Hydrocarbon Processing - May 2021 - 77

Process Controls, Instrumentation and Automation
moves will be made. As time passes, the level will approach the
limit and at some stage a small violation will be predicted. An
OP move will be calculated to change the rate-of-change of the
level such that the level will be on the limit at the ramp horizon.
At the next execution cycle, the prediction will show a small
violation again, as the level is still moving in the direction of
the limit. Once again, a small OP movement will be calculated
to bring the level to the limit at the ramp horizon. This will be
repeated until the cumulative OP moves will bring the rate-ofchange of the level to zero when the level reaches the limit. No
attempt is made to return the level to a setpoint (SP) value or to
move away from limits.
Because this method will allow the level to achieve limits while
making small OP moves to ensure the limits are not exceeded,
the risk remains that continuous or consecutive disturbances
in the same direction may occur once the level has reached the
limit. When this happens, the controller will not be able to keep
the level between the imposed limits. If this occurs and the level
moves outside a limit, the ramp horizon controller will return the
level to the limit that was exceeded using the same algorithm.
Because the method simplifies the response of the level by
calculating a gain only, it ignores any dynamic behavior. Combining this with measurement noise, unmeasured disturbances
and the possibility of an incorrect gain being used may lead to
imprecise control action. However, in a short execution cycle,
the level measurement that is taken as input and the rate-ofchange of the level that is calculated at every execution cycle
continuously update the controller error. This compensates for
the possible inaccuracies in measurement and control.
SOALC. Optimal averaging level control3,11,12 is accomplished

using model-based control software to calculate the smallest
moves that can be made continuously to allow the level to attain a zero rate-of-change when it reaches the limit. While optimal averaging level control requires model predictive control
software running on a dedicated server, the approach may be
simplified in the same way as the ramp horizon controller to
allow running the algorithm natively on a standard DCS at a
higher frequency.
If the dynamics of the level are ignored and only the absolute value of the level and its current rate-of-change are used
to calculate the future trajectory of the level, an approach
like the optimal averaging level controller may be developed.
If the current rate-of-change of the level is extrapolated from
the current value of the level, limit violations can be predicted. The OP move required during every execution cycle

until the level is balanced at the limit can then be calculated.
Because dynamics are ignored, this approach will not be as
accurate as a model-based controller. Like the ramp horizon
controller, a short execution cycle, the level measurement that
is taken as input and the rate-of-change of the level that is calculated at every execution cycle will continuously update the
controller error and will ensure adherence to limits.
If a level is currently at PV0 , with a positive rate-of-change
of ROC0 , and a high limit of H that will be exceeded based on
an extrapolation of ROC0 , then a sequence of n OP moves of
size x must be calculated to balance the level at H. The total
move of the OP over the control horizon must be (Eq. 6):
dOP = x.n

(6)

If a controller gain (G) is defined as the change per execution cycle in the rate-of-change of the level brought about by
increasing the OP by 1%, then (Eq. 7):
dOP = ROC0 /G

(7)

Combining Eqs. 1 and 2 yields Eq. 8:
x = ROC0 /(G.n)

(8)

If the level begins at the current PV with the current rateof-change and ends at the high limit with the rate-of-change at
0, the initial and final conditions must be as shown in TABLE 1.
If a step of size x is made every execution cycle, then the rateof-change of the level will be decreased by x.G every execution
cycle. The level will also increase by the current rate-of-change
per execution cycle. Therefore, TABLE 2 can be calculated.
In TABLE 2, the first column shows the Execution cycle. The
second column shows the Level measurement, calculated as
the previous value of the level plus the change in the level. The
change in the level will be the Rate-of-change in the level during the previous Execution cycle, as shown in Column 4.
For example, during Execution cycle 3, the previous value
of the level was calculated as PV0 + ROC0 + ROC0 - x.G. If the
change in level seen in Column 4 (ROC0 - 2.x.G) is added,
the value for the level at Cycle 3 is calculated as PV0 + ROC0 +
ROC0 - x.G + ROC0 - 2.x.G. This is simplified in Column 3 to
PV0 + 3.ROC0 - 3.x.G.
TABLE 1. Initial and final conditions for SOALC
Variable

Initial value

Final value

Level

PV0

H

Rate-of-change

ROC0

Zero

TABLE 2. Change in level and rate-of-change over control horizon
Execution
cycle

Level, showing changes per cycle

Level, changes added

Rate-of-change
of level

Change
in OP

0

PV0

PV0

ROC0

x

1

PV0 + ROC0

PV0 + ROC0

ROC0 - x.G

x

2

PV0 + ROC0 + ROC0 - x.G

PV0 + 2.ROC0 - x.G

ROC0 - 2.x.G

x

3

PV0 + ROC0 + ROC0 - x.G + ROC0 - 2.x.G

PV0 + 3.ROC0 - 3.x.G

ROC0 - 3.x.G

x

4

PV0 + ROC0 + ROC0 - x.G + ROC0 - 2.x.G + ROC0 - 3.x.G

PV0 + 4.ROC0 - 6.x.G

ROC0 - 4.x.G

x

5

PV0 + ROC0 + ROC0 - x.G + ROC0 - 2.x.G + ROC0 - 3.x.G + ROC0 - 4.x.G

PV0 + 5.ROC0 - 10.x.G

ROC0 - 5.x.G

x

n

H

PV0 + n.ROC0 - (0.5.n 2 - 0.5n)x.G

ROC0 - n.x.G

0

Hydrocarbon Processing | MAY 2021

77



Hydrocarbon Processing - May 2021

Table of Contents for the Digital Edition of Hydrocarbon Processing - May 2021

Contents
Hydrocarbon Processing - May 2021 - Intro
Hydrocarbon Processing - May 2021 - Cover1
Hydrocarbon Processing - May 2021 - Cover2
Hydrocarbon Processing - May 2021 - Contents
Hydrocarbon Processing - May 2021 - 4
Hydrocarbon Processing - May 2021 - 5
Hydrocarbon Processing - May 2021 - 6
Hydrocarbon Processing - May 2021 - 7
Hydrocarbon Processing - May 2021 - 8
Hydrocarbon Processing - May 2021 - 9
Hydrocarbon Processing - May 2021 - 10
Hydrocarbon Processing - May 2021 - 11
Hydrocarbon Processing - May 2021 - 12
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Hydrocarbon Processing - May 2021 - 14
Hydrocarbon Processing - May 2021 - 15
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Hydrocarbon Processing - May 2021 - 17
Hydrocarbon Processing - May 2021 - 18
Hydrocarbon Processing - May 2021 - 19
Hydrocarbon Processing - May 2021 - 20
Hydrocarbon Processing - May 2021 - 21
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Hydrocarbon Processing - May 2021 - 26
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Hydrocarbon Processing - May 2021 - Cover3
Hydrocarbon Processing - May 2021 - Cover4
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