10.450 Process Dynamics, Operations, and Control
Lecture Notes - 1
Lesson 1. Design of a surge tank to smooth out fluctuations in flow. Definition of
important process control terms.
1.0
Context
Much of the chemical engineering curriculum concerns continuous
processes operating at steady state. Well and good, but there's more to it:
continuous processes may be disturbed in a variety of ways, and the
effects propagate through the process as a function of time – throughout
the process, temperature, pressure, flow, and composition may rise or fall.
Process Control is about managing disturbances, for product quality, for
economics, for safety. We begin with a simple example:
1.1
Surge tank
Envision two continuous processes operating in series. Process 1 feeds a
stream wi to process 2.
from other processes
process 1
wi
process 2
to other processes
Stream wi has some steady design flowrate, but in practice it varies,
causing problems in process 2. We might attack the problem by reducing
the cause of variation in process 1; we might also attempt to mitigate the
effect of the variation on process 2. Propagation of disturbances between
processes is a common problem, and a common solution is the surge tank;
its job is to damp out changes in wi from the upstream process and thus
deliver a steadier wo to the downstream process.
from process 1
wi
h
to process 2
wo
1
10.450 Process Dynamics, Operations, and Control
Lecture Notes - 1
Notice that the inlet flow is unconstrained, and the outlet flow is pumped.
Because the surge tank itself is not a steady-state process, IN does not
equal OUT, and thus the liquid level will vary with time.
1.2
Designing the tank
We might approach the design by
(1) characterizing the inlet stream
(2) specifying limits on the outlet stream
(3) making a suitable process model to connect inlet with outlet Stated in this way, it's not so different from approaching a steady state
process design.
Inlet: suppose that the flow swings by ±40% over a 20-minute period.
wi = 10,000 + 4000sin
2πt
20
(1.2.1)
where flow is in kg h-1 and time in minutes. Of course, real data would be
more messy, but that's just a matter of detail. One can learn a lot about the
system by simplifying to the essential features.
Outlet: the desired flow wo is 10,000 kg h-1. Let's be hard-nosed and insist
on no variation.
Process model: by instinct a chemical engineer writes a material balance.
dh
= wi − wo
h(0) = ho
dt
t
1
(wi (t) − wo (t) )dt
h(t) = ho +
ρA ∫0
ρA
(1.2.2)
This is the process model; it describes how level varies with time as wi
changes. Substituting (1.2.1) into (1.2.2) and integrating, we find
h(t) = ho +
212 
2πt 

1 − cos
ρA 
20 
(1.2.3)
where height is in m, area in m2, time in minutes, and density in kg m-3.
To complete the design, we must choose the tank cross-sectional area A;
spending more money for a larger tank will reduce the amplitude of the
level variations.
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10.450 Process Dynamics, Operations, and Control
Lecture Notes - 1
This tank has a free inlet and a pumped outlet; intuitively it seems possible
that the tank may overflow or run dry. We can confirm this sobering
thought by applying our tank model (1.2.2) to a persistent imbalance
between wi and wo. Suppose the simple case of
wi − wo = C
(1.2.4)
Substituting (1.2.4) into (1.2.2), we find
h(t) = ho +
C
t
ρA
(1.2.5)
Therefore, we should protect our tank with some automatic process
control – something that will measure the level and take corrective action
should the level become too high or low.
1.3
Definitions to get us started
process: the equipment within some boundary, along with the streams of
matter and energy that cross that boundary -- what we usually
mean when we think of 'chemical process'. In this example, it's the
tank, pump, piping, and fluid.
disturbance: a change imposed on the process. In this example, the input
stream wi varies with time.
controlled variable: some feature of the process that we would like to
control. It may be a stream crossing the boundary or some
quantity within. We want to control it because the disturbance
makes it change with time, in a way that we don't like. In this
example, the controlled variable is the liquid level.
set point: the desired value of the controlled variable. In this example, we
have no set point, but we do want to confine the controlled variable
between high and low limits.
manipulated variable: some feature of the process that we adjust so that
we can exert influence on the controlled variable. In most
chemical processes, the manipulated variable will be the flowrate
of a stream. In this example, it seems reasonable to manipulate the
outlet flow.
final control element: a device that adjusts the manipulated variable. If the
manipulated variable is usually a stream, the final control element
is usually a valve, referred to as a control valve.
measured variable: most often, synonymous with the controlled variable –
we measure it so that we can tell how well our control scheme is
working. Of course, we may also measure the manipulated
variable and other variables, as well.
sensor: a measuring instrument. For chemical processes, the most
common measurements are of flow (F), temperature (T), pressure
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10.450 Process Dynamics, Operations, and Control
Lecture Notes - 1
(P), level (L), and composition (A, for analyzer). The sensor will
detect the value of the measured variable as a function of time.
controller: the device that detects the output of the sensor, decides how
seriously the controlled variable deviates from the set point, and
directs the final control element in response. The controller
performs calculations based on its control algorithm.
transducer: this may be more than you wanted to know. The controller
must be able to communicate with sensor and final element.
Transducers convert and transmit signals to make this possible.
There are more details, of course, but they can wait. We install a level
sensor on the tank, put a control valve at the pump discharge, and connect
the two with a controller. Notice the symbols: the circle containing L
represents the sensor, and LC represents the controller. The control valve
has a mushroom on it for reasons we'll cover later. In the schematic, the
sensor communicates with the process by a solid line, and with the
controller and valve by a dashed line. We call this control structure
feedback control - the value of the controlled variable is fed back to a
controller, which adjusts the manipulated variable in response.
wi
L = level sensor
C = calculation or controller
h
L
LC
final control element
(control valve)
wo
When the level sensor indicates approach to high or low limits, the
controller computes a response by its algorithm and directs the control
valve to open or close appropriately. The outlet flow wo may not be
constant, as we wanted, but by suitable choice of tank size and control
algorithm we can significantly reduce its variability, and hence the effects
on downstream processes.
1.4
That’s process control?
Enough for now. We've modeled a simple process, defined our terms, and
sketched out a control scheme. Before we attempt to specify more about a
controller, however, we must learn more about the ways in which
processes might be disturbed.
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