1. DESIGN OF PLANTWIDE CONTROL SYSTEMS WITH FOCUS ON MAXIMIZING THROUGHPUT
Elvira Marie B. Aske
Department of Chemical Engineering
Norwegian University of Science and Technology
Trondheim, March 27, 2009
Elvira Marie B. Aske, Ph.D. Defense

2. Presentation outline Introduction (Chapter 1)
Self-consistency (Chapter 2)
Maximum throughput (Chapter 3 (4,5,6))
Optimal operation
Bottleneck
Back off
Dynamic degrees of freedom for tighter bottleneck control (Chapter 4)
Coordinator MPC (Chapter 5,6)
Remaining capacity
Flow coordination
Industrial case
Concluding remarks and and further work

3. Introduction Optimal economic operation
This often corresponds to maximum throughput
Constrained optimization!
Identifying the constraints?
How does this affect the plantwide control structure?
Frequent disturbances?
Moving constraints?

4. Self-consistent inventory control
Chapter 2
Self-consistent inventory control

5. Self-consistent inventory control
Inventory (material) balance control is an important part of process control
How design an appropriate structure?
Many design rules in literature, but often poor justification
Propose one rule that applies to all cases
 self-consistency rule

6. Definitions
Consistency: steady-state mass balances (total, component and phase) for the individual units and the overall plant are satisfied.
Self-regulation: an acceptable variation in the output variable is achieved without the need for additional control when disturbances occur.
Self-consistency: local “self-regulation” of all inventories (local inventory loops are sufficient)
Self-consistency is a desired property because the mass balance for each unit is satisfied without the need to rely on control loops outside the unit
: A consistent inventory control system is said to be self-consistent if there is local “self-regulation” of all inventories. This means that for each unit the local inventory control loops by themselves are sufficient to achieve steady-state mass balance consistency for that unit.

7. Self-consistency rule
Rule 2.1. “Self-consistency rule”: Self-consistency (local “self-regulation” of all inventories) requires that
The total inventory (mass) of any part of the process (unit) must be “self-regulated” by its in- or outflows, which implies that at least one flow in or out of any part of the process (unit) must depend on the inventory inside that part of the process (unit).
... and the inventory of each component
.. and the inventory of each phase

8. Self-consistency: Example
Not “self-regulated”, depends on the other inventory loop
OK?
This structure is not self-consistent because the inventory of unit 2 is not “self-regulated
by its in- or outflows” and thus violates Rule 2.1. In addition, the inventory control
of unit 2 requires that the other inventory loop is closed, and thus violates
Definition 2.3 (self-consistent).
Consistent, but
not self-consistent

9. Self-consistency: Example
OK?
This structure is not self-consistent because the inventory of unit 2 is not “self-regulated
by its in- or outflows” and thus violates Rule 2.1. In addition, the inventory control
of unit 2 requires that the other inventory loop is closed, and thus violates
Definition 2.3 (self-consistent).
Self-consistent:
Interchange the inventory loops

10. Chapter 3,(4,5 & 6)
Maximum throughput

11. Depending on market conditions: Two main modes of optimal operation
Mode 1. Given throughput (“nominal case”)
Given feed or product rate
“Maximize efficiency”: Unconstrained optimum
Mode 2. Max/Optimum throughput
Throughput is a degree of freedom + good product prices
2a) Maximum throughput
Increase throughput until constraints give infeasible operation
Constrained optimum - identify active constraints (bottleneck!)
2b) Optimized throughput
Increase throughput until further increase is uneconomical
Unconstrained optimum
In operation/control there are two main modes of optimal operation:
Mode 1. Given throughput, feed or product rate is given. Optimal operation is where the operation is most efficient.
Mode 2. Max or optimum throughput. Here the throughput is a degree of freedom and the product prices is good compared to feed and utility costs.
We have two situations here. First, maximum throughput where it is optimal to increase the throughput until constraints give infeasible operation. This is a constrained optimum where the active constraints, that is, the bottlenecks should be identified.
Second, optimized throughput which is the unconstrained case, a further increase in throughput is uneconomical. For instance, a reactor conversion decreases rapidly (or purge streams increases sharply) at high feed rates.
Traditionally: Focus on mode I
But: Mode IIa is where we really can make “extra” money!

12. Throughput manipulator
Definition. A throughput manipulator is a degree of freedom that affects the network flows, and which is not indirectly determined by other process requirements.
At feed:
At product:
Inside:

13.  Maximum throughput requires tight control of the bottleneck unit
Definition: A unit is a bottleneck if maximum throughput (maximum network flow for the system) is obtained by operating this unit at maximum flow
If the flow for some time is not at its maximum through the bottleneck, then this loss can never be recovered
 Maximum throughput requires tight control of the bottleneck unit
The term bottleneck is, as far I have noticed, a term mostly used in network theory and design. Now we look at the term bottleneck in a dynamic perspective. That is, the bottleneck may move under presence of disturbances or the maximum flow through the bottleneck (“size”) may vary.
The term ”unit” in Definitions 3.5 and 3.6 needs some attention. For a simple
process, where the process units are in series, a ”unit” is the same as a single process
unit. However, for integrated processes, one may need to consider a combined
system of integrated units as a ”unit”.
capacity.
Note that if a flow inside a unit is at its maximum, this does not necessarily mean that the unit is a bottleneck. The unit is only a bottleneck if it
operates at maximum feed rate according to Definition 3.3. For example, the heat flow in a distillation column (the unit) may optimally be at its maximum, because
overpurification of the “cheap” product is optimal in order to recover more of the valuable product. This does not mean that the column is a bottleneck, because it is
possible, by reducing the overpurification, to increase the feed rate to the column. Only when all degrees of freedom are used to satisfy active constraints, do we have
a bottleneck.
Maximum flow is the maximum feed rate that the unit can accept subject to achieving feasible operation.
From the bottleneck definition the unit has no available capacity left when the unit its a bottleneck. Network theory: no augmenting paths (not possible to send more flow through the paths)
In some cases the bottleneck can not be located to a specific unit, but rather to a system of units (“system bottleneck”)
Example system bottleneck: Reactor-separator-recycle case.
If the flow its not at its maximum for some time in the bottleneck, then this loss can never be recovered.
This require tight control of the bottleneck unit!

14. Back off yconstraint y ys
Definition: The (chosen) back off is the distance between the (optimal) active constraint value (yconstraint) and its set point (ys) (actual steady-state operation point),
which is needed to obtain feasible operation in spite of:
1. Dynamic variations in the variable y caused by imperfect control
2. Measurement errors.
Time y
Back off
yconstraint ys
Remark 1 Here we assume integral action, such that on average ys = y where
y = lim T→¥ 1 T Z T 0 y(t)dt
In this case, only the steady-state measurement error (bias) is of importance, and not its
dynamic variation (noise).
Remark 2 Back off was defined by Govatsmark and Skogestad (2005, eq. 20) as the
difference between the actual set points and some reference values for the set points:
b = cs−cs,ref
where cs is the actual set point and cs,ref is some reference value for the set point which
depends on the method for set point computation (e.g. nominal, robust, on-line feasibility
correction). Definition 3.1 coincides with their definition.

15. Realize maximum throughput
Best result (minimize back-off) if TPM permanently is moved to bottleneck unit
Bottleneck
(active constraint)
= max
Note: reconfiguration of inventory loops
upstream TPM

16. Obtaining the back off Back off given by
Exact estimation of back off difficult in practice
Use controllability analysis to obtain “rule of thumb”
Estimate back off to find economic incentive:
Worst case amplification:
In the time domain the dynamic control error is given by
The expected dynamic variation in the controlled variable y in spite of disturbances and uncertainty.
Consider the case with a single input (TPM) that controls
an active output constraint (y) in the bottleneck unit. A back off is then required to
account for dynamic variations caused by imperfect control.
The magnitude of the back off for the dynamic control error should be obtained
based on information about the disturbances and the expected control performance.
Mathematically, this is given by the worst-case control error (variation) in terms of
the “infinity-norm” (maximum deviation). In the time domain the dynamic control error
(and hence the minimum back off) is given by

17. Back off example: PI-control of first order disturbance
Step response in d at t=0
Frequency response of Sgd

18. Obtaining the back off (controllability analysis)
“Easy disturbance”
Benefit of control to reduce the peak
Minimum back off:
“Difficult disturbance”
Control gives a larger back off (but needed for set point tracking)
“Smooth” tuning recommended to reduce peak (MS)
Consider the case with a single input (TPM) that controls
an active output constraint (y) in the bottleneck unit. A back off is then required to
account for dynamic variations caused by imperfect control.
The magnitude of the back off for the dynamic control error should be obtained
based on information about the disturbances and the expected control performance.
Mathematically, this is given by the worst-case control error (variation) in terms of
the “infinity-norm” (maximum deviation). In the time domain the dynamic control error
(and hence the minimum back off) is given by
Assumptions:
Disturbance is a first-order response ,
First-order lag process
PI-controlled process

19. USE DYNAMIC DEGREES OF FREEDOM
Chapter 4
USE DYNAMIC DEGREES OF FREEDOM

20. Reduce back off by using dynamic degrees of freedom
TPM often located at feed (from design)
Not always possible to move TPM
Reconfiguration undesirable (TPM and inventory)
Dynamic reasons (Luyben, 1999)
Alternative solutions:
Use dynamic degrees of freedom (e.g. holdup volumes)
For plants with parallel trains: Use crossover and splits
First, if the TPM is moved, the inventory loops must be reconfigured to ensure self-consistency.
Second, there may be dynamical reasons for avoiding a so-called on-demand control structure
with inventory control opposite the direction of flow, which is required upstream
of the TPM to ensure self-consistency. Luyben (1999) points out several inherent
dynamic disadvantages with the on-demand structure, including propagation
of disturbances, dynamic lags, process time constants and interactions.
Luyben, W.L. (1999). Inherent dynamic problems with on-demand
control structures. Ind. Eng. Chem. Res. 38(6), 2315–2329.

21. Dynamic degrees of freedom: Main idea
Main idea: change the inventory to make temporary flow rate changes in the units between the TPM (feed) and the bottleneck
Improvement: Tighter bottleneck control, the effective delay from the feed to the bottleneck may be significantly reduced
Cost: Poorer inventory control (usually OK)

22. Proposed control structure: Single-loop plus ratio control
Change all upstream flows simultaneously
No reconfiguration of inventory loops
Bottleneck control only weakly dependent on inventory controller tuning

23. Chapter 5 & 6
Coordinator MPC The approach and the implementation at Kårstø gas plant

24. Nyhamna
Europipe II
Europipe I
Norpipe
Emden
ÅTS
Norne
Åsgard
Haltenpipe
Heidrun
Franpipe
Zeebrugge
Zeepipe I
St Fergus
Vesterled
Frigg
Statfjord
Kårstø
Kollsnes
Melkøya
Snøhvit
Ormen Lange
Easington
Langeled
Ekofisk
Sleipner
Troll
Dunkerque
Kristin
Tjeldbergodden
North Sea gas network
Kårstø plant: Receives gas from more than 30 offshore fields
Limited capacity at Kårstø may limit offshore production (both oil and gas)
Norwegian
continental
shelf
TRONDHEIM
Oslo UK
Kårstø is a gas processing plant that plays an important role in gas transport and treatment.
It receives rich gas and condensate from more than 30 offshore producing fields.
This set high demands, not only to the plant efficiency and regularity, but
also to the plant throughput. Limited gas plant processing capacity means that one
or more fields must reduce production or even shut down. Therefore it is important
for the Kårstø plant to process as much as possible and not become a “bottleneck” in the Norwegian gas transport system.
Pipelines that affects the Kårstø plant
GERMANY

25. How manipulate feeds and crossovers?
Motivation for coordinator MPC: Plant development over 20 years
Europipe II sales gas
Halten/ Nordland rich gas
Tampen rich gas
Statpipe sales gas
Sleipner condensate
Propane N-butane I-butane Naphtha
How manipulate feeds and crossovers?
The diagram provides a schematic presentation of the development of the process plant over two decades.
This plant has been extended several times.
The plant has 3 different feeds and more than 10 crossovers.
How to manipulate on the feeds and crossover to obtain maximum throughput for this plant?
This is more than an operator can do manually.
Especially the extensions done in the latest years have been built with the possibility to distribute gas and liquid to different processing trains, wherever there are processing capacity.
1985 – Statpipe
1993 – Sleipner
2000 – Åsgard (KUP)
2003 – Mikkel (NET1)
2005 – Kristin (KEP2005)
Condensate
1985
1993
2000
2003
2005
Ethane

26. Maximum throughput Here: want maximum throughput
 Obtain this by “Coordinator MPC”:
Manipulate TPMs (feed valves and crossovers) presently used by operators
Throughput determined at plant-wide level (not by one single unit)
 coordination required
Frequent changes
 dynamic model for optimization
The throughput at the Kårstø plant is presently set by the operators who manipulate
the feed valves to satisfy orders from the gas transport system (operated
by another company). The orders are stated as pipeline pressures, feed rates and
export gas rates, which may change on an hourly basis. The objective of this work
is to coordinate the throughput manipulators (uc) to achieve economic optimal operation.
The overall feed rate (or more generally the throughput) affects all units in the
plant. For this reason, the throughput is usually not used as a degree of freedom for
control of any individual unit, but is instead left as an “unused” degree of freedom
to be set at the plant-wide level.
In this study, a different approach is used. We assume that the main economic
objective is to maximize the plant throughput, subject to achieving feasible operation
(satisfying operational constraints in all units) with the available feeds. This
corresponds to maximum flow through the bottleneck(s) within the operational
constraints. This insight may be used to implement an optimal operation strategy
without the need for dynamic optimization based on a detailed model of the entire
plant (Aske et al., 2008).
One option for solving the maximum throughput control problem for the entire
plant is to combine all the MPCs in the plant into a single application. However,
we choose to decompose the problem by using several local MPC applications and
a coordinator MPC (Aske et al., 2008). The coordinator uses the remaining degrees
of freedom (uc) to maximize the flow through the network subject to given
constraints.
If feed is limited: optimum= max NGL recovery, can be included in the coordinator as well

27. ”Coordinator MPC”: Coordinates network flows, not MPCs
(remaining capacity)
Illustration of the coordinator MPC

28. ? Approach Use Coordinator MPC to optimally adjust TPMs:
Coordinates the network flows to the local MPC applications
Decompose the problem (decentralized).
Assume Local MPCs closed when running Coordinator MPC
Need flow network model (No need for a detailed model of the entire plant)
Decoupling: Treat TPMs as DVs in Local MPCs
Use local MPCs to estimate feasible remaining capacity (R) in each unit

29. Remaining capacity (using local MPCs)
Feasible remaining feed capacity for unit k:
Obtained by solving “extra” steady-state LP problem in each local MPC:
subject to present state, models and constraints in the local MPC
Use end predictions for the variables
Recalculated at every sample (updated measurements)
Very little extra effort!
current feed to unit k
max feed to unit k within feasible operation
The remaining capacity for unit k is the difference between the current feed Flk
and the maximum feed Flk,max calculated at the current time.
The feed to the local unit Flk is a DV in the local MPC application and the maximum
feed to the unit k is then easily obtained by solving an additional steady-state LP-problem.
Here ulk is the vector of manipulated variables in the local MPCs,
and at the optimal solution, all these degrees of freedom (uk) are used to satisfy
constraints (feasibility limit)
To calculate the units current maximum feed, the
end predictions (steady-state model) for the variables are used. This assumes that
the closed-loop response time is faster for the local MPC than for the coordinator.
Note that Flk,max can change due to updated measurements, disturbances (i.e.
feed compositions changes), changes in the constraints and model changes (that
is, the steady-state gain in the models) in the local MPCs. The current feed to the
unit (Flk ) is measured, either by a flow transmitter or by a level controller output
(valve opening) if a flow transmitter is not available.
Backoff is needed due to unmeasured disturbances and possible long effective deadtime (at least for some units) in the plant. 29

30. Coordinator MPC: Design
Objective: Maximize plant throughput, subject to achieving feasible operation
MVs: TPMs (feeds and crossovers that affect several units)
CVs: total plant feed + constraints:
Constraints (R > backoff > 0, etc.) at highest priority level
Objective function: Total plant feed as CV with high, unreachable set point with lower priority
DVs: feed composition changes, disturbance flows
Model: step-response models obtained from
Calculated steady-state gains (from feed composition)
Plant tests (dynamic)
The coordinator uses individual (SISO) step response models, or more precisely a
single-input multiple-output representation of a multi-input multi-output system.
The advantage with SISO models is that it is easy to adjust the models independently
for input-output pairs. However, SISO models imply that the structure of
the process is lost and, for instance, disturbances do not propagate as they would
in a state-space model. The loss of structure leads to some additional work.
The sampling time for the coordinator MPC is 3 minutes. The prediction and
control horizon are set to 6 hours, whereas the longest response models reach
steady state at approximately 4.5 hours

31. Kårstø plant Gas processing area Control room
A picture of the Kårstø plant. The main gas processing area where the distillation columns, and most of the utility is located, like boilers and compressors, and also export compressors.
The tank area and harbor where storage tank for ethane, butane, naphtha and condenaste. Liquid propane are stored at Kårstø in two large rock caverns.
These caverns provide a combined capacity of 250,000 cubic metres. Each cavern is 195 metres long, 20 metres wide and 33 metres high. The carverns can be filled with 570 cubic metres of liquid propane per hour.
Some producing numbers:
Sales gas produced: 27 bn scm per year= 21 million tons of liquid
Liquids production in tonnes/year:
Ethane
Propane
I-butane
N-butane
Naphtha
Condensate
Total
The gas via Kårstø corresponds to 300 TWh/year.

32. 6 MVs 22 CVs 7 DVs KÅRSTØ MPC COORDINATOR IMPLEMENTATION (2008)
Export gas
Rich gas MV CV CV
Export gas MV CV CV
Rich gas CV CV CV CV CV CV MV
Half of the plant included:
6 MVs
22 CVs
7 DVs MV
Condensate CV MV CV CV MV CV CV CV CV CV

33. Step response models in coodinator MPC
Remaining capacity (R) goes down
when feed increases…
NB: Ikkje alle modellar får plass på bildet!
+ more…

34. Experiences
Using local MPCs to estimate feasible remaining capacity leads to a plant-wide application with “reasonable” size
The estimate remaining capacity relies on
accuracy of the steady-state models
correct and reasonable CV and MV constraints
use of gain scheduling to cope with larger nonlinearities (differential pressures)
Crucial to inspect the models and tuning of the local applications in a systematic manner
Requires follow-up work and extensive training of operators and operator managers
“New way of thinking”
New operator handle instead of feed rate: Rs (back-off)
Important prerequisite it that the local MPC applications are installed. Then we are able to operate coloser to constraints. In this case for distillation columns it means that lower internal trafic in column gives ”extra capacity”.

35. Concluding remarks and further work

36. Main contributions
Plantwide decomposition by estimating the remaining capacity in each unit by using the local MPCs
The idea of using a “decentralized” coordinator MPC to maximize throughput
The proposed self-consistency rule, one rule that applies to all cases to check whether a inventory control system is consistent
Single-loop with ratio control as an alternative structure to obtain tight bottleneck control

37. Further work Recycle systems not treated
Information loss in plantwide composition
Further implementation of coordinator MPC
Planned start-up autumn 2009 (after control system upgrade)
Acknowledgments: Gassco, StatoilHydro ASA