Ideal Flow Reactors - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 238

from the light reacting phase (and so from the heavy reacting phase), it provides heat to the
light reacting phase via heat transfer through the reactor wall surface (or internal tubular
insertion wall surfaces). The heavy reacting phase and the light reacting phase are in direct
contact, and thus mass transfer of active reacting agents in the fluid (liquid) phase occurs.
Each stream is specified by its (liquid or fluid) flow rate, temperature, and compositions.
There is an additional flow rate needed to specify for the heavy reacting phase: the solid
mass flow rate. Other than the solid mass flow (and the light reacting phase is similar to
the heavy reacting phase), the reactive extraction process is identical to a reactive distilla-
tion process. Therefore, the analysis for the reactive extraction can be applied to reactive
distillation as well.
At steady state, mass balance of the solid materials leads to

X

N S

d G H ¼ r j d V (5.101)

j¼1

where r j is the (mass) rate of formation of species j in the fluid phase associated with the solid
phase. For reactive extraction, there is a net loss in solid mass as components are being dis-
solved into the fluid phase.
In the heavy reacting phase, mass balance of species j at steady state leads

d Q H C H j

þ r j dV aJ j d V ¼ 0 (5.102)

where Q H is the volumetric flow rate of the heavy (fluid) reacting phase, C H j is the (mass)
concentration of species j in the heavy reacting phase, J j is the mass transfer flux of species
j from the heavy reacting phase, and a is the specific area of contact between the heavy
and light reacting phases.
In the light reacting phase, mass balance of species j at steady state leads

d Q L C L j þ aJ j d V ¼ 0 (5.103)

where Q L is the volumetric flow rate of the light reacting phase, C L j is the (mass) concentra-
tion of species j in the light reacting phase.
Mass transfer flux from the heavy reacting phase to the light reacting phase can be
computed via

J j ¼ K Cj C H j C L j

(5.104)

where K C j is the mass transfer coefficient for species j . Mass transfer coefficients are depen-
dent on the type of molecule, flow rates, temperature, and the properties of the solid phase.
In addition to the mass balances, energy balances for the three streams (heavy reacting
phase, light reacting phase, and the heat-exchanging fluid) are required to complete the
set of the governing equations. The rate of reaction is strongly dependent on the temperature
for reactions involved with solid materials.
Equations (5.101) through (5.104) are similar to those governing the extraction processes,
with an extra reacting term. Therefore, the reactive extraction can be solved similar to solving
an extraction column.