Reaction calorimeter

Heat flow calorimetry measures the heat flowing across the reactor wall and quantifies this in relation to the other energy flows within the reactor.

${\displaystyle Q=UA(T_{r}-T_{j})}$

where,

${\displaystyle Q}$ → process heating (or cooling) power (W)

${\displaystyle U}$ → overall heat transfer coefficient (W/(m²K))

${\displaystyle A}$ → heat transfer area (m²)

${\displaystyle T_{r}}$ → process temperature (K)

${\displaystyle T_{j}}$ → jacket temperature (K)

Heat flow calorimetry allows the user to measure heat while the process temperature remains under control. While the driving force T_r − T_j is measured with a relatively high resolution, the overall heat transfer coefficient U or the calibration factor UA is determined by means of calibration before and after the reaction takes place. They are affected by the product composition, the process temperature, the agitation rate, the viscosity, and the liquid level. Using reaction calorimeters to a high degree with accuracy requires understanding their limitations and having significant experience with the process.[1]

In heat balance calorimetry, the cooling/heating jacket controls the temperature of the process. Heat is measured by monitoring the heat gained or lost by the heat transfer fluid.

${\displaystyle Q=m_{s}C_{ps}(T_{i}-T_{o})}$

where,

${\displaystyle Q}$ → process heating (or cooling) power (W)

${\displaystyle m_{s}}$ → mass flow of heat transfer fluid (kg/s)

${\displaystyle C_{ps}}$ → specific heat of heat transfer fluid (J/(kg K))

${\displaystyle T_{i}}$ → inlet temperature of heat transfer fluid (K)

${\displaystyle T_{o}}$ → outlet temperature of heat transfer fluid (K)

Heat balance calorimetry is, in principle, the ideal method of measuring heat since the heat entering and leaving the system through the heating/cooling jacket is measured from the heat transfer fluid (which has known properties).

In heat balance calorimetry, the heat entering and leaving the system through the heating/cooling jacket is measured from the heat transfer fluid (which has known properties) - making the method a very effective way of measuring heat loss or gain. Most calibration problems encountered by heat flow and power compensation calorimetry therefore do not apply to heat balance calorimetry. Though the method does not work well in traditional batch vessels since the process' heat signal is obscured by large heat shifts in the cooling/heating jacket.[2]

A variation of the 'heat flow' technique is called 'power compensation' calorimetry. This method uses a cooling jacket operating at constant flow and temperature. The process temperature is regulated by adjusting the power of the electrical heater. When the experiment is started, the electrical heat and the cooling power (of the cooling jacket) are in balance. As the process heat load changes, the electrical power is varied in order to maintain the desired process temperature.[3] The heat liberated or absorbed by the process is determined from the difference between the initial electrical power and the demand for electrical power at the time of measurement. Power compensation calorimetry requires less preparation than heat flow calorimetry, however, it still experiences similar limitations, since any change in product composition, liquid level, process temperature, agitation or viscosity will impact the instrument's calibration. The presence of an electrical heating element is also suboptimal for process operations. A further limitation of the method is that the largest heat it can measure is equal to the initial electrical power applied to the heater.[4]

${\displaystyle Q=IV\,\,\,\,\,\mathrm {or} \,\,\,\,\,\,(I-I_{0})V}$

where,

${\displaystyle I}$ = current supplied to the heater

${\displaystyle V}$ = voltage supplied to the heater

${\displaystyle I_{0}}$ = current supplied to the heater at equilibrium (assuming constant voltage / resistance)

Constant flux heating and cooling jackets use variable geometry cooling jackets and can operate with cooling jackets at substantially constant temperature. These reaction calorimeters tend to be much simpler to use and are much more tolerant of changes in the process conditions (which would affect calibration in heat flow or power compensation calorimeters).[5]

In essence, constant flux calorimetry is a highly developed temperature control mechanism which can be used to generate highly accurate calorimetry. It works by controlling the jacket area of a controlled lab reactor while keeping the inlet temperature of the thermal fluid constant. This allows the temperature to be precisely controlled even under strongly exothermic or endothermic events as additional cooling is always available by simply increasing the area over which the heat is being exchanged.

This system is generally more accurate than heat balance calorimetry (on which it is based), as changes in the delta temperature (T_out - T_in) are magnified by keeping the fluid flow as low as possible.

One of the main advantages of constant flux calorimetry is the ability to dynamically measure heat transfer coefficient (U). We know from the heat balance equation that:

${\displaystyle Q=m_{f}\;C_{p}\;(T_{in}-T_{out})}$

We also know that from the heat flow equation that

${\displaystyle Q=U\;A\;LMTD}$

We can therefore rearrange this such that

${\displaystyle U={\frac {m_{f}\;C_{p}\;(T_{in}-T_{out})}{A\;LMTD}}}$

This will allow us therefore to monitor U as a function of time.