HX in WTS

Formulation:

322 Nm³/h moist air ( j₁ = 100 %) is drawn in at J₁ = 53 °C and p₁ = 1 bar and is compressed to p₂ = 3,5 bar, resulting in a  temperature of J₂ = 195 °C. Then, the air is cooled down to J₂ = 40 °C in the tubes of a shell-and-tube heat exchanger, which condenses water. The cooling media is water which is heated from 30 °C to 40 °C.

For this calculation the heat exchanger has to be divided into two partial exchangers:

1.       Cooling the vapour/air mixture from inlet temperature to dew temperature

2.       Cooling the mixture at condensation from dew temperature to outlet temperature.

Both partial exchangers have to be calculated by ‘WTS’ separately.

Procedure:

a) Calculation of the moisture rate (water quota) of the air at 1 bar and 53 °C (draw state) with the HX module

-          start HX

-          enter temperature J1 = 53 °C, relative moisture j1 = 100 %  and total pressure P1 = 100000 Pa

-          result : -> moisture rate saturation xs1 = 0,1038 kg/kg

b) Calculation of the dew temperature at 3,5 bar and a moisture rate x₁ = 0,1038 with the HX module

-          delete temperature J1

-          enter total pressure P1 = 350000 Pa, relative moisture j1 = 100%  and moisture rate x1 = 0,1038

-          result : -> temperature J1 = 81,4 °C

c) Calculation of the air mass flow (initial setting: normal volume flow)

For the desuperheating part it is assumed that the gas mixture consists only of air (The vapour is handled like air. Alternatively, the properties of the mixture can be calculated with ‘Proper’).

-          start WTS

-          As basic data for the medium in the tubes select ‘air’ and click ‘OK’ (medium around the tubes and geometry are disregarded because it is only a partial calculation).

-          In the WTS mask enter the normal conditions: pressure P_i = 101300 Pa,

-          inlet  temperature J_e,i = -1 °C, outlet temperature J_a,i = 1 °C (= mean temp. = 0 °C),

-          volume flow V_i = 322 m³/h = 0,089444 m³/s

-          result : -> mass flow m_i = 0,115535 kg/s 

d) Calculation of the total heat flow (desuperheating and condensation part) and of the total cooling water mass flow

Desuperheating part (heat flow)

-          terminate the program and start WTS again

-          as medium in the tubes select ‘air’ and click ‘OK’

-          in the WTS mask enter mass flow m_i =  0,115535 kg/s, pressure P_i = 350000 Pa,

inlet temperature J_e,i = 195 °C, outlet temperature J_a,i = 81,4 °C

result: -> heat flow Q_i = -13362 W

Condensation part (heat flow)

-          terminate the program and start WTS again

-          as medium in the tubes select ‘humid gases’ and click ‘OK’

-          in the WTS mask enter mass flow m_i = 0,115535 kg/s, pressure P_i = 350000 Pa,

        inlet temperature J_e,i = 81,4 °C, outlet temperature J_a,i = 40 °C

-          automatic switch to the HX module: enter relative moisture j₁ = 100 %

-          automatic switch back to WTS

result: -> heat flow Q_i = -29603 W

Total heat flow and cooling water mass flow (manual calculation)

-          Q_ges = -13360 W - 29534 W = -42963 W

-          Q_ges = m_ges × cp × DT -> m_ges = 42894 /(4177 × 10) = 1,029 kg/s

Design of both partial exchangers:

e) Calculation of the desuperheating part with WTS

-          terminate the program and start WTS again

-          in basic data select tube medium ‘air’, shell medium ‘water’, geometry

-          in the WTS mask enter mass flow inside m_i = 0,115535 kg/s, pressure inside P_i = 350000 Pa, inlet     temperature inside J_e,i = 195 °C, outlet temperature inside J_a,i = 81,4 °C,
        mass flow outside m_a = 1,029 kg/s, pressure outside P_a = 500000 Pa,

        outlet temperature outside J_a,a = 40 °C

result: -> J_e,a = 36,891 °C

-          scroll down and enter real length

-          enter nozzle diameter (calculation of pressure loss)

-          save tubesheet in SPIE module

f) Calculation of the condensation part with WTS

-          terminate the program and start WTS again

-          in basic data select tube medium ‘humid gases’ and shell medium ‘water’, load tubesheet

-          in the WTS mask enter
         mass flow inside m_i = 0,115535 kg/s, pressure inside P_i = 350000 Pa,
         inlet temperature inside J_e,i = 81.4 °C, outlet temperature inside J_a,i = 40 °C

-          automatic switch to the HX module: enter relative moisture j₁ = 100 %

automatic switch back to WTS

-          enter mass flow outside m_a = 1,029 kg/s, pressure outside P_a = 500000 Pa,

inlet temperature outside J_e,a = 30 °C

-          outlet temperature outside is calculated:

-           

result: -> J_a,a = 36,885 °C (This temperature is equal to the calculated inlet temperature outside J_e,a in

the desuperheating part.

Otherwise, there is an error in the secondary calculation of heat balance or mass flow.)

-          scroll down and enter real length

-          enter nozzle diameter (calculation of pressure loss)

g) Total area of the exchanger is equal to the sum of individual areas of both part exchangers

h) Pressure drop

The total pressure drop of the heat exchanger (inside resp. outside) is equal to the sum of the pressure losses of both part exchangers minus once pressure loss in the nozzles.

(The pressure loss in the nozzles has been considered for both calculations of the pressure loss of the individual exchangers.)