Like the
heat exchanger and
gravity drained tanks case studies, the jacketed stirred reactor is a self regulating
processes. That is, the measured process variable (PV) naturally seeks a
steady operating level if the controller output (CO) and major disturbance
(D) are held constant for a sufficient length of time.
And like the heat exchanger and the gravity drained tanks, the jacketed
stirred reactor process is actually a sophisticated simulation derived from first principals
theory and available in
commercial software. Nevertheless, the methods and procedures we
establish during these investigations are directly applicable to a broad range of
industrial processes with streams
comprised of liquids, gases, powders, slurries and melts.
The Jacketed Stirred Reactor
The process, shown below in manual mode,
is often called a continuously stirred tank reactor (CSTR).
As labeled in the figure (click for large view), a reactant feed stream enters the top of the
vessel. A
chemical reaction converts most of this feed into the desired product as
the material passes through what is essentially a stirred tank. The stream
exiting the
bottom of the vessel includes the newly created product plus that portion
of the feed that did not convert while in the vessel.
This well mixed reactor has additional considerations we use later in the
discussion:
▪ The
residence time,
or overall flow rate of reactant feed plus product through the vessel, is
constant.
▪ The chemical reaction that occurs is
exothermic, which means that heat energy is released as feed converts to
product.
The Function of the Cooling Jacket
The chemical reaction releases heat and this energy causes the
temperature of the material in the vessel to rise. As temperature rises, the
conversion of feed to product proceeds faster, leading to the release of even
more heat.
To stop the upward spiral of hotter temperatures increasing the rate of
reaction that produces even more heat, the vessel is enclosed with a jacket
(or outer shell). A cooling liquid flows through the jacket, collecting heat
energy from the outer surface of the reactor vessel and carrying it away as
the cooling liquid exits at the jacket outlet.
When the flow of cooling liquid through the jacket increases, more heat
is removed. This lowers the reactor temperature, slowing the rate of
the reaction, and thus decreasing the amount of feed converted to product
during passage through the reactor.
When the flow of cooling liquid through the jacket decreases, some of the energy from the heat-producing reaction,
rather than being carried away with the cooling liquid, accumulates in the
vessel and drives the
reactor temperature higher. The result is an increased conversion of
reactant feed to product.
As shown
in the figure below (click for large view),
the flow rate of cooling liquid is adjusted with a valve on the cooling jacket
outlet stream.
Control Conversion by Controlling Temperature
In this case study, we do not seek 100% conversion of reactant feed to
product. Rather, our operating specification is a precise 89% conversion.
Because the reactor has a constant residence time, the amount of heat
energy released inside the vessel is directly related to the percent of feed
converted to product. By controlling the temperature in the reactor, we can
maintain the percent conversion to the desired value.
The vessel is well mixed, so the bulk temperature inside the reactor is
about the same as the temperature flowing out the exit stream. Thus, as
shown in the process graphic above, we place a temperature sensor in the
stream at the bottom of the vessel and our measured process variable (PV)
becomes reactor exit temperature.
| Practitioner’s Note:
as discussed
in this article, there can be benefits to measuring and controlling a
related
variable that is linked to the actual process variable of interest. In this
reactor application, for example, a temperature sensor is significantly
less expensive to purchase, install and maintain relative to the
alternative of an online analyzer that directly measures chemical
composition. Temperature sensors are also rugged and reliable, have a
rapid response time, and provide a high accuracy and precision compared
to most all online analyzers. If it provides sufficiently useful
information, a "fast, cheap and easy" sensor is the smart choice. |
As
the figure reveals, we can achieve our desired 89% conversion
by maintaining the reactor exit stream temperature at 90 oC. From
an operational view, this means the reactor exit temperature will have a
fixed set point (SP) value of 90 oC.
During bump testing, operations personnel tell us that we may briefly
move the reactor exit temperature up and down by 2 oC, but they
strongly discourage anything more. Thus:
▪
design PV and SP = 90 oC with approval for brief dynamic testing
of ±2 oC
The Disturbance
Because we seek to hold conversion to a
constant 89% at all times (which is achieved by holding reactor exit stream
temperature at 90 oC), disturbance rejection becomes our main
controller design concern.
The major disturbance in this jacketed stirred reactor is the result of an unfortunate design.
Specifically, the temperature of the cooling liquid entering the jacket changes
over time (this situation is surprisingly more common in industrial
installations than one might first believe).
As the temperature of the cooling liquid entering the jacket changes, so
does its ability to remove heat energy. Warm liquid removes less energy than
cool liquid when flowing through the jacket at the same rate.
So "disturbance rejection" in this case study means minimizing the impact
of cooling liquid temperature changes on reactor operation.
As labeled in the process graphic, the temperature of the cooling liquid
is normally at about 43 oC. On occasion, however, this temperature
can climb, sometimes rather rapidly, to as high as 50 oC.
We will design for the worst-case scenario and test our controller when the cooling liquid
temperature (our disturbance, D) spikes from 43 oC up
to 50 oC in a single step. Thus:
▪
design D = 43 oC with spikes up to 50 oC
The Design Level of Operation (DLO)
The first step of the our four step
design and tuning recipe is to establish the design level of operation.
In the discussion above, we have completed step 1 by establishing the DLO
as:
•
Design PV and SP = 90 oC with approval for brief dynamic testing
of
±2 oC
•
Design D = 43 oC with spikes up to 50 oC
Return to the
Table of Contents to learn more.
Copyright © 2007 by Douglas J. Cooper. All Rights Reserved.
