Drag to select inlet temperature before heat exchange (on the right)
and outlet temperature after heat exchange (on the left)

flow rate

How much biomass is available to be burnt?

Do you know the Low Heating value of your Biomass?
YesNo

	kWh/kgJ/kgkcal/kg
Drag to Choose the Low Heating Value of your Biomass

YesNo

Choose a cold source for the heat produced by your plant:

Drag to select the inlet temperature of the cooling fluid before heat exchange (on the left)
and the outlet temperature of the cooling fluid after heat exchange (on the right)

Note: if you have selected air (no thermal use) as the cooling fluid, we suggest you use the annual mean temperature of the source site as the inlet temperature and the annual mean temperature+10-12°C (or equivalent) as outlet temperature

Power Results

• Net electric power (kW):
• Mechanical power (kW):
• Thermal power to the condenser (kW):

Assumptions ΔT constant for finite heat exchange area:
* ΔTpreheater + evaporator = 15 K
* ΔTcondenser = 10 K

For biomass, Lorenz Cycle efficiency is calculated with the thermal oil inlet/outlet temperature

Real efficiency to Lorenz efficiency ratio (finite exchange area)
* X=0.5

Yellow: Heat Source, thermal oil in case of Biomass

Red: working fluid, hot side

Green: working fluid, cold side

Blue: cooling fluid

Lorenz cycle efficiency

In the same way as Carnot cycle is the maximum efficiency cycle that can be retrieved from a perfect gas between two constant temperature sources, the Lorenz cycle is the one that can get the maximum efficiency from a cycle between two variable temperature sources with constant heat capacity.

The Lorenz cycle is made of the four following transformations:

• 1-2 isentropic compression
• 2-3 heating at constant heat capacity and constant temperature variation both equal to that of the heat source
• 3-4 isentropic expansion
• 4-1 cooling at constant heat capacity and constant temperature variation both equal to that of the cooling source

Efficiency of Lorenz cycle:

where T_lm,cold and T_lm,hot are the log mean temperatures of the cold and the hot sources respectively.

If the thermal exchange areas are finite, as in the real case, the temperature of the working fluid can not match exactly the temperatures of the heating and cooling sources. Through the assumption of constant temperature differences between the working fluid and the sources fluids, it is possible to calculate a new Lorenz cycle efficiency:

where T*_cold = T_cold + ΔT_condenser and T*_hot = T_hot - ΔT _{preheater + evaporator}

Real cycle efficiency

The real cycle efficiency is lower than the corresponding Lorenz cycle, since:

• expansion and compression are not isentropic;
• phase changes occur at near constant temperature;
• a compression work has to be considered;
• the heat capacity of the working fluid is neither constant nor equal to the source fluid heat capacity.

It is possible to take into account all these aspects by means of a global factor X lower than 1. Real cycle efficiency can be defined as:

η _{real cycle} = X * η _{Lorenz, finite exchange area}

Power

It is possible to calculate the mechanical power as the product of the thermal power from the heat source, which is known, by the real cycle efficiency.

The electric power can be derived from the mechanical power by multiplying it by the generator efficiency.

Since it can be assumed that compression and expansion are adiabatic, the thermal power to the condenser can be calculated by subtracting the mechanical power from the thermal power given by the heat source.

The thermal power to the condenser is available for thermal applications such as drying (sawmills, pellet factories), pre-heating (MDF industries), district heating networks, refrigeration.