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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

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

Condenser Design Calculation Excel Spreadsheet

With

Air Cooled Condenser Design Calculation Excel

h_shellv = heat exchange coefficient on the shell side for vertical tubes (W.m^-2.K^-1)
λ = thermal conductivity of the condensate fluid (W/(m.K)) (m⋅kg⋅s⁻³⋅K⁻¹) - please refer to paragraph 2.6.1 for the calculation of T_film
ρ = density of the condensate fluid (kg/m3)
g = 9.81 m.s-2
μ = viscosity of the condensate (Pa.s) - please refer to paragraph 2.6.1 for the calculation of T_film
G_v = mass flowrate of condensate per unit of length of tube (kg/s/m) = m_c / (π*d_o*N_t)

Horizontal tubes

h_shell = h_shellh = 1.51*[λ³*ρ²*g/μ²]^1/3[(4*G_h) / μ]-1/3

With

Condenser Design Calculation Excel Example

h_shellh = heat exchange coefficient on the shell side for horizontal tubes (W.m^-2.K^-1)
λ = thermal conductivity of the condensate fluid (W/(m.K)) (m⋅kg⋅s⁻³⋅K⁻¹) - please refer to paragraph 2.6.1 for the calculation of T_film
ρ = density of the condensate fluid (kg/m3) - please refer to paragraph 2.6.1 for the calculation of Tfilm
g = 9.81 m.s^-2
μ = viscosity of the condensate (Pa.s) - please refer to paragraph 2.6.1 for the calculation of T_film
G_h = mass flowrate of condensate per unit of length of tube (kg/s/m) = m_c / (L*N_t)

2.5.3 Turbulent flow (Re < 10000)

Vertical tubes

h_shell = h_shellv = 0.0076*[λ³*ρ²*g/μ²]^1/3[(4*Gv) / μ]^0.4

With

h_shellv = heat exchange coefficient on the shell side for vertical tubes (W.m^-2.K^-1)
λ = thermal conductivity of the condensate fluid (W/(m.K)) (m⋅kg⋅s⁻³⋅K⁻¹) - please refer to paragraph 2.6.1 for the calculation of T_film
ρ = density of the condensate fluid (kg/m3) - please refer to paragraph 2.6.1 for the calculation of Tfilm
g = 9.81 m.s-2
μ = viscosity of the condensate (Pa.s) - please refer to paragraph 2.6.1 for the calculation of T_film
G_v = mass flowrate of condensate per unit of length of tube (kg/s/m) = m_c / (π*d_o*N_t)

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 :

Condenser Design Excel