Spray drying Heat and Mass Balance calculation : step by step

1. Spray Dryer heat and mass balance

Spray Drying is a drying unit operation that has found many applications across industries (food, pharma, chemicals...). As a drying operation, it is inherently a high consumer of energy. In a world marked by global warming and that will be more and more scarce in natural resources, optimization and improvement of the efficiency of industrial processes is critical, if not just a matter of survival over the long run. Companies manufacturing product by spray drying must therefore improve the thermal efficiency of their spray dryers in order to have an economical and reduce at best the impact on the environment.

Heat and Mass Balance is the tool at the disposal of Engineers to calculate the amount of heat entering the dryer, the amount of heat leaving the dryer, and thus calculate its efficiency. From the calculation and analysis of each of the stream, recommendations can be drawn in order to improve the thermal efficiency of a dryer.

Note that this page is a work in progress, it will be updated soon

2. Spray dryer heat and mass balance calculation

All heat and mass balance starts by defining the system studied, with inlet and outlet streams. A simple single stage spray dryer is represented on the drawing below :

With :

Ga = dry air inlet mass flow (kg/h)
Ta1 = temperature of the hot air entering the dryer (c)
Qa1 = enthalpy of inlet air (J/kg)
H1 = absolute humidity inlet air (kg water / kg dry air)

Ta2 = temperature of the air outlet of the dryer (c)
Qa2 = enthalpy of outlet air (J/kg)
H2 = absolute humidity outlet air (kg water / kg dry air)

Ms = dry solid inlet mass flow (kg/h)
Ts1 = temperature of the inlet feed (c)
Qs1 = enthalpy of inlet feed (J/kg)
Ws1 = moisture of the feed (kg water / kg dry product)

Ts2 = temperature of the outlet solids (c)
Qs2 = enthalpy of inlet solids (J/kg)
Ws2 = moisture of the outlet solids (kg water / kg dry product)

An assumption is made that no solids is exiting the system with the air stream which is not totally correct especially when cyclones are used as solids / gas separation equipment, it is probably closer to reality when bag filters are used.

All balances follow this principle :

Inlet + production = Outlet + Accumulation

2.1 Mass Balance

A Mass balance can be done on water (moisture). The dryer is assumed to be started for a while and in steady stage (no accumulation term in the balance), there is also no moisture production in the dryer, which means [inlet = outlet] :

Inlet :

• Water in air (kg water / h) : Ga (kg dry air / h) * H1 (kg water / kg dry air)
• Water in feed (kg water / h) = Ms (kg dry solid / h) * Ws1 (kg water / kg dry solid)

Outlet :

• Water in air (kg water / h) : Ga (kg dry air / h) * H2 (kg water / kg dry air)
• Water in outlet solids (kg water / h) = Ms (kg dry solid / h) * Ws2 (kg water / kg dry solid)

Which gives :

Ga*H1 + Ms*Ws1 = Ga*H2 + Ms*Ws2

Ms*(Ws1-Ws2) = Ga*(H2-H1)

2.2 Heat Balance

The heat balance is done as well on a dryer assumed to be in steady state (no accumulation term), there is also no production of heat in the dryer (air and feed are heated up beforehand), however a loss term, due to heat escaping via the walls of the dryer, must be taken into account.

Inlet :

• Heat inlet with air (W) : Ga (kg dry air / h) / 3600 * Qa1 (J / kg dry air)
• Heat in feed (W) = Ms (kg dry solid / h) / 3600 * Qs1 (J / kg dry solid)

Outlet :

• Heat outlet with air (W) : Ga (kg dry air / h) / 3600 * Qa2 (J / kg dry air)
• Heat in outlet solids (W) = Ms (kg dry solid / h) / 3600 * Qs2 (J / kg dry solid)
• Heat loss (W) = QL

Which gives :

Ga*Qa1 + Ms*Qs1 = Ga*Qa2 + Ms*Qs2 + QL

2.2.1 Humid air enthalpy calculation

The enthalpy of the humid air stream can be calculated with the following formula :

Qa = Cs*(ΔT) + H.λ

With :

Qa1 = enthalpy of humid air (J/kg)
Cs = specific heat of humid air (J/K/kg dry air)
ΔT = T - T0 = difference between actual temperature and temperature of reference (K)
H = absolute humidity air (kg water / kg dry air)
λ = vaporization enthalpy at temperature of reference (J/kg)

The temperature of reference is often taken as the freezing point of water (T0 = 273 K)

In practice, humid air calculation formula at 273 K :

Qa = (1005 + 1884*H).(T-273) + 2.5023.10⁶.H

2.2.2 Solid stream enthalpy calculation

The enthalpy of the solids stream can be calculated with the following formula :

Q_s = Cp_ds*(ΔT) + W_s*Cp_w*(ΔT)

With :

Q_s = enthalpy of humid solid stream (J/kg)
Cp_ds = specific heat of dry solid (J/K/kg)
ΔT = T - T₀ = difference between actual temperature and temperature of reference (K)
W_s = moisture of the stream (kg water / kg dry product)
Cp_w : specific heat of water (J/K/kg)

3. Spray dryer thermal efficiency calculation

The operation of interest in a spray dryer is drying. The thermal efficiency of the spray dryer is thus estimated by calculating the amount of heat that is actually used for evaporating water, and by comparing it to the total heat brought to the dryer.

Thermal efficiency = (heat used for evaporation) / (total heat input to the dryer)

3.1 Overall thermal efficiency

The overall thermal efficiency can be estimated thanks to the temperatures of the air streams :

With :

T₀ = atmospheric temperature of inlet air before heating (c)
T₁ = heated inlet air temperature (c)
T₂ = outlet air temperature in case of adiabatic operation (c)

The temperature T₂ must be read on a psychrometric diagram. Define the heated air conditions (dry bulb temperature, absolute humidity), then follow the line of constant enthalpy until the saturation curve. The tempertare on the saturation curve is T2.

In the example below, air at 15c (T₀) and 5 g water / kg dry air absolute humidity is heated up to 45c (T₁). There is no change in absolute humidity while heating up. In the dryer, the air will be cooled down and will pick up humidity (as it will dry the solids), if the operation was adiatabtic, no energy would be exchanged with outside, which means that it would be done at constant enthalpy. Temperature T₂ can then be determined by following the line of constant enthalpy until the saturation curve. (follow A -> B -> C -> T₂ on the example graph)

3.2 Evaporative efficiency

The evaporative efficiency can be estimated thanks to the temperatures of the air streams :

With :

T₀ = atmospheric temperature of inlet air before heating (c)
T₁ = heated inlet air temperature (c)
T_sat = adiabatic saturation temperature (c)

The temperature T_sat must be read on a psychrometric diagram.

3.3 Energetic Specific Consumption (ESC)

The ESC is defined as the ratio of consumed energy in the dryer, over the amount of water that has been evaporated. It is expressed in kJ/kg (of evaporated water).

With :

ESC = Energetic specific consumption (kJ/kg)
ΔH = energy consumed in the spray drying process (kJ/h)
m_water = mass flow of water evaporated (kg/h)

4. Experimental measurements

In order to be able to complete the heat and mass balance of a spray dryer, it is necessary to measure some process parameters, typically :

• The feed mass flow rate (can be done thanks to a flowmeter)
• The feed total solids (TS - can be done by sampling the feed)
• The feed temperature (temperature sensor)
• The atmospheric air temperature (use of a temperature sensor)
• The atmospheric air inlet humidity
• The hot air temperature
• The air outlet temperature

It is then possible to calculate the heat and mass balance and then the energetic efficiency of the spray dryer.

5. Free Excel calculation tool : Spray Dryer Heat and Mass Balance (HMB)

You can access a free heat and mass balance calculator Excel to make the spray drying Heat and Mass Balance calculation explained above : Spray Drying Heat and Mass Balance download (click here !)

Warning : this calculator is provided to illustrate the concepts mentionned 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.

---

Source
Spray Drying, K. Masters, Leonard Hill Books, 1972, pages 54-64