functions Fixed Heat Transfer Area

• In the case of fixed heat transfer area, in
  comparison to the baffle free shell, the baffle
  arrangement will lead to a reduction in the
  monetary flow rates associated with the exergy
  destruction.
• The advantage of baffling is the considerable
  reduction it offers in the total cost associated
  with exergy destruction.
• Nevertheless, the increase in total cost because
  of the requirement for additional baffling comes
  as a disadvantage.
• Thus, there may exist an optimum baffle spacing
  that maximizes the amount of net saving
  associated with the exergy.
• The effect of the baffle arrangement on total
  annual cost may be calculated by taking the
  difference between the costs associated with the
  exergy profit and the baffle costs.

9

• In this case, the objective function can be
  expressed as

where Sex is the net exergy saving, top is the
period of operation per year, Cex is the unit
cost of exergy, Pex is the net exergy profit
caused by baffling, af is the capital recovery
factor and CB is the capital cost of the baffle
arrangement.
10
An Alternative Approach .

• Profit due to Baffling ..

11
Profit due to Baffling

• In the case of the baffle free shell, a
  significant reduction occurs in the pressure
  component of exergy destruction because of the
  fact that the pressure drop is invariably much
  lower than that of the baffled shell.
• On the otherhand, a decrease in the heat transfer
  coefficient of the shell side occurs, which
  considerably increases the thermal component of
  exergy destruction.
• This leads to an increase in the total exergy
  destruction rate in comparison to the case of the
  baffled shell.
• However, due to the baffle arrangement on the
  shell side, it is often possible to take
  advantage of the total exergy destruction in
  comparison to the case of the baffle free shell.

12

• It is apparent that the exergy destruction
  difference between the baffled and baffle free
  shell varies considerably with baffle spacing and
  baffle cut.
• An exergy profit is calculated by taking the
  exergy destruction difference between the cases
  of baffle free and baffled heat exchangers as
  follows

where Pex is the net exergy profit, ED, Baffle
free is the exergy destruction rate of the baffle
free exchanger and ED, Baffle is the exergy
destruction rate of the baffled exchanger.
13
Effect of Baffle Spacing on Energy Profits
14
Selection of Cost Functions
15
Capital Cost of STHE

• Several different correlations regarding cost
  estimations of shell and tube heat exchangers can
  be found in the relevant literature.
• In general, the total cost of the heat exchanger
  is directly proportional to heat transfer area
  and hence a strong function of baffling.
• The capital cost of a shell and tube exchanger
  for steel-steel material can be estimated by
  using the Hall Method

where A is the heat exchanger area required for a
given duty.
16
Baffling Cost

• The baffling cost is also considered as a
  significant cost for cost analysis.
• This cost for a piece of equipment consists of
  three major components weight of material, labor
  hours and labor costs.
• Labor hours significantly depend on the drilling
  of the raw baffle material and are strongly
  affected by the variation of the number of tubes.
  
• The baffle cost may be calculated by the
  following expressions

17

• where CM is the cost of raw baffle material and
  CD is the drilling cost of the baffle
  arrangement.
• Material cost and drilling cost may be expressed
  simply as

where cM is the price of material, Nb is the
number of baffles, n is the number of tubes, Ds
is the shell diameter, db is the baffle
thickness, rSt is the material density, cL is
the labor costs and tD is the drilling labor per
unit hole depth.
18
Effect of Baffle Spacing on Total Cost
19
Cost Vs Experience
Min. Total Cost based Baffle Spacing
20
Minimum cost Design Chart -1
21
Minimum cost Design Chart -2
22
Minimum cost Design Chart -3
23
Minimum cost Design Chart - 4
24
Performance of Minimum Cost Design
25
Limitations of STHE Optimization

• Optimization is possible only if following
  parameters are uniform through out the HX.
• Tube spacing, layout, diameter.
• Baffle type, spacing, cut .
• All the clearances..
• Most popular applications of STHE are required to
  be designed with non-uniform parameters.

26
Closed Feed Water Heaters

• A closed feedwater heater is a shell-and-tube
  heat exchanger that warms up feedwater or
  condensate by means of steam or condensate.
• It is used in almost all power plants with steam
  turbines.
• Purpose Closed feedwater heaters are used in a
  regenerative feedwater cycle to increase thermal
  efficiency and thus provide fuel savings.
• An economic evaluation will be made to determine
  the number of stages of feedwater heating to be
  incorporated into the cycle.
• Condensing type steam turbine units often have
  both low pressure heaters (suction side of the
  boiler feed pumps) and
• high pressure heaters (on the discharge side of
  the feed pumps).