1. Coordinator MPC for maximization of plant throughput
Elvira Marie B. Aske*&, Stig Strand& and Sigurd Skogestad*
*Department of Chemical Engineering, Norwegian University of Science and Technology, Trondheim, Norway
&Statoil R&D, Process Control, Trondheim, Norway

2. Outline Introduction Modes of optimal operation Maximum throughput
Bottleneck
Implementation of maximum flow
Coordinator MPC
Case study
Improvements

3. How manipulate feeds and crossovers?
Case Study: Statoil/Gassco Gas Plant
Motivation for coordinator MPC: Plant development over 20 years
How manipulate feeds and crossovers?
To understand the use of the coordinator MPC better, we will show development of a large gas processing plant in Norway.
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?
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4. Control hierarchy Conventional real-time optimization
Regulatory control layer
(PID, FF,..)
Stationary
optimization
(RTO)
Planning
Supervisory control (e.g. MPC)
Control hierarchy
Conventional real-time optimization
(RTO) offers a direct method of
maximizing an economic
objective function
Identifies optimal active constraints and optimal setpoints
Challenge: Implement optimal solution in real plant with dynamic changes and uncertainty
Special case considered here (very important and common in practice):
Maximize throughput
Real-time optimization (RTO) is the traditional way to optimize a plant.
Based on rigorous, stationary models. These are often expensive to develop and time consuming to solve, but they gives the active constraints and optimal set points.
Can we solve the optimization problem in an easier way?
We consider a special case – maximize production.
This is a common mode of optimization.
A challenge is to implement the optimal solution in a real plant (special case or not). Collecting data from the process, calculating and sending out new optimal setpoint can take hours  the new setpoint may not be optimal anymore.

5. Depending on marked conditions: Two main modes of optimal operation
Mode I. Given throughput (“nominal case”)
Given feed or product rate
“Maximize efficiency”: Unconstrained optimum (“trade-off”) that may require RTO
Mode II. Max/Optimum throughput
Throughput is a degree of freedom + good product prices
IIa) Maximum throughput
Increase throughput until constraints give infeasible operation
Do not need RTO if we can identify active constraints (bottleneck!)
IIb) Optimized throughput
Increase throughput until further increase is uneconomical
Unconstrained optimum (with low efficiency...) that may require RTO
Operation/control:
Traditionally: Focus on mode I
But: Mode IIa is where we really can make “extra” money!

6. Maximum throughput in networks
Operation research community: max-flow min-cut theorem (Ford et.al (1962)): Maximum flow through the network is equal to the minimum capacity for all cuts
Assumption: The mass flow through the network is represented by a set of units with linear flow connections
Maximum throughput achieved by maximizing the flow through the bottleneck
Maximum throughput closely related to the problem of maximum flow in networks considered in the operation research community
From there we have the max-flow min-cut theorem: maximum flow through the network is equal to the minimum capacity for all cuts.
To apply network theory to process engineering systems:
- unit with a single product is an arc
- flow splits and flow junctions are nodes
- unit with several products (for example distillation column) is a combination of an arc and a node, but usually al limited DOFs to adjust the split because of product constraints
Make one assumption to apply network theory: the mass flow through the network is represented by a set of units with linear flow connections. One solution to avoid these sources of nonlinearity is to treat certain combinations of units (like reactor-recycle systems) as a single combined unit as seen from the maximum throughput point of view.
Then from the max-flow min-cut theorem we can derive that maximum throughput achieved by maximizing the flow through the bottleneck
This leads to two issues
find the bottleneck
Implement maximum throughput at the bottleneck.

7.  Maximum throughput requires tight control of the bottleneck unit
Definition: a unit is a bottleneck if maximum throughput 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
Maximum flow is the maximum feed rate that the unit can accept subject to achieving feasible operation.
From the bottleneck definition the unit has now available capacity left when the unit its a bottleneck.
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.
For control purposes this require tight control of the bottleneck unit
There are actually two cases:
Identify the bottleneck(s)
Implement maximum throughput at the bottleneck

8. Bottlenecks in plant Max-flow min-cut
Examples on where the bottlenecks can be placed in a plant and where the minimum cut will be (illustrates max-flow min-cut theorem).

9. Throughput manipulator (TPM)
Some background on inventory control.
Inventory control deals with how the mass balance is maintained in the plant.
First, a definition: Throughput manipulator (TPM): The TPM is the degree of freedom used to set the throughput in the primary process path (from the major feed to the major products)
Buckley and Price, Lyman and Georgakis points out three basic schemes for inventory control
TPM at feed, inventory control in direction of flow
TPM at product, inventory control in direction opposite to flow
TPM inside plant, radiating inventory control
Direction of inventory control is due to self-consistency, which is that the flow is maintained through the plant by use of the inventory loops only.
Buckley (1964). Techniques of Process Control
Price, Lyman and Georgakis (1994). Throughput manipulation
in plantwide control structures. Ind. Eng. Chem. Res. 33, 1197–1207.

10. Rules for achieving max throughput
Maximize flow through bottleneck at all times
Use TPM* for control of bottleneck unit
Locate TPM to achieve tight control at bottleneck
Back off: usually needed to ensure feasibility dynamically
yset point
Time
ymax
ymeasure
Back off
How to control the bottleneck?
Use TPM for control of the bottleneck unit. This follows because TPM is a DOF for throughput, which should be maximized.
However, some back off is needed to ensure feasibility dynamically due to disturbances etc.
Back off gives loss, and therefore important to reduce the back off
*TPM = throughput manipulator

11. Implementation of maximum flow
Bottleneck fixed*:
Single-loop control sufficient: Use TPM to control bottleneck unit
Best result (minimize back-off) if TPM permanently is moved to bottleneck unit
Bottleneck moves:
Need to find bottleneck
Keep maximum flow at bottleneck, but avoid reassigning loops
Proposed solution: Coordinator MPC
Estimate of remaining capacity in each unit is obtained from local MPCs
Coordinator MPC manipulate TPMs and crossovers to maximize flow through bottlenecks FC
Two different approaches, depending on if the bottlenecks moves or not:
Bottleneck fixed at a unit: single-loop control sufficient.
Has been discussed in literature, e.g. Skogestad “Control structure design for complete chemical plants”
If the bottleneck moves, then reassigning loops are probably unavoidable if we want to obtain optimal operation.
However, reassigning loops are undesired. A better approach is to use a multivariable controller (for example MPC).
Here we can use the local MPCs to estimate the remaining feed capacity in each unit, whereas the coordinator MPC is used to manipulate on the TPMs (usually feeds) and crossovers inside the plant.
This is our focus in our case study
max
*Skogestad (2004) Control structure design for complete chemical plants Comp. Chem. Eng 28 p

12. Coordinator MPC Feeds and crossovers as manipulated variables
affects throughput in each unit
Local MPCs
Provide available capacity in each unit
Decomposition
Local MPCs work as before
Coordinator uses extra DOFs
Advantages:
dynamic
fast execution
It is an ”ordinary” MPC.
Coordinator monitor the local MPCs, here by the remaining feed capacity measure.
Coordinator MPC can realized maximum throughput: done by plant throughput as a CV with a high, not reachable set point
Take decisions involving several MPCs. Uses feed and crossovers to realized maximum throughput.
The local MPCs and the coordinator could be collected in one large MPC. But it will lead to a complex MPC which would be difficult to understand and maintained.
By using remaining feed capacity, we decompose the problem.
The coordinator MPC executes much faster than an RTO (in the case study we used 3 minutes, whereas the local MPCs executed every minute).

13. Identify bottleneck
Use RTO based on a detailed steady-state model of the plant
Better: use local MPC to calculate remaining feed capacity in each unit!
Remaining feed capacity for unit k:
Jk – present feed to unit k
Jk,max – max feed to unit k within feasible operation,
Obtained by solving “extra” steady-state LP problem in each local MPC:
Jk,max = max (Jk)
subject to: satisfying existing CV& MV constraints
+ models in local MPC
(At least) two different ways to identify the bottlenecks
0. Increase feed to the plant can not achieve feasible operation (seldom allowed in practice.....)
1. Use a steady state model of the plant
needs a model
may not be accurate (disturbances etc)
2. Dynamic calculations. Use local MPC to calculate. MPC is a common tool in industry today and more or less a necessity when implementing optimal plant operation.
Our suggestion is to slightly extend the steady state calculations in the local MPC with an estimate of the remaining feed capacity
models already available
constraints available (CVs and MVs)
use end prediction values of MVs and CVs in the calculations to include past MV moves and disturbances
back off can be included in the calculations to avoid loss of control (that is, the coordinator sees a smaller capacity than it actually exist)
not as exact as rigorous models, however, the estimate tends to be better when operating closer to the bottleneck, and this is the important thing here.

14. Coordinator MPC
Degrees of freedom (MVs,u): feeds (TPMs) and crossovers.
Outputs (CVs, y): Remaining capacities in all units
Maximize throughput: Use “standard MPC” to solve LP problem:
max (throughput)
subject to:
1. y > 0 + back off
2. umin < u < umax
3. Δumin < Δu < Δumax
4. Dynamic model from feeds
and crossovers (u) to capacities (y) u
Model for train 100
u1 = crossover fra bunn etantårn (Note: get MORE capacity in 100-train because this is a crossover)
u2 = føde train 100
u3 = fødesplitt fra DPCU (lik u2 her pga. lik fødesammensetning)
y1= etantårn
y2 = propantårn
y3 = butantårn (c4/c5): Why overshoot. Not clear (Elvira)
y4 = butansplitter y
Step response models for columns in 100-train

15. Case study: Gas processing plant
Simulation study based on detailed dynamic model
Case: maximize throughput
We have done a case study of the plant displayed on the previous slide.
A dynamic simulator (D-SPICE) is available
We considered parts of the gas processing plant
- avoid large simulation time. The whole simulator uses 20 computers to simulate
Case: maximum throughput
Our case consist of two fractionation trains, T-100 and T-300, both
have a deethanizer, depropanizer, debutanizer and a butane splitter. In addition
T-300 has two stabilizers in parallel.
There are two separate train feeds, a liquid stream from a
dew point control unit (DPCU) that is divided between the two trains, and
a crossover. The five streams are MVs in the coordinator MPC and indicated
by valves in the figure

16. Coordinator MPC MVs (u): CVs (y):
Feed to train 100 and 300
Feed split from DPCU
Crossover from T100 to T300
CVs (y):
Remaining feed capacity for each column (10 units)
Sump level in ET-100 (to avoid loosing control due to crossover)
Total plant feed (“trick” to use QP-MPC: high unreachable set point)
The coordinator MPC and all the local MPCs are implemented in SEPTIC.
SEPTIC stands for Statoil Estimation and Prediction Tool for Identification and Control, which is an in-house developed MPC
The local MPCs are implemented in the same way as in the plant
The coordinator MPC is set up with MVs, indicated with blue valves in the figure:
Feed to train 100 and 300
Feed split from DPCU
Crossover from T100 to T300
The CVs in the coordinator is:
Remaining feed capacity for each column (10 units)
Sump level controller output in ET-100 (avoid to loose control due to crossover)
Total plant feed (high, unreachable set point with lower priority)
The priority of the CVs make the coordinator maximum throughput, since the capacity limits have high priority and the total plant feed as ha lower priority
The coordinator is demonstrated with tree different cases.
First, we turn the coordinator MPC on and the coordinator moves the plant from an unconstrained operation to a constrained operation
Then a feed composition change is introduced in one of the train feed. This is a common disturbance at the real plant, and comes suddenly because of the plug-flow in pipelines. In the plant the gas chromatographs have a delay which makes them unsuitable for control. Therefore any feed forward from the feed composition is not included in the case study either.
Then there is implemented a change in a local MPC, that is, in the butane splitter in T100. At this time, the column is a bottleneck and an operator reduces the high limit in the top product impurity, which leads to a reduction in remaining feed capacity.
The for both the local MPCs and the coordinator MPC are found by step-tests in the simulator.

17. Feeds and crossovers (u, MVs)
Complete set of
Step response models
in the coordinator
Available capacity (y, CVs)
All step response models in the coordinator

18. Simulations: t=0: move the plant to maximum throughput
t=360 min: feed composition change in T100
t=600 min: change in CV high limit in butane splitter T100 MPC (reducing the remaining feed capacity which is already operated at its maximum)

19. Simulation results: CVs (available capacity)
So, lets take a look at the results.
The controlled variables in the coordinator. Here the remaining feed capacity for each column is displayed, together with the sump level controller output and the total plant feed.
T=0 min: ET100 and Stab1&2 bottlenecks at the optimal operation point. BS300 bottleneck in the beginning, but the coordinator uses crossover to reroute, unload the BS300.
T=360 min: In the composition change, the ethane content in the feed is reduced whereas the butane content are increased. The composition change gives ET100 more capacity, hence the T100 feed can be increased even more. The BT100 reaches the bottleneck due to the feed composition change and the feed increase. The coordinator uses the crossover to keep BST100 within its capacity.
T=600 min: change in BST100 quality high limit (local MPC), gives less capacity in a column which is already operating at maximum. The propane column in T300 and its downstream columns have some available capacity, however butane splitter in T300 also meets constraints, so the plant feed must be reduced some. However, the feed reduction is less than if the crossover had not been used.

20. Simulation results: MVs (feeds and crossovers)
Train feed
Feed split
Crossover
First case:
Feeds are increased
Crossover used to unload BST300
Second case:
Less ethane in T100 feed, ET100 can receive more feed
Higher butane content, crossover used to unload BS100 this time
Third case:
Reduction in BS100 capacity (operator actions-higher demands on product purity)
Have to reduce feed and uses crossover to unload BS100 until BS300 can’t take any more
Conclusions/experience from case study:
Maximum throughput realized by a total plant feed as a CV with a high, unreachable set point with lower priority
Uses crossover to exploit columns with capacity
Important that the local MPC is well tuned for the operation region
Reached ”new” limitations in the local MPC as the feed was increased (typical: maximum boilup). Needed to be considered in the local MPC to obtain more correct capacity measurements.
”Correct” limitations are important for the estimate of the actual capacity
Feed composition should be included as a DV in the coordinator. Here only corrected by feedback.

21. Improvements (further work): Reduce back-off
Use inventories (buffer tanks) as additional MVs in the coordinator
MV closer to bottleneck: reduce back-off
Improve estimate of remaining feed capacity
column pressure drop not always a good indicator. More detailed column capacity model?
Include feed forward, e.g from feed composition
Composition measurements at the pipelines into the plant
The main potential for improvement is to reduce back off.
In the case study there are back off on the MVs in the local MPCs to avoid saturation (loss of control and strongly nonlinear)
There are back of on remaining feed capacity measure in the coordinator MPC. That is remaining capacity > back off > 0
First, we can include inventories as additional MVs in the coordinator. In the case study we have considered conventional inventory control, that is feed valves as TPM. Hence, we may get a “long” loop from the TPM to the bottleneck unit. We can obtain a faster loop if we include dynamic degrees of freedom
Second, as experienced in the case study, feed composition changes should be included as feed forward. Large impact on the maximum throughput, and should avoid to do all the correction by feedback.
Third, using column pressure drop is not always a good indicator for its capacity. At least not for tray columns and at least not in practice. Other column capacity measure to consider?
Not directly back off reduction:
Flow changes in relative (%) changes
most of steady state gains in the models = 1
E.M.B. Aske and S. Skogestad, “Coordinator MPC with focus on maximizing throughput”,
Proceedings PSE-ESCAPE’07, Garmisch-Partenkirchen, Germany, July 2007

22. Conclusion Often: Optimal operation = max. throughput
Usually: Max. throughput = max. through bottleneck
max-flow min-cut theorem
Fixed bottleneck: Single-loop control
Moving bottleneck: Propose coordinator-MPC where local MPCs estimate remaining capacity
Simulations promising
Implementation planned in 2007
May later include inventories as dynamic degrees of freedom