process systems engineering lessons learned from the pulp and paper industry - pablo rolandi
TRANSCRIPT
Process Systems Engineering – Lessons learned from the pulp and paper industry
Pablo A. Rolandi, PhD
With thanks to Prof. José A. Romagnoli, my PhD supervisor at the PSE@USyd Group at the University of Sydney from 2001 to 2005.
● A simple goal…
… to facilitate a successful information sharing session
● About…
… Process Systems Engineering:
● techniques● methodologies● approaches● outcomes and insights● tools
● Using...
… an industrial pulp-and-paper plant as a holistic case-study
Goals
2
Outline
Background:
● Industrial process
● Process model
Process Systems Engineering:
● Dynamic process simulation
● Dynamic parameter estimation and model validation
● Steady-state process optimisation
● Dynamic process optimisation
● Multi-objective process optimisation
● Dynamic data reconciliation
● Other process systems engineering techniques
● Summary and conclusions3
Industrial process:Pulp and paper manufacturing
Process systemAn industrial pulp-and-paper mill
● Tightly integrated and closed-cycle processes● Operability and controllability issues
– reduction of fixed capital costs– elimination of redundant (back-up) equipment– reduction of inventories (hold-ups)– relatively short response times
● Profitability and environmental pressures 5
Process systemA continuous pulping area
The continuous pulping area of a pulp and paper plant is a process system of
interconnected units:i) a feed line (right), ii) a heat exchange and
recovery network (top, right), and iii) a single-vessel hydraulically-full digester (top, middle;
also colour image on the top right).
6
Process systemA continuous pulping area
Continuous cooking digesters
● Equipment function
– deplete lignin from cellulosic wood matrix
● Equipment characteristics
– co-current/counter-current flow patterns
– solid-liquid multi-phase flow
– compressible chip-column
● Equipment operation
– key process variable measurements are unavailable
● unmeasured yield (always) and selectivity (usually)
– disturbances (wide-ranging time-scales)
● composition and moisture of wood chips (raw materials)
● concentration of pulping chemicals
– planned/unplanned transitions● rate- and grade-production
changes
Continuous pulping systems
● Novel manufacturing technologies: feeding, recovery, cooking and washing
– very flexible process● Feed-line
– raw material transportation● Continuous cooking digester
– chemical reactions and washing by diffusion
– complex physico-chemical phenomena
– complex process operation● Heat exchange and recovery network
– increased process integrationPulp and paper mills – process areas
● Fibre line● Paper machine● Evaporators● Lime kiln● Power boiler 7
Process model
“All models are wrong; some are useful.”George E.P. Box
Process models and the modelling process
● From elementary models to composite models…
● From unit-level models to system-level models…
9
Process modelAt a glance*
Continuous cooking digester
● Distributed parameter system
– DAE approximation of PDAE
– ~20 discretisation points
– 6 reaction zones
● Chemical species
– 5 wood-matrix species
– 7 free/entrained liquid species
● Phenomena
– reaction
– diffusion: intra- e inter-particle
– 3 phases: heterogeneous system
● Mass and energy balances
– dynamic
● Physical properties
– simple correlations
Continuous pulping area
● Number of units
– 1 continuous cooking digester
– 6 heat exchange and recovery units
– 8 material and energy sources
– 21 tees and junctions and 8 flow transportation units
– 25 controllers and 51 sensors
● System of equations
– 1.5 10^4 differential-algebraic equations
– 1.0 10^3 ordinary differential equations
– 1.4 10^4 algebraic equations
– 2.5 10^2 degrees-of-freedom
– 2.1 10^2 discontinuities
● Modelling tools
– gPROMS** (v2.3) ~2005
10 *Rolandi (2005); ** Process Systems Enterprise Ltd.
Dynamic process simulation
“As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”Albert Einstein
Design-driven process analysis*
● Economic analysis
● Control system design/analysis
● Process flexibility analysis
● Standard/emergency operating procedure verification
● Start-up/shut-down operating procedure verification
12 *not an exhaustive list.
Data-driven process analysis*
● From plant “historian”
● Simulation of historical process conditions (normal/abnormal)
Engineering training
● Operator training simulators (OTS)
Dynamic process simulationDomain problems and engineering tasks
Dynamic process simulationMathematical formulation
● Given a mathematical model (M+N equations; index-1 DAE):
● A dynamic simulation problem entails solving:
● This is a so-called Initial Value Problem (IVP)
● Numerical solution algorithms: “integrators”
– linear multi-step, single-step multi-stage, implicit/explicit, stiff/non-stiff, etc.
– Adams, Backward Differentiation Formulae (BDF), Runge-Kutta (RK), etc.
13
time horizoninput variable trajectories*
initial conditions** (N equations)
differential variables(and time derivatives) (2N) algebraic variables (M) degrees-of-freedom
process parameters
*time evolution of input process variables; **initial value of state process variables.
Dynamic process simulationModelling operating procedures
● Operating procedures with an extraordinary level of detail can be modelled* and solved
– e.g., start-ups, production/grade shifts, batch sequences, etc.
– >> multi-stage IVP with implicit and explicit discontinuities
14 *A “Task” snapshot in gPROMS v4.0 (Process Systems Enterprise Ltd).
Dynamic process simulationSimulation of historical process conditions
● Smoothing is not sufficient– reduces noise/variability but does not produce continuous (input) functions
● Reconstruction of process trajectories (RPT)– combined continuous / discrete modelling paradigm (i.e., multi-stage IVP)
– explicit parameterisation w.r.t. time (independent variable)
– partition of time domain in multiple stages
– characterisation of trajectories by basis functions● for example, Lagrange polynomials, spline polynomials, etc.
sampling reconstruction
15
from continuous trajectories todiscrete set of measurements
“historian” plant datacannot be used directly
from discrete set of measurementsto continuous trajectories
original trajectorynot known
approximate trajectoriesfitness of reconstruction?
Simulation of historical process conditionsStudy results and discussion
● Simulation-based process troubleshooting
– where: impregnation zone (at the top of the digester)– observation: kappa number increases, yield decreases– conclusion: cellulose solubilisation at impregnation stages
– diagnosis: undesired side reactions taking place
– issue: pulping targets lignin degradation… not cellulose solubilisation!● Can we do better? What should the optimal operation be like?
selectivity profiles [#K] vs height [#];absolute (lhs) and relative (rhs) values
yield profiles [%] vs height [#];absolute (lhs) and relative (rhs) values
16
Process simulationIn a nutshell
● It is the “work horse” of chemical process engineering
– steady-state and/or dynamic– addresses a wide range of domain problems and engineering tasks
● It provides an effective mechanism for establishing process understanding
– computational experiments enable inspection of the full state of the process
● Steady-state simulation
– requires attention to the correct specification of degrees-of-freedom
● Dynamic simulation
– requires attention to the design of process scenarios for analysis that are meaningful and useful
● A wide range of tools are available
– equation-oriented and sequential-modular modelling technologies exist– custom modelling is key for complex or non-conventional processes 17
Dynamic parameter estimationand model validation“Doubt is not a pleasant condition, but certainty is an absurd one.”Voltaire
Parameter estimationIntroduction
● What are the reasons for the ubiquitous plant/model mismatch?
– Process-model uncertainty
● Structural uncertainty: model structure may not be known accurately, or it may be impractical to implement detailed mechanistic models
– e.g., anisotropic/isotropic raw materials, identity of chemical species● Parametric uncertainty: model parameters may not be known accurately
– e.g., fouling resistance, kinetic constants
– Process-data errors
● Random errors: noise and outliers
● Systematic errors: biases
● How do we tackle plant/model mismatch?
19
~Z
tune model parameters such that they minimisethe error ||.|| between the experimental ( ) and predicted (z) values of a subset of process variables
subject to the constraints F(.) and H(.) imposed by the models of the process and the sensors, respectively
Dynamic parameter estimationMathematical formulation
simple bounds
● Given a mathematical model:
● A dynamic parameter estimation problem entails solving:
20
initial conditions
systematic errorsrandom errors
sensor variance modelsensor model
sensor variancemodel parameters
sensor bias parameters
objective function(e.g., maximum likelihood)
control variables(i.e., input measurements)
process parameters(e.g., kinetic constant)
decision variables
time horizon
Parameter estimation from historical dataStudy definition
● Objective function
– maximum likelihood
● Decision variables
– 1 process parameter● kinetic factor (pre-multiplier)
– 1 sensor parameter● SPP* variance
● Measured output variables
– 1 sensor (SPP)
● Measured input variables
– 21 controlled variables– 5 disturbances
● Time horizon
– 24 hr of operation
● Initial conditions
– implicit state initialisation procedure**
● Process variable trajectories
– reconstruction of process trajectories (30 min)
● Goal:
– calibrate process model ● i.e., tune kinetics
21 *SPP: smart pulp platform; IR-based in-line process instrumentation; ** Rolandi (2005).
Parameter estimation from historical dataStudy results and discussion historian-based
Statistical analysis at 95% confidence
● confidence intervals
● coefficients of variation
– kinetic pre-multiplier: 0.83 %
– SPP sensor variance: 35.9 %● confidence ellipsoid
– parameters are not correlated
Non-parametric test
● non-random residuals (90% confidence)
kinetic pre-multiplier (KinPreMult) and SPP sensor variance (Omega): optimal parameter estimates (EST), confidence intervals (CI), lower and upper confidence bounds (LB and UB) at 95%, engineering units (EU)
SPP sensor variance [#K] vs kinetic pre-multiplier [adim]: optimal parameter estimates (EST), joint confidence region (REG), individual
confidence intervals (INT) at 95%
selectivity/kappa number [#K] vs time [hr]; experimental selectivity
values (SPP) vs model predictions (CS1) and outlier
(OUT); top: overlay plot; bottom: residuals plot; data from plant
historian
Model validation from historical dataStudy results and discussion
Model validation observations
● good agreement
● greater variability in measured process data than in model predictions
Likely causes of mismatch*
● chip composition fluctuations
● chip size distribution
● reaction/diffusion phenomena
● chip column movement and compaction
● momentum transfer phenomena
23
selectivity/kappa number [#K] vs time [hr]: overlay plots of experimental values (SPP) and model predictions (VE1, VE2) at two different production levels; VE1 at 541
ton/day and VE2 at 473 ton/day); data from plant historian
* most probably in increasing order of importance.
Parameter estimation and model validationIn a nutshell
● It provides a mechanism for rigorous calibration of mechanistic process models
– steady-state and/or dynamic– from laboratory, pilot-plant and industrial-plant data– usually sensitive to outliers
● The formulation of a PE problem requires special attention
– PE is an unconstrained (nonlinear) optimisation problem (i.e., a NLP)– it usually involves a workflow with iterative refinements
● There is a well-established theory for the assessment of the quality of fit
– including (but not limited to) significance tests and confidence intervals/regions
● Model validation must use a different data set than used in PE
24
Steady-state process optimisation
“The more unpredictable the world is the more we rely on predictions.”Steve Rivkin
Steady-state process optimisationDomain problems and engineering tasks
Process synthesis/design*
● Economic optimisation
– throughput optimisation
– raw material and energy consumption optimisation
– set-point optimisation
● Process synthesis
● Process equipment design
● Process flexibility design
● Process robustness design
● Process integration design
Via rigorous optimisation…
● … instead of via heuristics and rules-of-thumb
– i.e., removing any unnecessarya-priori simplifications
Benefits:
● Effective exploration of high-dimensional decision-variable space
● Ability to deal with significant complexities
26 *not an exhaustive list.
Steady-state process optimisationMathematical formulation
● Given a (steady-state) mathematical model:
● A steady-state optimisation problem entails solving:
● This is a so-called Nonlinear Programming (NLP) problem
● Numerical solution algorithms: “optimisers”
– gradient-based, gradient-free– constrained, reduced gradient, Lagrangian, augmented penalty, etc.– Sequential Linear/Quadratic Programming (SLP/SQP), Interior Point (IP),
Conjugate Gradient (CG), Particle Swarm, etc. 27
objective function
control variables(e.g., PID set-points)process parameters
(e.g., equipment sizing)
inequality constraintsequality constraints
simple bounds
(no time derivatives )
decision variables
Engineering problem description
● Maximise
– production● Satisfy
– target production rate and selectivity (i.e., pulp quality)
● downstream impact…● single process unit!
– consumption of pulping chemicals
● Change
– nine set-points of the regulatory control layer (PID)
● feed rate of wood chips● alkali distribution policy● wash addition policy● column heating policy
Optimisation problem description
● Objective function
– pulp yield● Constraints
– achieving a given production target (600 ton/day)
– meeting standard quality specifications (selectivity; 90 #K)
– white liquor and wash filtrate (2x) rates
● Decision variables
– set point of white liquor (3x) and wash filtrate (3x) addition controllers
– set point of heater's temperature controllers (2x)
– set point of screw meter controller (1x)
28
Dynamic process optimisationStudy formulation
Steady-state process optimisationStudy results and discussion
● Optimal operating conditions
– maximum production
● White liquor set-points
– reduction: from 16.50 % to 16.37 %
– same level of addition but significant redistribution:
● less to the make-up line
● more to the lower circulation line
● Wash filtrate set-points
– from 2.500 L/ton to 2.636 L/ton
● Temperature set-points
– increased lower circulation heater temperature by 3.25 K
– decreased wash circulation heater by 4.00 K
29
Steady-state process optimisationStudy results and discussion
temperature profile [°C] vs height [#];absolute (ABS) values and delta (REL) w.r.t. base case
selectivity (S) [#K] and yield (Y) [%] vs height [#];delta w.r.t. base case
Temperature profiles
● more even temperatures throughout the whole reactor
– kinetic effects (and diffusion)● high-temperature zone
– gradient change from 17.4 K to 11.8 K
Key process variable profiles
● low-temperature zone
– higher yield and constant selectivity● high-temperature zone
– reduced yield and selectivity● at the exit
– constant yield, improved selectivity● >> less lignin, more cellulose!
30
Steady-state process optimisationStudy results and discussion – outputs
● Optimal operating conditions
– maximum production
● Production performance
– pulp yield improvement of approximately 1.2 %
● more wood-pulp production at same wood-chip consumption
● Economic performance
– net profit increase by approximately 1.04 US$/min
● +0.52 million US$/year
– higher pulp throughput
● 1.68 US$/min revenue increase
– higher flow of black liquor for evaporation
● 0.64 US$/min cost increase
● Is this the best we can achieve?
31
Steady-state process optimisation – reloadedStudy results and discussion – outputs
● Optimal operating conditions
– maximum net profit
● i.e., let’s only change the nature of the objective function!
● Production performance
– pulp yield reduction of approximately 0.15 %
● Economic performance
– net profit increase by approximately 3.00 US$/min (incremental)
● +2.03 million US$/year (compared with the original operating policy)
– lower pulp throughput
● 0.17 US$/min revenue decrease
– lower flow of black liquor for evaporation
● 3.18 US$/min expense decrease
● How can this be achieved?
32
Steady-state process optimisation – reloadedStudy results and discussion – decision variables
● Optimal operating conditions
– maximum net profit
● White liquor set-points
– from 16.36 % to 15.26 %
● 6.75 % relative change!
● Wash filtrate set-points
– from 2.636 L/ton to 2.250 L/ton
● 14.6 % relative change!
● Temperature set-points
– increased lower circulation heater temperature by 7.28 K (!)
– wash circulation heater unchanged
– as a matter of fact, stuck on lower bound! >> elasticity (i.e., shadow prices)
● Quantitative results for process improvement33
Steady-state process optimisationIn a nutshell
● It is an efficient and effective way of exploring a high-dimensional decision-variable space*
– investigates feasibility (set of realisable solutions) and optimality (best possible solution)
– addresses a wide range of domain problems and engineering tasks
● It provides an effective mechanism for establishing process understanding
– usually leading to locally optimal solutions (global optimality is computationally intensive**)
● The formulation of a steady-state optimisation problem requires special attention
– its structure and numerical values● objective function, decision variables, constraints and bounds
– optimisation studies can produce analyses that are not meaningful or useful● avoid “GIGO” >> garbage in, garbage out
● The solution of a constrained NLP is reasonably straightforward
– still, equation-oriented modelling technologies have a clear advantage34*i.e., a large proportion of “decision spaces” of practical interest; **but can be justified for some applications.
Dynamic process optimisation
“With the availability of much more powerful computers,should not the basic approaches (…) be reconsidered?”*Richalet, Rault, Testud & Papon
*originally said in the context of advanced process control, but equally applicable to any computationally-intensive engineering task.
Dynamic process optimisationDomain problems and engineering tasks
Process synthesis/design*
● Economic optimisation
– throughput optimisation
– raw material and energy consumption optimisation
– set-point optimisation
● Process synthesis
● Process equipment design
● Process flexibility design
● Process robustness design
● Process integration design
Via rigorous optimisation…
● … instead of via heuristics and rules-of-thumb
– i.e., removing any unnecessarya-priori simplifications
Benefits:
● Effective exploration of high-dimensional decision-variable space
● Ability to deal with significant complexities
36 *not an exhaustive list.
All of these… and more:
● Control system design/analysis
● Standard/emergency operating procedure design
● Start-up/shut-down operating procedure design
● Transition planning
Benefits:
● Ability to deal with transient conditions and complex dynamics
simple bounds interior-pointinequality constraints
path inequality constraints
Dynamic process optimisationMathematical formulation
37
objective function
time-invariant controls(e.g., nominal PID set-points) end-point inequality constraints
end-point equality constraints
● A dynamic optimisation problem entails solving:
● This is a so-called Dynamic Optimisation Problem (DOP)● Numerical solution algorithms
– simultaneous solution: full discretisation (of differential-algebraic equations)– sequential solution (Control-Vector Parameterisation -CVP): discretisation of
decision variables (and constraints) only
time-varying controls(e.g., PID set-points)
decision variables
time horizoninitial conditions
Transient process operation
● Minimise
– selectivity deviation● Satisfy
– target production rate increase● Change
– two set-points of the regulatory layer (PID)
● feed rate of wood chips– 2.0 rpm / 50 ton/day
● lower circulation heater– 0.50 K / 50 ton/day
● wash circulation heater– no-change!
– all other set-points follow fixed-ratio changes
Dynamic optimisation study
● Objective function
– selectivity deviation (from 90 #K)● Constraints
– achieving a given production target increase (+50 ton/day)
● Decision variables
– set point of screw meter controller (1x)– set point of heater temperature
controllers (2x)– >> note difference of control structure
(we’ll revisit this)● Horizon
– 12 hr of transient operation● Control intervals* (discretisation)
– 1x 1 hr + 6x 1 hr + 1x 2 hr + 1x 3 hr38 *in accordance with standard operating procedures and operators’ practices.
Dynamic process optimisationTransient operation and study formulation
Dynamic process optimisationStudy results and discussion – decision variables
Transition planning profiles
● Chip-meter
– smother speed-up– feed load starts 2 hr earlier!
● Lower circulation heater
– gradual temperature increase– temperature boost starts
immediately!
● Wash circulation heater
– sharp temperature increase duringchip-meter speed-up
– settles to small temperature increase
39
top: chip-meter [rpm]; middle: lower circulation heater [ºC]; bottom: wash circulation heater [ºC] vs time [hr]
Dynamic process optimisationStudy results and discussion – outputs/revisited
● Goal
– minimise selectivity deviation● Outcome
– very tight control of key quality variable is possible!
● by actively using 3 set-points!● Analysis
– coarse and fine control● lower and wash heaters,
respectively
Transition planning study
● Let’s consider the following set-up instead…
● Decision variables
– set point of screw meter controller (1x)
– set point of lower-circulation heater temperature controller only (1x)
– >> same active control structure as in base case
● How different will the outcome be?
40
selectivity [#K] vs time [hr]; standard (SUB) and optimised (OPT) production rate transition procedure
Dynamic process optimisation – revisitedStudy results and discussion
Transition planning profiles
● Chip-meter
– no significant changes
● Lower circulation heater
– higher temperatures sooner– compensating for wash circulation
heater
● Selectivity deviation
– no significant changes● constant kappa number
● Outcome
– equivalent selectivity results– >> alternative operating procedure!
41
top: chip-meter [rpm]; middle: lower circulation heater [ºC]; bottom: selectivity [#K] vs time [hr]
Dynamic process optimisationIn a nutshell
● It can produce significant insights into the transient behaviour and optimal transient operating procedures of complex processes
● An effective formulation requires attention to detail (and benefits from previous experience)
– its structure and numerical values● time horizon; control-interval and control-vector parameterisations● initial- and end-point constraints; interior-point and path constraints
– the chances of formulating a problem that fails to solve are high● but such infeasible formulations are usually too restrictive, unrealistic or simply
incorrect– alternatively, the problem formulation may not be sufficiently constrained
● or the constraints are “surrogate” measures of performance with poorer predictive capabilities
● The solution of a constrained DOP requires advanced numerical solution algorithms
– equation-oriented modelling technologies have a clear advantage● in terms of scope and solution speed
42
Multi-objective process optimisation
“Complex goals are generally best achieved obliquely.”John Kay
Multi-objective process optimisationIntroduction
● We found that in the pulp-and-paper mill…
– maximum productivity and maximum profitability are incompatible performance objectives
– maximum profit leads to less efficient use of raw materials
– optimal steady-state conditions or dynamic transitions may be considered be too aggressive to be implemented in the plant...
● Perhaps more importantly…
– not all process constraints of importance for the operation of a continuous cooking digester were added to the optimisation problem formulation >> incomplete study*
● Multi-objective process optimisation is an holistic framework for computing and contrasting a family of solutions of a single process design/optimisation problem in a rigorous fashion
– it is based on the concept of a Pareto set
a Pareto optimal solution is a set of non-inferior solutions in the objectivespace defining a boundary beyond which none of the objectives can be improved
without sacrificing at least one of the other objectives
*e.g., the minimum concentration of chemicals in the wood chip matrix (e.g., to avoid condensation reactions). 44
Multi-objective process optimisationResults and discussion
Multi-objective trade-offs
● Point “CS1”
– high yield, low profit● Point “CS3”
– high profit, low yield● Point “CS2”
– high profit (1.4% loss)– intermediate yield (50% loss)– “safe” operation*
● Which one is the best?
– which constraints are active?– could any constraints be violated
due to small disturbances?● >> robust optimisation
45 *it includes minimum reactant concentration (residual alkali) constraints.
Pareto optimal set (three points);net profit [US$/min] vs pulp yield [%]
left (clockwise): chip meter speed, white liquor addition make-up, recirculation flows 2x (lower and wash circulation lines), wash filtrate addition 3x (lower and wash circulation lines and
digester bottoms), heater temperatures 2x (lower and wash circulation heaters);
right (clockwise): pulp yield, net profit, while liquor addition charge, wash filtrate addition charge, minimum residual alkali,
washing efficiency and weak black liquor flow.
Multi-objective process optimisationIn a nutshell
● There are at least two distinct criteria (and usually more) in any engineering design/operation problem
– economic and technological
– safety, environmental, etc...
● Multi-objective optimisation is a framework for rigorous quantification of the associated trade-offs
– this results in a Pareto set of equivalent solutions
46
Dynamic data reconciliation
“Reality is merely an illusion, albeit a very persistent one.”Albert Einstein
Dynamic data reconciliationIntroduction
● How do we tackle plant / model mismatch?
● Parameter estimation (PE)
– inaccurate model– process parameters (θ)
● Data reconciliation (DR)
– inaccurate data– random (ε) and systematic (β)– measurement errors
● Joint parameter estimation / data reconciliation (JPEDR*)
48
F(z,y,u,d,θ)
y
zuu
d
*the formulation of this problem fits the description on page 20.
F(z,y,u,d)
y
zu
d
yd
F(z,y,u,d,θ)zu
tune model parameters such that they minimisethe error ||.|| between the experimental ( ) and predicted (z) values of a subset of process variables
subject to the constraints F(.) and H(.) imposed by the models of the process and the sensors, respectively
~Z
Dynamic data reconciliationStudy formulation
● Objective function
– weighted least squares● Decision variables
– 2 process parameters● kinetic factor● wood chip moisture
– 3 sensor biases● white liquor addition flow● wash filtrate addition flow● upper extraction flow
● Measured output variables
– 8 sensors (7 flow measurements)
● Measured input variables
– 21 manipulations– 5 disturbances
● Time horizon
– 24 hr of operation
● Initial conditions
– implicit state initialisation procedure*
● Process variable trajectories
– reconstruction of process trajectories (30 min)
● Goal
– investigate the closure of the general mass balance in the continuous cooking digester
49 * Rolandi (2005).
Dynamic data reconciliationStudy results and discussion – biases
● Kinetic pre-multiplier vs chip impregnation factor– correlated: cannot fully distinguish
between higher velocities of reaction and higher chip moisture values
● Upper extraction screen flow bias– 6.4 % bias– 46.71 % precision (at 95%)– identifiable with given experimental
set-up!● from plant historian
– but not identifiable if 1 sensor is eliminated!
● Upper extraction screen flow bias vs chip impregnation factor– correlated: higher moisture values
can be explained by lower sensor biases
● this relationship can be explained mechanistically 50
coefficient of variation (CV) and bias (ERR) for the three reconciled volumetric flow measurement
sensors; white liquor charge, wash filtrate to digester bottoms; upper extraction screen
confidence ellipsoid;upper extraction screen
flowrate [m3/min] vschip impregnation
factor [m3/kg]
confidence ellipsoid;kinetic pre-multiplier
[adim] vs chip impregnation factor
[m3/kg]
Dynamic data reconciliationStudy results and discussion – inventory/balance
● Inventory analysis
– 32% of 3.1 m3/min
– >> 32,000 m3/yr
● Cost analysis
– 56% of 88 US$/min
– >> 0.50 million US$/yr
Mass balance closure
● Raw volumetric flowrate data
– purely data-driven– 11.3 % error (to be expected)
● Raw mass flowrates
– model-based simulation– 3.5 % error (better)
● Mass balance reconciliation
– found 3 biases: 6.4, 7.1, 8.2 %
● Reconciled mass flowrates
– model-based optimisation– 0.7 % error (best!)
51
relative error in mass-balance closure; raw volumetricflowrates (red), raw mass flowrates (blue) andreconciled mass flowrates (green) vs time [hr]
Data reconciliationIn a nutshell
● Models are not the only source of errors and uncertainty; lab, pilot-plant and industrial-plant data also are
– data reconciliation provides a more balanced perspective on the issue of plant / model mismatch
● Accurate inventory analysis requires model-based tools
– unfortunately, industrial process instrumentation is usually insufficient to enable the application of hybrid techniques using process data and process models
● Advanced model-based technologies promote the formulation imaginative process engineering techniques and methodologies and solution of important process engineering problems
– steady-state and dynamic data reconciliation is one such technique– process controllability, process flexibility, process robustness and optimal
sensor placement are others
52
Other process systems engineering techniques
“For every expert there is an equal and opposite expert.”Arthur C. Clarke
Other process systems engineering techniques
● Stochastic simulation and optimisation
– uncertainty analysis >> impact of variability (the “known unknowns”); propagation of uncertainty
● Local and global sensitivity analysis
– LSA >> moderately useful– GSA >> apportion “output” uncertainty to “input” uncertainty/variability
● e.g., enables rigorous (and effective) meta-modelling and surrogate (approximate) models
● Mathematical programming
– Linear Programming (LP) (i.e., linearity “assumption”)– Mixed Integer Linear/Nonlinear Programming (MILP/MINLP*)
● enables rigorous synthesis and design
● Real-time on-line applications
– Soft-sensing / State-estimation– Model Predictive Control (MPC) & Real-time Dynamic Optimisation (RTDO)
54* it exhibits many local optima (non-convexities & multiple -sometimes degenerate- all-integer solutions).
Summary and conclusions
“Give me where to stand, and I will move the Earth.”Archimedes
Summary and conclusions
● Large-scale, plant-wide, process models are a fundamental component of sophisticated, state-of-the-art process-systems engineering techniques, methodologies and workflows
● Equation-oriented process modelling tools (e.g., gPROMS*) enable the efficient development and maintenance of these models throughout thelife-cycle
– via custom modelling (from scratch) of from pre-existing model libraries(in-house or third-party)
● The problem you define is the problem you solve!
– avoid GIGO >> revisit the engineering problem and refine the problem formulation several times (iterative process), usually involving colleagues and clients
● Model-based techniques enable engineers to manage complexity more effectively and efficiently, to deliver technological breakthroughs faster and to realise massive economic improvements.
56 * Process Systems Enterprise Ltd.
Background slides
Model-centric Framework forIntegrated Operations Support*
PROCESS SYSTEM (PILOT-PLANT / INDUSTRIAL PLANT)
CONTROL SYSTEM (DCS / PLC / PKS)
CONDITIONING & PREPROCESSING
PARAMETER ESTIMATION
DATA RECONCILIATION
PROCESS SIMULATION
ADVANCED CONTROL
TRANSITION MANAGEMENT
PROCESS OPTIMISATION
SURROUNDINGS (WORLD / MARKET)
DECISION-MAKERS (OPERATORS / PROCESS ENGINEERS)
MECHANISTICPROCESS
MODEL
Future ScenariosPast Scenarios
OPTIMAL NOMINALTRANSITION
CONTROL ACTIONS
OPTIMAL NOMINALOPERATING POINT
RAW DATA
RECONCILIED DATA
CONSISTENT DATA& STATISTICS
DA
TA /
KN
OW
LED
GE
AC
TIO
NS
/ DE
CIS
ION
S
PROCESS SIMULATION
BIAS ESTIMATES
PARAMETER ESTIMATES
PROCESS DATA PROCESS DATA
* Rolandi (2005); Rolandi & Romagnoli (2009).58
