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Condenser design : calculation method

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Section summary
1. Condenser definition
2. Condenser calculation procedure
3. Free Excel condenser calculation tool

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1. Condenser definition

What is a condenser ?

A condenser aims at sufficiently cooling down a vapor, thanks to a cooling fluid, so that its state changes towards a liquid. Condensers can have different kind of design, including direct condensing which consists in contacting the vapor with the cooling fluid. This page is focusing however on condensers designed as shell - tube heat exchangers and installed in vertical or horizontal position. The vapor and the cooling fluid are not in contact and condensation can happen in the shell or in the tubes even if condensing in the shell is the most common case.

Condensers are very widely used in process industries : in food processing, refineries or even air conditioning. When having to generate a vacuum, condensers are installed to reduce the flow of vapor to suck and therefore increase the vacuum reached. It is a very energy demanding unit operation so most of the time cold fluid available in quantity such as water, or air, are used as cooling fluid to perform the condensation.

Note that the vapor to condense can be very varied and can include non condensable vapor such as air, which has a very strong influence on the performances of the condenser. The explanations given on this page focus however on the simpler case which is a pure susbtance to condense.

2. Calculation procedure : condenser sizing

How to design a shell-tube condenser ?

2.1 STEP 1 : get the design data

The following data must be defined in order to check the design, or size a condenser :

• Fluid properties (viscosity, specific heat, latent heat for the fluid to be condensed... if possible as a function of temperature)
• Inlet and outlet temperature of each fluids (note : the procedure here is to size a heat exchanger knowing those data, but it can be adapted after, using Excel, to calculate the outlet temperature knowing the characteristics of the heat exchanger for example)
• Inlet pressure of fluids
• Allowable pressure drop

It is assumed that the vapor to condensate is in the shell side.

2.2 STEP 2 : calculate the required heat flux

The heat flux can be calculated knowing the flowrate, the in and out temperatures, the specific heat of the fluid, and the latent heat of the fluid to condensate. If possible, it is easier to calculate the heat flux on the cold side as there is normally no phase change.

With

m_c = mass flowrate on cold side (kg/s)
Cp_c = specific heat of cold fluid
T_co = outlet temperature of cold side (K)
T_ci = inlet temperature of cold fluid (K)
m_h = mass flowrate of vapor to condense on hot side (kg/s)
Cp_h1 = specific heat of vapor (J/kg/K)
T_hi = inlet temperature of vapor to condense (K)
T_hcond = condensation temperature of the pure vapor (K)
ΔH_vap = latent heat of vaporization of the pure sustance (J/kg/K)
Cp_h2 = specific heat condensed liquid (J/kg/K)
T_ho = outlet temperature of hot side (K)

It is then possible to approximate the size of the heat exchanger by estimating the overall heat transfer coefficient H.

H for condensers is often in between 75 to 1100 kcal/h.m².c = 0.1 to 1.3 kW/m².K.

H = overall heat exchange coefficient (kW/m².K)
S = area of the heat exchanger (m²)
ΔT_ml (K)

The value of S can thus be calculated, as a 1st approximation of the heat exchanger size.

2.3 STEP 3 : define a tentative geometry

At this stage, assume a geometry (number of tube, diameter of tube, diameter of shell) reaching the surface area required. If you have a manufacturer brochure, you can refer to it.

2.4 STEP 4 : Calculation of the heat exchange coefficient on the tube side

It is assumed that the cooling fluid, thus the fluid that is not submitted to a change of state, is located in the tubes. As a consequence, a general relation correlating the Nusselt number to the Reynolds and Prandtl number can be used for assessing the heat transfer coefficient :

Nu = (h_tube.d_i)/λ_c

With :

Nu = Nusselt number, calculated by the correlations below
h_tube = heat transfer coefficient on tube side (W.m^-2.K^-1)
λ_c = thermal conductivity of the cooling fluid (W/(m.K)) (m⋅kg⋅s⁻³⋅K⁻¹)

2.4.1 Laminar flow (Re < 2100)

The following correlation is from Sieder and Tate

Nu = 1.86.Re^1/3.Pr^1/3.(d_i / L)^1/3.(μ/μ_t)0.14

With :

Re = Reynolds number
Pr = Prandtl number = Cp.μ / λ
d_i = internal diameter of the tube in m
L = length of the tube in m
μ = viscosity of the fluid at bulk temperature in Pa.s (kg/m/s)
μ_t = viscosity of the fluid a wall temperature in Pa.s (kg/m/s) - please refer to paragraph 2.6.1 for the calculation of T_wall
C_p = specific heat of the fluid in J/kg/K (m²/s²/K)
λ = thermal conductivity of the fluid (W/(m.K)) (m⋅kg⋅s⁻³⋅K⁻¹)

2.4.2 Turbulent flow (Re > 10000)

The following correlation is from Colburn.

Nu = 0.027.Re^0.8.Pr^1/3.(μ/μt)^0.14

2.4.3 Calculation of Reynold number

The Reynolds number can be calculated as a function of the mass flow, number of tubes, number of passes, tube diameter.

Re = G.d_i / μ

G = m / [(Nt/nt).π.d_i²/4]

With

G = mass flux in the tube in kg/s/m²
ṁ = mass flow in the heat exchanger on the tube side in kg/s
N_t = number of tubes in the shell tube heat exchanger
n_t = number of passes tube in the shell tube heat exchanger
μ = viscosity of the fluid at bulk temperature in Pa.s (kg/m/s)

2.5 STEP 5 : Calculation of the heat exchange coefficient on the shell side

The calculation of the heat exchange coefficient on the shell side depends on the orientation of the condenser, vertical or horizontal, and on the flow regime in the shell, laminar or turbulent.

2.5.1 Reynolds calculation

Vertical tubes

The Reynolds number is, for the liquid condensate, expressed as :

Re = (4*Gv) / μ

With :

Re = Reynolds number (-)
G_v = mass flowrate of condensate per unit of length of tube (kg/s/m) = m_c / (π*d_o*N_t)
μ = viscosity of the condensate (Pa.s) - please refer to paragraph 2.6.1 for the calculation of T_film
m_c = mass flowrate of vapor (= condensate if all the vapor is condensed) (kg/s)
d_o = tube outside diameter (m)
N_t = number of tubes in the shell (-)

Horizontal tubes

The Reynolds number is, for the liquid condensate, expressed as :

Re = (4*Gh) / μ

With :

Re = Reynolds number (-)
G_h = mass flowrate of condensate per unit of length of tube (kg/s/m) = m_c / (L*N_t^1/4)
μ = viscosity of the condensate (Pa.s) - please refer to paragraph 2.6.1 for the calculation of T_film
m_c = mass flowrate of vapor (= condensate if all the vapor is condensed) (kg/s)
L = tube length (m)
N_t = number of tubes in the shell (-)

To be noted that, for horizontal condensers, the flow regime of the condensate in the shell is actually laminar, the calculation above is thus not really necessary

2.5.2 Laminar flow (Re < 2100)

Vertical tubes

The heat transfer coefficient on the shell side, for vertical tubes, with the condensate in laminar flow can be expressed as :

h_shell = h_shellv = 1.47*[λ³*ρ²*g/μ²]^1/3[(4*Gv) / μ]^-1/3

2.6 STEP 6 : calculation of the actual overall heat transfer coefficient H_calculated

The heat transfer coefficient is the sum of the convection inside the tube, the conduction through the tubes, the convection outside the tube, also considering the fouling resistances on both sides of the tube. The actual overall heat transfer coefficient is thus :

H_calculated = overall heat transfer coefficient (W.m^-2.K^-1)
h_tube = heat transfer coefficient on tube side (W.m^-2.K^-1)
R_tube = fouling resistance on tube side (K.W^-1.m^-2)
h_shell = heat transfer coefficient on shell side (W.m^-2.K^-1)
R_shell = fouling resistance on shell side (K.W^-1.m^-2)
d_i = tube inside diameter (m)
d_o = tube outside diameter (m)
λ_m = thermal conductivity of the material of the tubes (W.m^-1.K^-1)

2.6.1 Calculation of the film temperature

In order to calculate properly the overall heat exchange temperature, it is required to know what is the actual temperature of the condensing liquid on the tube where the liquid is making a thin film. In order to approximate this temperature, the following calculation can be done :

T_film = (T_hcond+T_wall)/2

With :

T_film = temperature of the film of condensed liquid on the tube (K)
T_hcond = temperature of the vapor = condensation temperature of the vapor (K)
T_wall = wall temperature of the tube (K)

The temperature Twall of the tube can be calculated by :

With :

T_hcond = temperature of the vapor = condensation temperature of the vapor (K)
T_wall = wall temperature of the tube (K)
h_tube = heat transfer coefficient on tube side (W.m^-2.K^-1)
h_shell = heat transfer coefficient on shell side (W.m^-2.K^-1)
d_i = tube inside diameter (m)
d_o = tube outside diameter (m)
T_f = average temperature of the cooling fluid (K) = (T_ci+T_co)/2
T_co = outlet temperature of cold side (K)
T_ci = inlet temperature of cold fluid (K)

It is actually an iterative process. Indeed, at the beginning of the calculation the film temperature is not known. To get a 1st approximation and start the calculation it can be assumed for example that h_tube = h_shell. The procedure is then :

1. Assume h_tube = h_shell
2. Calculate T_wall and T_film
3. Calculate h_shell and h_tube
4. Recalculate T_wall and T_film
5. If T_{wall_step2} = T_{wall_step4} AND T_{film_step2} = T_{film_step4}, then go to step 6, if not return to step 2
6. Calculate the overall heat transfer coefficient H_calculated

2.6.2 Verify that the the available heat transfer is sufficient

It is then required to compare H calculated with H assumed.

If H_calculated = H_assumed, the calculation is valid, the size of the heat exchanger, with the total heat exchange area S is correct.

If H_calculated ≠ H_assumed, then the calculation needs to be run again, this time using H_assumed as starting point, or, if values are really far, changing the design of the heat exchanger size / design and running it again.

2.7 STEP 7 : Calculation of the pressure drop

The design defined in step 6 is only valid if the pressure drop on both sides is less than the allowable pressure drop. If yes, the design can be kept, if not, some design choices such as the size of the tube, number of tubes... On the tube side, the pressure drop can be calculated with the same formula as for a standard shell tube heat exchanger.

On the shell side, the vapor pressure drop is usually very low.

2.8 STEP 8 : optimization and detail design

Even if the design done satisfies the process conditions, it may be possible to improve the design by making it less costly, more compact... the design procedure can then be re-run for the basic design calculated by changing the number of tubes, diameter of tube, tube length...etc...

The procedure above will be helpful to get an idea but cannot be used to such details. It should be done with a specialized company. Detail design and construction drawing must always be done with the support of such a company.

3. Free Excel condenser calculation tool

You can access a free Excel calculation tool to size a shell-tube condenser, or control the size of an existing condenser, as explained above : Condenser design calculation tool (click here)

Warning : this calculator is provided to illustrate the concepts mentioned in this webpage, it is not intended for detail design. It is not a commercial product, no guarantee is given on the results. Please consult a reputable designer for all detail design you may need.