- Email: [email protected]
Energy-based Fault Detection for an Autothermal Reformer
11th IFAC Symposium on Dynamics and Control of 11th IFACSystems, Symposium on Dynamics and Control of Process including Biosystems 11th IFAC Symposium on and 11th IFACSystems, Symposium on Dynamics Dynamics and Control Control of of Process including Biosystems June 6-8,Systems, 2016. NTNU, Trondheim, Norway Available online at www.sciencedirect.com Process including Biosystems Process including Biosystems June 6-8,Systems, 2016. NTNU, Trondheim, Norway June June 6-8, 6-8, 2016. 2016. NTNU, NTNU, Trondheim, Trondheim, Norway Norway
ScienceDirect
IFAC-PapersOnLine 49-7 (2016) 353–358
Energy-based Fault Energy-based Fault Energy-based Fault Energy-based Fault Autothermal Autothermal Autothermal Autothermal
Detection Detection Detection Detection Reformer Reformer Reformer Reformer
for for for for
an an an an
Henri-Jean Marais, George van Schoor, Kenneth R. Uren Henri-Jean Marais, George van Schoor, Kenneth R. Uren Henri-Jean Henri-Jean Marais, Marais, George George van van Schoor, Schoor, Kenneth Kenneth R. R. Uren Uren School of Electrical, Electronic, and Computer Engineering. School of Electrical, Electronic, and Computer Engineering. School Electrical, Electronic, Computer North-West Province 2531, School of ofUniversity, Electrical, Potchefstroom, Electronic, and and North-West Computer Engineering. Engineering. North-West University, Potchefstroom, North-West Province 2531, North-West University, Potchefstroom, North-West South Africa (e-mail: [email protected]). North-West University, Potchefstroom, North-West Province Province 2531, 2531, South Africa (e-mail: [email protected]). South South Africa Africa (e-mail: (e-mail: [email protected]). [email protected]). Abstract: Condition monitoring has traditionally been deployed for the monitoring of a single Abstract: Condition monitoring has traditionally been deployed for the monitoring of a single Abstract: has been for monitoring of component, such as amonitoring rotating machine. The application of condition monitoring techniques Abstract: Condition Condition monitoring has traditionally traditionally been deployed deployed for the themonitoring monitoring techniques of aa single single component, such as a rotating machine. The application of condition component, such as a rotating The application of condition monitoring techniques to entire petrochemical process machine. plants, however, remains lacking. This can be ascribed to the component, such as a rotating machine. The application of condition monitoring techniques to entire petrochemical process plants, however, remains lacking. This can be ascribed to the to process plants, however, remains lacking. be to significant complexity involved in applying existing techniques to This such can plants. In this work to entire entire petrochemical petrochemical process in plants, however, remains lacking. This can be ascribed ascribed to the theaa significant complexity involved applying existing techniques to such plants. In this work significant complexity involved in applying applying existing techniques to such such plants. plants. In of thisa work work novel energy-based fault detection scheme isexisting appliedtechniques to an autothermal reformer gas-to-aa significant complexity involved in to In this novel energy-based fault detection scheme is applied to an autothermal reformer of a gas-tonovel detection is to of liquids process. Thefault performance ofscheme the technique is evaluated, against a reformer set of representative novel energy-based energy-based fault detectionof scheme is applied applied to an an autothermal autothermal reformer of aa gas-togas-toliquids process. The performance the technique is evaluated, against a set of representative liquids process. The performance of the technique is evaluated, against aa set of representative faults, and it is shown to provide adequate fault detection performance. The use of the energyliquids process. The performance of the technique is evaluated, against set of representative faults, and it is shown to provide adequate fault detection performance. The use of the energyenergyfaults, and to provide adequate performance. use of based detection scheme shows promise in fault termsdetection of reduced modellingThe efforts and increased faults, detection and it it is is shown shown to shows providepromise adequate fault detection performance. The use and of the the energybased scheme in terms of reduced modelling efforts increased based detection detectionefficiency. scheme shows shows promise promise in in terms terms of of reduced reduced modelling modelling efforts efforts and and increased increased computational based scheme computational efficiency. computational efficiency. computational efficiency. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Condition Monitoring, Energy, Process, Industrial, Fault Detection Keywords: Condition Monitoring, Energy, Process, Industrial, Fault Detection Keywords: Keywords: Condition Condition Monitoring, Monitoring, Energy, Energy, Process, Process, Industrial, Industrial, Fault Fault Detection Detection 1. INTRODUCTION vided. The first step towards providing these estimates is 1. INTRODUCTION vided. The first step towards providing these estimates is 1. vided. towards providing estimates determining the step current condition of thethese component. 1. INTRODUCTION INTRODUCTION vided. The The first first step towards providing these estimates is is determining the current condition of the component. determining the current condition of component. determining the current condition of the thebackground, component. with In section 2 we provide some relevant It is a well-known fact that the world is facing an energy In section 2 we provide some relevant background, with It is aa well-known fact that the world is facing an section 22 we some background, with aIn more detailed discussion of relevant the applied technique in It well-known fact that world is an energy energy crisis, and that this crisis isthe mainly due to depletion of In section we provide provide some relevant background, with more detailed discussion of the applied technique in It is is a and well-known fact thatis the worlddue is facing facing an energy crisis, that this crisis mainly to depletion of aasection more discussion of the in 3.detailed In section 4 we develop aapplied simple technique model of an crisis, and that this crisis is mainly due to depletion of fossil fuel resources. Although this has spawned many a more detailed discussion of the applied technique in 3. In section 44 we develop a simple model of an crisis, fuel and resources. that this crisis is mainly due spawned to depletion of section fossil Although this has many section 3. In section we develop simple model of an autothermal reformer, and also listaa some representative fossil fuel resources. Although this has spawned many research efforts into alternative energy sources, it has also section 3. In section 4 we develop simple model of an reformer, and also list some representative fossil fuelefforts resources. Although energy this has spawned many research into alternative sources, it has also autothermal autothermal reformer, and representative faults. The resulting performance of some the fault detection research into alternative energy sources, has prompted research into more energy efficient processes. autothermal reformer,performance and also also list listof some representative The resulting the fault detection research efforts efforts into into alternative energy efficient sources, it it has also also faults. prompted research more energy processes. faults. The resulting performance of the fault detection technique is presented in section 5 and a discussion of the prompted research into more energy efficient processes. Traditionally the efficiency of energy a process couldprocesses. be max- technique faults. Theis resulting of the fault detection presentedperformance in section 5 and aa discussion of the prompted research into more efficient Traditionally the efficiency of aa process could be maxtechnique is in section discussion of suitability of presented the technique follows55inand section 6. Concluding Traditionally the efficiency of process could be maximised by improving the control scheme or by upgrading technique is presented in section and a discussion of the the suitability of the technique follows in section 6. Concluding Traditionally the efficiency of a process could be maximised by improving the control scheme or by upgrading suitability of the technique follows in section 6. Concluding remarks and further work are presented in section 7. imised by improving the control scheme or by upgrading the process technology. However, for certain industrial prosuitability of the technique follows in section 6. Concluding remarks imised by improving control for scheme or industrial by upgrading the process technology.the However, certain proremarks and and further further work work are are presented presented in in section section 7. 7. the certain industrial processes this istechnology. simply notHowever, feasible for as the improvement that the process process technology. However, for certain industrial that pro- remarks and further work are presented in section 7. cesses this is simply not feasible as the improvement 2. BACKGROUND cesses this is simply not feasible as the improvement that can be this obtained is overshadowed by significant process cesses is simply not feasible by as the improvement that 2. BACKGROUND can be obtained is overshadowed the significant process 2. can be obtained is overshadowed by the significant process risk incurred in doing so. As a typical example consider a 2. BACKGROUND BACKGROUND can be obtained is overshadowed by the significant process risk incurred in doing so. As a typical example consider a risk doing so. consider 2.1 Condition monitoring petrochemical plant. Upgrading of the example control technology risk incurred incurred in inplant. doingUpgrading so. As As aa typical typical example consider aa 2.1 Condition monitoring petrochemical of the control technology petrochemical plant. Upgrading of the an control technology is estimated byplant. WhiteUpgrading (2010) to of yield improvement of 2.1 2.1 Condition Condition monitoring monitoring petrochemical the control technology is estimated by White (2010) to yield an improvement of is estimated White (2010) to yield of less than 5%,by whilst there is little that an canimprovement be done to the Historically condition monitoring has its roots in the moniis estimated by White (2010) to yield an improvement of less than 5%, whilst there is little that can be done to the Historically condition monitoring has its roots in the moniless than 5%, whilst there little that can be done to the underlying technology usedis to implement the process. Historically condition monitoring has in monitoring of large scale industrial machines, typically rotating less than 5%, whilst there is little that can be done to the Historically condition monitoring has its its roots roots in the the moniunderlying technology used to implement the process. toring of large scale industrial machines, typically rotating underlying technology used to implement the process. toring of large scale industrial machines, typically rotating machines according to a review by Jardine et al. (2006). In underlying used to implement theenvironment process. toring of large scale industrial machines, typically rotating When one technology considers the entire operational machines according to aa review by Jardine et al. (2006). In machines according to review by Jardine et al. (2006). In When one considers the entire operational environment recent years, condition monitoring has also been applied to machines according to amonitoring review by has Jardine et al. applied (2006). In When considers the environment of suchone a plant, the maintenance processes become inter- recent years, condition also been to When one considers the entire entire operational operational environment recent years, condition monitoring has also been applied to of such a plant, the maintenance processes become interother electrical machines, such as transformers and switch recent years, condition monitoring has also been applied to of aa plant, maintenance become esting. Time-based methods can processes provide high-reliability electrical machines, such as transformers and switch of such such Time-based plant, the the methods maintenance become interinter- other other machines, such as and esting. can processes provide high-reliability high-reliability mode power supplies (Yang et al. (2010)). However, when other electrical electrical machines, such as transformers transformers and switch switch esting. Time-based methods can provide systems (often at excessive costs) and alsohigh-reliability assumes that mode power supplies (Yang et al. (2010)). However, when esting. Time-based methods can provide mode power supplies (Yang et al. (2010)). However, when systems (often at excessive costs) and also assumes that one attempts to find applications of condition monitormodeattempts power supplies et al. (2010)). However, when systems at costs) and equipment failures will occur at fixed time assumes intervalsthat ac- one to find(Yang applications of condition monitorsystems (often (often at excessive excessive costs) and also also assumes that one attempts to applications of monitorequipment failures will occur at fixed time intervals acing in the process industries (beyond electrical machines one in attempts to find find applications of condition condition monitorequipment failures will occur at fixed time intervals according to Kothamasu et al. (2009). Although not all of ing the process industries (beyond electrical machines equipment failures will et occur at fixedAlthough time intervals ing process industries electrical cording to Kothamasu al. (2009). not allacof within process plants as was(beyond done by Almasi machines (2011)), ing in in the the process industries (beyond electrical machines cording to et al. Although not of the key components being replaced necessarily needs to be process plants as was done by Almasi (2011)), cording to Kothamasu Kothamasu et replaced al. (2009). (2009). Althoughneeds not all all of within within process plants as was done by Almasi (2011)), the key components being necessarily to be scarcely any published works can be found. within process plants as was done by Almasi (2011)), the key being replaced necessarily needs to replaced, the risk (and associated costs) associated with a scarcely any published works can be found. the key components components being replacedcosts) necessarily needswith to be be any published works can be found. replaced, the risk (and associated associated aa scarcely scarcely any published works can be found. replaced, the risk (and associated costs) associated with component failure simply exceeds the replacement cost of Fundamentally, condition monitoring can be considered as replaced, thefailure risk (and associated costs) associated cost withofa Fundamentally, component simply exceeds the replacement condition monitoring can as component failure simply exceeds the replacement cost of said component. Fundamentally, condition can be be considered considered as aFundamentally, classification problem. Amonitoring signal (or signals) of interest as is component failure simply exceeds the replacement cost of conditionA monitoring can be considered said component. a classification problem. signal (or signals) of interest is said component. a classification problem. A signal (or signals) of interest is measured, submitted to a diagnostic algorithm, and finally said component. a classification problem. signal (oralgorithm, signals) ofand interest is Several alternative strategies to time-based maintenance measured, submitted to aAdiagnostic finally measured, submitted to algorithm, finally Several alternative strategies to time-based maintenance to a prognostic algorithm to determine the effectand of the dimeasured, submitted to aa diagnostic diagnostic algorithm, and finally Several alternative strategies to time-based maintenance exist, and of these, risk-based maintenance (RBM) and to a prognostic algorithm to determine the effect of the diSeveraland alternative time-based maintenance to algorithm to the the exist, of these,strategies risk-basedtomaintenance (RBM) and agnosis on the overall condition of the component. The to aa prognostic prognostic algorithm to determine determine the effect effect of ofThe the didiexist, of maintenance predictive maintenance (PM) are the most (RBM) commonand as agnosis on the overall condition of the component. diexist, and and maintenance of these, these, risk-based risk-based maintenance (RBM) and agnosis on the overall condition of the component. The dipredictive (PM) are the most common as agnostic functions are primarily concerned with determinagnosis on the overall condition of the component. The dipredictive maintenance (PM) are the most common as per the review by Jardine(PM) et al. are (2006). Although Foldvari agnostic functions are primarily concerned with determinpredictive maintenance the most common as agnostic functions are primarily concerned with determinper the review by Jardine et al. (2006). Although Foldvari ing the current state of the monitored system, for which agnostic functions are of primarily concerned with determinper the review by Jardine et al. (2006). Although Foldvari (2012) estimates that cost savings could be as high as 20%ing the current state the monitored system, for which per theestimates review bythat Jardine et al. (2006). state monitored system, for (2012) cost savings could Although be as highFoldvari as 20%- ing artificial neural networks (ANNs) are most commonly used ing the the current current state of of the the monitored system, for which which (2012) estimates cost be as as 40%, widespread adoption of RBMcould or PM remains lacking. neural networks (ANNs) are most commonly used (2012)widespread estimates that that cost savings savings could beremains as high high lacking. as 20%20%- artificial artificial neural networks (ANNs) are most commonly used 40%, adoption of RBM or PM according to Venkatasubramanian et al. (2003). Prognostic artificial neural networks (ANNs) are most commonly used 40%, widespread adoption of RBM or PM remains lacking. to Venkatasubramanian et al. (2003). Prognostic 40%, likely widespread PMthat remains lacking. according according to Venkatasubramanian et al. (2003). Prognostic algorithms aim to provide a future state estimate of the One reasonadoption for thisofisRBM the or fact an accurate according to Venkatasubramanian et al. (2003). Prognostic algorithms aim to provide future state state estimate estimate of of the the One likely reason for this is fact an aim to provide aaa future One reason for is the the fact that that must an accurate accurate system, based on current system information. However, estimation of component failure probability be pro- algorithms algorithms aim on to current provide system futureinformation. state estimate of the One likely likely of reason for this this is the fact that an accurate system, based However, estimation component failure probability must be proestimation probability must must be be propro- system, system, based based on on current current system system information. information. However, However, estimation of of component component failure failure probability Copyright © 2016, 2016 IFAC 353 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2016 IFAC 353 Copyright © 2016 IFAC 353 Peer review under responsibility of International Federation of Automatic Copyright © 2016 IFAC 353Control. 10.1016/j.ifacol.2016.07.325
IFAC DYCOPS-CAB, 2016 354 Henri-Jean Marais et al. / IFAC-PapersOnLine 49-7 (2016) 353–358 June 6-8, 2016. NTNU, Trondheim, Norway
in a review by Peng et al. (2010) current research efforts with regards to prognostic algorithms have been shown to present less than stellar results. The high variability in the accuracy of prognostic algorithms makes these algorithms a largely academic interest at current. If one disregards prognostics, there is a large correlation between the fields of condition monitoring and fault detection and identification. The area of fault detection and diagnosis (FDD) is primarily concerned with the detection, and diagnosis (insofar as location and magnitude are concerned) of fault conditions. Gertler (1998) considers fault detection and diagnosis to be more complete than fault detection and isolation (FDI) schemes (see Figure 1), as the magnitude of faults can also be detected by FDD schemes. FAULT IDENTIFICATION
FDI
FAULT DETECTION
The need for multi-domain modelling techniques is not new and was identified in early works by Chinneck and Chandrashekar (1984). Since energy is a well defined, multi-domain concept, it poses the question, whether energy can be used as the monitoring domain? Theoretically this would:
Fig. 1. Comparison of FDI and FDD 2.2 Fault detection and isolation In Figure 2 a classification of various common fault detection schemes is presented (based on the work of Venkatasubramanian et al. (2003)). Broadly, fault detection methods can be classified as either being of the model-based or model-free type. In model-free detection schemes an explicit model is unavailable, and only process history data is used for fault detection. Typically detection is accomplished using statistical techniques which offers fast detection capabilities, but isolation and identification of faults are significantly more difficult. The main disadvantage of the model-free methods is the large labelled historic database that is required.
Kalman Filters Parity Space
Observers
Process History Based
Qualitative Model-based Causal models
Digraphs
Qualitative Physics Fault trees
Abstraction hierarchy
Structural
Functional
• Reduce the input space to a single dimension; • Allow for hierarchical monitoring; • Provide inherently multi-domain models.
Consider a generalised energy model of a unit operation (see Figure 3).
Fig. 3. Generalised energy model of unit operation
Diagnostic Methods Quantitative Model-based
Qualitative model-based methods make use of qualitative modelling techniques such as qualitative physics, or simple signed directed graphs and can be seen as a compromise between analytical rigour and ease of implementation. No single FDI technique will be equally applicable to all problem domains and Venkatasubramanian et al. (2003) argues that a hybrid approach will likely provide optimal FDI performance. If one considers hierarchical decomposition schemes the main advantages are an improvement in the performance of the classifier (less complex) as well as a decoupling of process units. The latter has been identified by Jardine et al. (2006) as a critical area for improvement. 2.3 Energy as modelling domain
FDD
FAULT ISOLATION
industrial chemical processes, the derivation of analytical models are widely considered to be either too complex or too costly to be feasible.
Qualitative
Qualitative Trend Analysis
Expert systems
Quantitative
Artificial Neural Networks
Statistical
Principal Component Analysis (PCA) Partial Least Squares (PLS)
Statistical Classifiers
Fig. 2. Diagnostic method classification
Since only a single parameter domain is concerned (energy) various unit operations can be coupled together to form a process. Additionally, a process can be simplified to a single model block with the various energy flows simply being the algebraic sum of each unit operation’s energy flows. Interestingly, by modelling the problem space in the energy-domain, model reduction is achieved whilst maintaining a large degree of similarity between the energy model and the physical process plant. 3. ENERGY-BASED FAULT DETECTION
The model-based methods require a model of the process. In the quantitative sphere, these models typically take the form of analytical or differential equations. Analytical models have the advantage of generally being more accurate, and the modelling fidelity can be adjusted according to the specific monitoring requirements. However, the major disadvantage of analytical models, as identified by Juslin et al. (2005) is the high degree of complexity inherent in the process, as well as the amount of time required to construct even a relatively simple model. For 354
Du Rand et al. (2009) developed a method that allowed condition monitoring of a nuclear-powered closed Brayton cycle, by monitoring the entropy s, and enthalpy h, at each point in the cycle. Effectively this transforms the measurement space into an energy domain. This transformation reduces the input space to only two dimensions, which is computationally more efficient, and allows a simple diagram (see Figure 4), referred to as the entropyenthalpy graph by Du Rand and Van Schoor (2012a), to
IFAC DYCOPS-CAB, 2016 June 6-8, 2016. NTNU, Trondheim, Norway Henri-Jean Marais et al. / IFAC-PapersOnLine 49-7 (2016) 353–358
be constructed (hereafter referred to as a signature) for each operating condition.
Fig. 4. Illustrative example of an h-s signature By comparing the signatures of various operating points, Du Rand et al. (2009) was able to determine whether errors occurred, as well as the magnitude of these errors (Du Rand and Van Schoor (2012b)). Du Rand’s technique is based on the thermodynamic properties of enthalpy and entropy. When one considers a thermodynamically open system the application of the first law of thermodynamics is cumbersome. To address this, a new quantity enthalpy h, which combines the internal energy of the working fluid u, and the work done on the fluid P v, into a single quantity, is introduced such that: h = u + Pv (1) where P is the pressure and v the volume of the fluid. It is simple to show that the heat transfer Q, for a closedsystem undergoing a constant pressure process can be expressed as: Q = m(h2 − h1 ). (2) For an ideal gas the equation of state is: P v = RT (3) where R is the gas constant and T the temperature, with P , and v as before. For an ideal gas it can be shown that the enthalpy h, is simply a function of the temperature of the gas, thus h = h(T ). This allows the enthalpy of the gas to be related to the specific heat cp of the gas by: dh = cp (T )dT. (4) Specific heat cp defines the amount of energy that is required to raise a specific amount of substance’s temperature by one degree, and is usually either provided at constant pressure or constant volume. In the case of constant pressure specific heat the pressure of the substance is kept constant, and for the constant volume case the volume is kept constant during the heating process. By making use of (2) and (4), and assuming constant specific heat cp , it is easy to show that: ∆h = cp (T2 − T1 ). (5) From (5) one can deduce that, for an ideal gas, a change in temperature will result in a similar change in enthalpy. By the first law of thermodynamics energy cannot be created or destroyed, but only changed from one form to another. The second law, provides the rate limits under which the first law holds, expressed as entropy s. For a compressible gas the associated change in entropy can be expressed as: T2 P2 ∆s = cp ln − R ln (6) T1 P1 355
355
where R is the gas constant which is equal to 8.314510 J/mol.K, and T1 , T2 , P1 , and P2 refers to the initial and final temperatures and pressures respectively. At this point a distinction must be made between reversible and irreversible processes. An irreversible process is one in which the process cannot be reversed without energy input from the environment. A typical example of an irreversible process is fluid flow in a pipe with friction considered. Pipe friction will reduce the amount of energy in the fluid, which cannot be recovered by reversing the fluid flow. Most real processes can be considered to be irreversible and as such enthalpy and entropy relations can be derived. Based on the preceding section (h, s) data points could be used to determine the thermodynamic state. Du Rand argues that since the normal irreversibility of the process can be calculated or estimated, any deviations from the normal state would be indicative of a fault. However, the system considered by Du Rand et al. (2009) was closed (physically and thermodynamically), and most petrochemical processes are open systems (meaning they exchange both matter and energy across system boundaries). Although a closed system can be considered as a collection of open systems, it is unclear how the open vs. closed nature of the process will affect the effectiveness of the h−s technique. Additionally, and perhaps more importantly, in the Brayton cycle considered by Du Rand and Van Schoor (2012a) no chemical variation takes place in the working fluid. This is most certainly not the case in a petrochemical process. 4. PLANT MODELLING In order to apply the proposed fault diagnostic technique of Section 3, a suitable model must first be developed. Autothermal reforming is the first operation in a gas-toliquids (GTL) process. Existing models of GTL processes were mainly techno-economically focused, or investigated specific chemistry intricacies. A more pragmatic modelling approach was taken with regards to the modelling of the autothermal reformer (ATR). Based on the available literature the key chemistry as well as practical operating points were identified, and some simplifying assumptions were made. Since the primary focus of this work is investigating the applicability of Du Rand’s energy-based FDI scheme to petrochemical process plants only steady-state conditions were considered. The primary reason for this is that dynamic systems poses a greater challenge from an FDI perspective. Thus, if the technique fails in the steady-state scenario it will also fail in the dynamic scenario. 4.1 Relevant chemistry The feedstock for a typical ATR is natural gas, a varying composition of hydrocarbons, sulphurous oxides (SOX ), and nitrous oxides (NOX ). Depending on the location of the natural gas reservoir the exact composition varies but, methane (CH4 ) typically constitutes the bulk fraction. In the work of Chan et al. (2005) eight reactions were identified for the ATR, of which four could be disregarded due to insignificant reaction rates. Panahi et al. (2011) only modelled three reactions in the ATR namely oxidisation
IFAC DYCOPS-CAB, 2016 356 Henri-Jean Marais et al. / IFAC-PapersOnLine 49-7 (2016) 353–358 June 6-8, 2016. NTNU, Trondheim, Norway
of methane, steam methane reforming, and the water-gasshift reaction (see below) which proved to be adequate. CH4 +
3 2
O2 ←−→ CO2 + 2 H2 O
CH4 + H2 O ←−→ CO + 3 H2
(7) (8)
CO + H2 O ←−→ CO2 + H2
(9)
4.2 Validated model
4.4 Fault conditions When considering the possible faults that could manifest in an ATR, an exhaustive search would be tedious and error prone. In order to avoid an exhaustive search, a distinction was made between different types of faults. The types of faults that were considered included faults that: • • • •
Directly affect physical properties of material streams; Induce gross model changes; Appear due to failed control systems; Are related to chemical composition variation.
For the purposes of this work, perfect sensors were assumed. This is in line with previous assertions made with regards to simplifying the application domain in an attempt to determine the suitability of a new technique, rather than exploring the limits of said technique.
Fig. 5. Model of the ATR in Aspen Hysys
R
The developed model is shown in Figure 5. The model was validated against the operating points provided in Table 1. In Figure 5, the feed gas, together with steam and oxygen is reacted in the reactor vessel. Flow rates of oxygen and carbondioxide is adjusted automatically to attain the required syngas characteristics. Table 1. ATR model parameters Parameter Inlet Temperature Outlet Temperature Operating Pressure H2 O:C ratio O2 :C ratio CO2 :CH4 ratio H2 :CO ratio
Expected Value
Simulated Value
Unit
675 1020 - 1030 30 ≈ 0.5 ≈ 0.5 ≈ 0.1 2-2.1
675 1025 30 0.5 0.53 0.12 2.001
◦C
◦C bar
Table 2. Summary of considered faults Fault No.
Fault description
F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F13
Temperature of feed stream is high (+5%) Temperature of feed stream is low (-5%) Pressure of feed stream is high (+10%) Pressure of feed stream is low (-10%) Flowrate of feed stream is high (+10 %) Flowrate of feed stream is low (-10%) Reformer bed fouled (5 bar pressure drop) Syngas leak (10% leak) CO2 valve stuck open (200 kgmol/h) CO2 valve stuck closed (0 kgmol/h) Feed stream contaminated with 10 % inert components Oxygen is contaminated with Nitrogen (10% contamination) Feed and Oxygen is contaminated (10% SO2, 10% N2)
5. RESULTS
4.3 Assumptions and operating point The following assumptions were made with regards to the modelling of the ATR vessel: • • • •
In addition to the common faults listed, a single multiple fault was considered. Primarily, this was simply included to assess whether or not the technique would be able to handle multiple faults. Multiple faults are typically not considered in FDI literature due to the likelihood of combinatorial explosion occurring with regards to the number of possible fault conditions. The list of faults considered in this work, together with a brief description and fault number is provided in Table 2.
Perfect mixing; No pressure drop; Adiabatic operation; Equilibrium reactor model.
Typical ATR vessels are designed such that near perfect mixing of the reagents is achieved, and the catalyst bed presents a minimal pressure drop to the flow of material. The reaction chemistry involved is such that chemical equilibrium is achieved during operation therefore Aspen R Hysys can employ an equilibrium criterion during the simulation process. Adiabatic operation implies that no energy is lost to the environment. While this is not achievable in practise, ATR vessels are designed as close to this point as possible. 356
5.1 Extended enthalpy-entropy method For the ATR system the graph-based approach followed by Du Rand and Van Schoor (2012b) could not be deployed. The (h, s)-graphs were based on the notion of a thermodynamically closed system. Thus, one would expect a cycle to have certain points that would be cycled through during the cycle’s operation. However, for an open system a similar argument does not hold. For this reason an alternative means of presenting the (h, s) data-pairs were devised. Initially, the ATR was operated under normal conditions (as per Table 1) so as to establish a baseline. This would be considered akin to determining the normal irreversibility of the system. For each fault condition, the resulting data was normalised with respect to the normal state. This provided a unitless quantity indicative of the magnitude
IFAC DYCOPS-CAB, 2016 June 6-8, 2016. NTNU, Trondheim, Norway Henri-Jean Marais et al. / IFAC-PapersOnLine 49-7 (2016) 353–358
of the deviation. To avoid false positives, due to rounding errors, a limit function was deployed. x ≥ 1 + threshold → x = 1 1 − threshold < x < 1 + threshold → x = 0 (10) x ≤ 1 − threshold → x = −1 was implemented. The threshold function is applied to the normalised data, with the results being transformed into a qualitative vector such that: (11) Fx = [h1 , s1 , h2 , s2 , ..., hn , sn ]. For each of the faults listed in Table 2, the resulting qualitative fault vector is presented in Table 3. Note that in Table 3 Input1 to Input4 correlates with the Feed, Steam, Oxygen, and Carbondioxide steams in Figure 5 respectively, and that Output refers to Syngas (in the same figure). Table 3. Mole-base qualitative vectors based on (h, s) data pairs Fault ID
Input1
Input2
Input3
Input4
Output
F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F13
-1 1 0 0 0 0 0 0 0 0 1 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
-1 1 -1 1 -1 1 1 -1 1 -1 1 -1 1
1 -1 -1 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 1 -1 1 1 0 1 -1 0 0 0
357
Table 4. Rate-base qualitative vectors based on (h, s) data pairs Fault ID
Input1
Input2
Input3
Input4
Output
F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F13
-1 1 0 0 1 -1 0 0 0 0 1 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0
-1 1 -1 1 1 -1 1 -1 1 -1 -1 1 1
1 -1 -1 -1 -1 1 -1 -1 1 -1 0 0 0
-1 1 -1 1 1 -1 1 -1 1 -1 1 0 1
1 -1 -1 1 1 -1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
-1 1 -1 1 1 -1 1 -1 1 -1 -1 1 1
1 -1 -1 -1 -1 1 -1 -1 1 -1 0 0 0
1 1 -1 1 1 -1 1 -1 1 -1 0 1 0
Constant specific heat One possible reason for the lack of isolability of the h − s technique is the assumption of constant specific heat. Typically, specific heat is a function of temperature. However, the only effect this would have on (5), is the introduction of an integral from the initial temperature to the final temperature, T2 cp (T )dT (12) ∆h = T1
which should only introduce minor variations. Indeed if one considers, for example pure Hydrogen gas (H2 ), the specific heat at constant pressure varies from 14.3117 kJ/kg.K at 300 K to 14.96137 kJ/kg.K at 1000 K. In a more realistic range of temperature variation the varying specific heat should not have a big effect.
6. PERFORMANCE ANALYSIS 6.1 Fault detection and isolation The lack of a zero vector in Table 3 indicates that the h − s technique can perform fault detection for the faults considered. For fault isolation, the situation is very different. There are some similar qualitative fault vectors in Table 3 (which have been suitably indicated). This shows that the h − s technique breaks down in terms of fault isolation. More specifically, those faults dealing with chemical composition variations (either in feedstocks or products) F9 -F12 are commonly affected. Not surprisingly, the multiple fault (which also dealt with chemical composition variations) could also not be isolated from other singular faults. 6.2 Shortfalls Molar quantities In Du Rand et al. (2009) molar quantities were used for the (h, s) data-pairs. It is thus not surprising that the technique fails to adequately isolate flowrate variations since flowrate variations is an extrinsic property. Attempting to determine an extrinsic property from only an intrinsic property is nonsensical. However, even when extrinsic properties were used in conjunction with the intrinsic properties, the technique failed to perform isolation (see Table 4). 357
Mixing of gasses When one considers the chemical composition variations of interest it typically excludes chemical reactions. The Gibbs energy G, of a mixture of two, ideal, non-reacting gasses is represented by: (13) G = n1 G1 + n2 G2 which combines the partial Gibbs energy of each species by their respective molar quantities ni . Considering that the partial Gibbs energy of an ideal gas can be represented by: Pi , (14) Gi = µ◦i + RT ln 1bar where µ◦i is the standard chemical potential of a species, and Pi the partial pressure of the species in question. By combining (13) and (14) the Gibbs energy of the system before mixing (assuming pressure of P ) is: Ginitial = n1 (µ◦1 + RT ln P ) + n2 (µ◦2 + RT ln P ). (15) After mixing each of the constituent gasses will exert a partial pressure on the other such that P1 + P2 = P and Gf inal = n1 (µ◦1 + RT ln P1 ) + n2 (µ◦2 + RT ln P2 ). (16) It is then simple to show that: ∆Gmix = Gf inal − Ginitial (17) P1 P2 + n2 RT ln ∆Gmix = n1 RT ln P P which simplifies to (18) ∆Gmix = nRT (x1 ln x1 + x2 ln x2 ) if Pi = xi P and (19) ni = xi n.
IFAC DYCOPS-CAB, 2016 358 Henri-Jean Marais et al. / IFAC-PapersOnLine 49-7 (2016) 353–358 June 6-8, 2016. NTNU, Trondheim, Norway
Since Gibbs energy is considered as a generating quantity in thermodynamics, the change in entropy (under constant pressure) can be expressed as: δG = −S. (20) δT P Substitution of (18) into (20) results in:
∆Smix = −nR(x1 ln x1 + x2 ln x2 ).
(21)
From (21) it is interesting to note that although mixing of the gasses will result in a change in entropy, the fractions of the mixture cannot be determined from the resulting change. Thus a molar fraction of 80:20 and one of 20:80 will result in the exact same change in entropy. Furthermore it is trivial to show that the change in enthalpy associated with the mixing of ideal gasses is: ∆Hmix = ∆Gmix + T ∆Smix , (22) ∆Hmix = 0. With reference to (22) the h − s technique will thus not be able to detect the mixing of perfect gasses from an enthalpy perspective. 7. CONCLUSION If one considers the performance of the h−s fault detection technique (as per Table 3) the results are less than stellar from an isolability perspective. Based on the fundamental equations for enthalpy and entropy it is not surprising that variations in temperatures and pressures could be accurately detected and isolated from another. Similarly, flow rate variations became detectable and isolable when the energy flow rate was considered (Table 4), but chemical composition variations remained a problem. Theoretically, assuming ideal gasses and an ideal equation of state it was shown in Section 6 that the h − s FDI scheme is severely limited in terms of detecting chemical composition variations. Insofar as the enthalpy is concerned ideal mixing has a zero net effect. Entropy fares slightly better but is only sensitive to variations in the fractional composition, and not the exact composition. Keeping in mind that the h − s technique was originally developed for a closed-loop system with a single working fluid the breakdown of the technique is not entirely surprising. It should be noted though that for industrialscale systems the reduction of the measurement space to fewer dimensions is highly advantageous. Additionally, the advantages afforded by the energy domain as far as it pertains to hierarchical FDI and process unit decoupling cannot be denied. What remains to be done then is to investigate whether or not Du Rand’s technique can be extended to provide suitable isolability performance for petrochemical processes. 8. ACKNOWLEDGEMENT This work is based on the research supported wholly or in part by the National Research Foundation (NRF) of South Africa under grant number 91093. Opinions expressed and conclusions arrived at are those of the authors and are not necessarily to be attributed to the NRF. 358
REFERENCES Almasi, A. (2011). Power plant condition monitoring. Power Engineering, 115(8), 60–63. Chan, S., Hoang, D., and Ding, O. (2005). Transient performance of an autothermal reformera 2-d modeling approach. International journal of heat and mass transfer, 48(19), 4205–4214. Chinneck, J. and Chandrashekar, M. (1984). Models of large-scale industrial energy systemsii: Optimization and synthesis. Energy, 9(8), 679–692. Du Rand, C.P., Van Schoor, G., and Nieuwoudt, C. (2009). Enthalpy–entropy graph approach for the classification of faults in the main power system of a closed brayton cycle htgr. Annals of Nuclear Energy, 36(6), 703–711. Du Rand, C. and Van Schoor, G. (2012a). Fault diagnosis of generation iv nuclear htgr components–part i: The error enthalpy–entropy graph approach. Annals of Nuclear Energy, 40(1), 14–24. Du Rand, C. and Van Schoor, G. (2012b). Fault diagnosis of generation iv nuclear htgr components–part ii: The area error enthalpy–entropy graph approach. Annals of Nuclear Energy, 41, 79–86. Foldvari, A. (2012). Risk-based condition monitoring and reliability-centred maintenance of industrial plants: Improved safety, reduced maintenance costs. Technical report, TUV Rheinland. Gertler, J. (1998). Fault detection and diagnosis in engineering systems. CRC press. Jardine, A.K., Lin, D., and Banjevic, D. (2006). A review on machinery diagnostics and prognostics implementing condition-based maintenance. Mechanical systems and signal processing, 20(7), 1483–1510. Juslin, K. et al. (2005). A companion model approach to modelling and simulation of industrial processes. VTT Technical Research Centre of Finland. Kothamasu, R., Huang, S.H., and VerDuin, W.H. (2009). System health monitoring and prognostics a review of current paradigms and practices. In M. Ben-Daya, S.O. Duffuaa, A. Raouf, J. Knezevic, and D. Ait-Kadi (eds.), Handbook of Maintenance Management and Engineering, 337–362. Springer London. Panahi, M., Rafiee, A., Skogestad, S., and Hillestad, M. (2011). A natural gas to liquids process model for optimal operation. Industrial and Engineering Chemistry Research, 51(1), 425–433. Peng, Y., Dong, M., and Zuo, M.J. (2010). Current status of machine prognostics in condition-based maintenance: a review. The International Journal of Advanced Manufacturing Technology, 50(1), 297–313. Venkatasubramanian, V., Rengaswamy, R., Yin, K., and Kavuri, S.N. (2003). A review of process fault detection and diagnosis: Part i: Quantitative model-based methods. Computers & Chemical engineering, 27(3), 293– 311. White, D.C. (2010). Save energy through automation. Chemical Engineering Progress, (1), 26. Yang, S., Xiang, D., Bryant, A., Mawby, P., Ran, L., and Tavner, P. (2010). Condition monitoring for device reliability in power electronic converters: A review. Power Electronics, IEEE Transactions on, 25(11), 2734– 2752.
ScienceDirect
IFAC-PapersOnLine 49-7 (2016) 353–358
Energy-based Fault Energy-based Fault Energy-based Fault Energy-based Fault Autothermal Autothermal Autothermal Autothermal
Detection Detection Detection Detection Reformer Reformer Reformer Reformer
for for for for
an an an an
Henri-Jean Marais, George van Schoor, Kenneth R. Uren Henri-Jean Marais, George van Schoor, Kenneth R. Uren Henri-Jean Henri-Jean Marais, Marais, George George van van Schoor, Schoor, Kenneth Kenneth R. R. Uren Uren School of Electrical, Electronic, and Computer Engineering. School of Electrical, Electronic, and Computer Engineering. School Electrical, Electronic, Computer North-West Province 2531, School of ofUniversity, Electrical, Potchefstroom, Electronic, and and North-West Computer Engineering. Engineering. North-West University, Potchefstroom, North-West Province 2531, North-West University, Potchefstroom, North-West South Africa (e-mail: [email protected]). North-West University, Potchefstroom, North-West Province Province 2531, 2531, South Africa (e-mail: [email protected]). South South Africa Africa (e-mail: (e-mail: [email protected]). [email protected]). Abstract: Condition monitoring has traditionally been deployed for the monitoring of a single Abstract: Condition monitoring has traditionally been deployed for the monitoring of a single Abstract: has been for monitoring of component, such as amonitoring rotating machine. The application of condition monitoring techniques Abstract: Condition Condition monitoring has traditionally traditionally been deployed deployed for the themonitoring monitoring techniques of aa single single component, such as a rotating machine. The application of condition component, such as a rotating The application of condition monitoring techniques to entire petrochemical process machine. plants, however, remains lacking. This can be ascribed to the component, such as a rotating machine. The application of condition monitoring techniques to entire petrochemical process plants, however, remains lacking. This can be ascribed to the to process plants, however, remains lacking. be to significant complexity involved in applying existing techniques to This such can plants. In this work to entire entire petrochemical petrochemical process in plants, however, remains lacking. This can be ascribed ascribed to the theaa significant complexity involved applying existing techniques to such plants. In this work significant complexity involved in applying applying existing techniques to such such plants. plants. In of thisa work work novel energy-based fault detection scheme isexisting appliedtechniques to an autothermal reformer gas-to-aa significant complexity involved in to In this novel energy-based fault detection scheme is applied to an autothermal reformer of a gas-tonovel detection is to of liquids process. Thefault performance ofscheme the technique is evaluated, against a reformer set of representative novel energy-based energy-based fault detectionof scheme is applied applied to an an autothermal autothermal reformer of aa gas-togas-toliquids process. The performance the technique is evaluated, against a set of representative liquids process. The performance of the technique is evaluated, against aa set of representative faults, and it is shown to provide adequate fault detection performance. The use of the energyliquids process. The performance of the technique is evaluated, against set of representative faults, and it is shown to provide adequate fault detection performance. The use of the energyenergyfaults, and to provide adequate performance. use of based detection scheme shows promise in fault termsdetection of reduced modellingThe efforts and increased faults, detection and it it is is shown shown to shows providepromise adequate fault detection performance. The use and of the the energybased scheme in terms of reduced modelling efforts increased based detection detectionefficiency. scheme shows shows promise promise in in terms terms of of reduced reduced modelling modelling efforts efforts and and increased increased computational based scheme computational efficiency. computational efficiency. computational efficiency. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Condition Monitoring, Energy, Process, Industrial, Fault Detection Keywords: Condition Monitoring, Energy, Process, Industrial, Fault Detection Keywords: Keywords: Condition Condition Monitoring, Monitoring, Energy, Energy, Process, Process, Industrial, Industrial, Fault Fault Detection Detection 1. INTRODUCTION vided. The first step towards providing these estimates is 1. INTRODUCTION vided. The first step towards providing these estimates is 1. vided. towards providing estimates determining the step current condition of thethese component. 1. INTRODUCTION INTRODUCTION vided. The The first first step towards providing these estimates is is determining the current condition of the component. determining the current condition of component. determining the current condition of the thebackground, component. with In section 2 we provide some relevant It is a well-known fact that the world is facing an energy In section 2 we provide some relevant background, with It is aa well-known fact that the world is facing an section 22 we some background, with aIn more detailed discussion of relevant the applied technique in It well-known fact that world is an energy energy crisis, and that this crisis isthe mainly due to depletion of In section we provide provide some relevant background, with more detailed discussion of the applied technique in It is is a and well-known fact thatis the worlddue is facing facing an energy crisis, that this crisis mainly to depletion of aasection more discussion of the in 3.detailed In section 4 we develop aapplied simple technique model of an crisis, and that this crisis is mainly due to depletion of fossil fuel resources. Although this has spawned many a more detailed discussion of the applied technique in 3. In section 44 we develop a simple model of an crisis, fuel and resources. that this crisis is mainly due spawned to depletion of section fossil Although this has many section 3. In section we develop simple model of an autothermal reformer, and also listaa some representative fossil fuel resources. Although this has spawned many research efforts into alternative energy sources, it has also section 3. In section 4 we develop simple model of an reformer, and also list some representative fossil fuelefforts resources. Although energy this has spawned many research into alternative sources, it has also autothermal autothermal reformer, and representative faults. The resulting performance of some the fault detection research into alternative energy sources, has prompted research into more energy efficient processes. autothermal reformer,performance and also also list listof some representative The resulting the fault detection research efforts efforts into into alternative energy efficient sources, it it has also also faults. prompted research more energy processes. faults. The resulting performance of the fault detection technique is presented in section 5 and a discussion of the prompted research into more energy efficient processes. Traditionally the efficiency of energy a process couldprocesses. be max- technique faults. Theis resulting of the fault detection presentedperformance in section 5 and aa discussion of the prompted research into more efficient Traditionally the efficiency of aa process could be maxtechnique is in section discussion of suitability of presented the technique follows55inand section 6. Concluding Traditionally the efficiency of process could be maximised by improving the control scheme or by upgrading technique is presented in section and a discussion of the the suitability of the technique follows in section 6. Concluding Traditionally the efficiency of a process could be maximised by improving the control scheme or by upgrading suitability of the technique follows in section 6. Concluding remarks and further work are presented in section 7. imised by improving the control scheme or by upgrading the process technology. However, for certain industrial prosuitability of the technique follows in section 6. Concluding remarks imised by improving control for scheme or industrial by upgrading the process technology.the However, certain proremarks and and further further work work are are presented presented in in section section 7. 7. the certain industrial processes this istechnology. simply notHowever, feasible for as the improvement that the process process technology. However, for certain industrial that pro- remarks and further work are presented in section 7. cesses this is simply not feasible as the improvement 2. BACKGROUND cesses this is simply not feasible as the improvement that can be this obtained is overshadowed by significant process cesses is simply not feasible by as the improvement that 2. BACKGROUND can be obtained is overshadowed the significant process 2. can be obtained is overshadowed by the significant process risk incurred in doing so. As a typical example consider a 2. BACKGROUND BACKGROUND can be obtained is overshadowed by the significant process risk incurred in doing so. As a typical example consider a risk doing so. consider 2.1 Condition monitoring petrochemical plant. Upgrading of the example control technology risk incurred incurred in inplant. doingUpgrading so. As As aa typical typical example consider aa 2.1 Condition monitoring petrochemical of the control technology petrochemical plant. Upgrading of the an control technology is estimated byplant. WhiteUpgrading (2010) to of yield improvement of 2.1 2.1 Condition Condition monitoring monitoring petrochemical the control technology is estimated by White (2010) to yield an improvement of is estimated White (2010) to yield of less than 5%,by whilst there is little that an canimprovement be done to the Historically condition monitoring has its roots in the moniis estimated by White (2010) to yield an improvement of less than 5%, whilst there is little that can be done to the Historically condition monitoring has its roots in the moniless than 5%, whilst there little that can be done to the underlying technology usedis to implement the process. Historically condition monitoring has in monitoring of large scale industrial machines, typically rotating less than 5%, whilst there is little that can be done to the Historically condition monitoring has its its roots roots in the the moniunderlying technology used to implement the process. toring of large scale industrial machines, typically rotating underlying technology used to implement the process. toring of large scale industrial machines, typically rotating machines according to a review by Jardine et al. (2006). In underlying used to implement theenvironment process. toring of large scale industrial machines, typically rotating When one technology considers the entire operational machines according to aa review by Jardine et al. (2006). In machines according to review by Jardine et al. (2006). In When one considers the entire operational environment recent years, condition monitoring has also been applied to machines according to amonitoring review by has Jardine et al. applied (2006). In When considers the environment of suchone a plant, the maintenance processes become inter- recent years, condition also been to When one considers the entire entire operational operational environment recent years, condition monitoring has also been applied to of such a plant, the maintenance processes become interother electrical machines, such as transformers and switch recent years, condition monitoring has also been applied to of aa plant, maintenance become esting. Time-based methods can processes provide high-reliability electrical machines, such as transformers and switch of such such Time-based plant, the the methods maintenance become interinter- other other machines, such as and esting. can processes provide high-reliability high-reliability mode power supplies (Yang et al. (2010)). However, when other electrical electrical machines, such as transformers transformers and switch switch esting. Time-based methods can provide systems (often at excessive costs) and alsohigh-reliability assumes that mode power supplies (Yang et al. (2010)). However, when esting. Time-based methods can provide mode power supplies (Yang et al. (2010)). However, when systems (often at excessive costs) and also assumes that one attempts to find applications of condition monitormodeattempts power supplies et al. (2010)). However, when systems at costs) and equipment failures will occur at fixed time assumes intervalsthat ac- one to find(Yang applications of condition monitorsystems (often (often at excessive excessive costs) and also also assumes that one attempts to applications of monitorequipment failures will occur at fixed time intervals acing in the process industries (beyond electrical machines one in attempts to find find applications of condition condition monitorequipment failures will occur at fixed time intervals according to Kothamasu et al. (2009). Although not all of ing the process industries (beyond electrical machines equipment failures will et occur at fixedAlthough time intervals ing process industries electrical cording to Kothamasu al. (2009). not allacof within process plants as was(beyond done by Almasi machines (2011)), ing in in the the process industries (beyond electrical machines cording to et al. Although not of the key components being replaced necessarily needs to be process plants as was done by Almasi (2011)), cording to Kothamasu Kothamasu et replaced al. (2009). (2009). Althoughneeds not all all of within within process plants as was done by Almasi (2011)), the key components being necessarily to be scarcely any published works can be found. within process plants as was done by Almasi (2011)), the key being replaced necessarily needs to replaced, the risk (and associated costs) associated with a scarcely any published works can be found. the key components components being replacedcosts) necessarily needswith to be be any published works can be found. replaced, the risk (and associated associated aa scarcely scarcely any published works can be found. replaced, the risk (and associated costs) associated with component failure simply exceeds the replacement cost of Fundamentally, condition monitoring can be considered as replaced, thefailure risk (and associated costs) associated cost withofa Fundamentally, component simply exceeds the replacement condition monitoring can as component failure simply exceeds the replacement cost of said component. Fundamentally, condition can be be considered considered as aFundamentally, classification problem. Amonitoring signal (or signals) of interest as is component failure simply exceeds the replacement cost of conditionA monitoring can be considered said component. a classification problem. signal (or signals) of interest is said component. a classification problem. A signal (or signals) of interest is measured, submitted to a diagnostic algorithm, and finally said component. a classification problem. signal (oralgorithm, signals) ofand interest is Several alternative strategies to time-based maintenance measured, submitted to aAdiagnostic finally measured, submitted to algorithm, finally Several alternative strategies to time-based maintenance to a prognostic algorithm to determine the effectand of the dimeasured, submitted to aa diagnostic diagnostic algorithm, and finally Several alternative strategies to time-based maintenance exist, and of these, risk-based maintenance (RBM) and to a prognostic algorithm to determine the effect of the diSeveraland alternative time-based maintenance to algorithm to the the exist, of these,strategies risk-basedtomaintenance (RBM) and agnosis on the overall condition of the component. The to aa prognostic prognostic algorithm to determine determine the effect effect of ofThe the didiexist, of maintenance predictive maintenance (PM) are the most (RBM) commonand as agnosis on the overall condition of the component. diexist, and and maintenance of these, these, risk-based risk-based maintenance (RBM) and agnosis on the overall condition of the component. The dipredictive (PM) are the most common as agnostic functions are primarily concerned with determinagnosis on the overall condition of the component. The dipredictive maintenance (PM) are the most common as per the review by Jardine(PM) et al. are (2006). Although Foldvari agnostic functions are primarily concerned with determinpredictive maintenance the most common as agnostic functions are primarily concerned with determinper the review by Jardine et al. (2006). Although Foldvari ing the current state of the monitored system, for which agnostic functions are of primarily concerned with determinper the review by Jardine et al. (2006). Although Foldvari (2012) estimates that cost savings could be as high as 20%ing the current state the monitored system, for which per theestimates review bythat Jardine et al. (2006). state monitored system, for (2012) cost savings could Although be as highFoldvari as 20%- ing artificial neural networks (ANNs) are most commonly used ing the the current current state of of the the monitored system, for which which (2012) estimates cost be as as 40%, widespread adoption of RBMcould or PM remains lacking. neural networks (ANNs) are most commonly used (2012)widespread estimates that that cost savings savings could beremains as high high lacking. as 20%20%- artificial artificial neural networks (ANNs) are most commonly used 40%, adoption of RBM or PM according to Venkatasubramanian et al. (2003). Prognostic artificial neural networks (ANNs) are most commonly used 40%, widespread adoption of RBM or PM remains lacking. to Venkatasubramanian et al. (2003). Prognostic 40%, likely widespread PMthat remains lacking. according according to Venkatasubramanian et al. (2003). Prognostic algorithms aim to provide a future state estimate of the One reasonadoption for thisofisRBM the or fact an accurate according to Venkatasubramanian et al. (2003). Prognostic algorithms aim to provide future state state estimate estimate of of the the One likely reason for this is fact an aim to provide aaa future One reason for is the the fact that that must an accurate accurate system, based on current system information. However, estimation of component failure probability be pro- algorithms algorithms aim on to current provide system futureinformation. state estimate of the One likely likely of reason for this this is the fact that an accurate system, based However, estimation component failure probability must be proestimation probability must must be be propro- system, system, based based on on current current system system information. information. However, However, estimation of of component component failure failure probability Copyright © 2016, 2016 IFAC 353 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2016 IFAC 353 Copyright © 2016 IFAC 353 Peer review under responsibility of International Federation of Automatic Copyright © 2016 IFAC 353Control. 10.1016/j.ifacol.2016.07.325
IFAC DYCOPS-CAB, 2016 354 Henri-Jean Marais et al. / IFAC-PapersOnLine 49-7 (2016) 353–358 June 6-8, 2016. NTNU, Trondheim, Norway
in a review by Peng et al. (2010) current research efforts with regards to prognostic algorithms have been shown to present less than stellar results. The high variability in the accuracy of prognostic algorithms makes these algorithms a largely academic interest at current. If one disregards prognostics, there is a large correlation between the fields of condition monitoring and fault detection and identification. The area of fault detection and diagnosis (FDD) is primarily concerned with the detection, and diagnosis (insofar as location and magnitude are concerned) of fault conditions. Gertler (1998) considers fault detection and diagnosis to be more complete than fault detection and isolation (FDI) schemes (see Figure 1), as the magnitude of faults can also be detected by FDD schemes. FAULT IDENTIFICATION
FDI
FAULT DETECTION
The need for multi-domain modelling techniques is not new and was identified in early works by Chinneck and Chandrashekar (1984). Since energy is a well defined, multi-domain concept, it poses the question, whether energy can be used as the monitoring domain? Theoretically this would:
Fig. 1. Comparison of FDI and FDD 2.2 Fault detection and isolation In Figure 2 a classification of various common fault detection schemes is presented (based on the work of Venkatasubramanian et al. (2003)). Broadly, fault detection methods can be classified as either being of the model-based or model-free type. In model-free detection schemes an explicit model is unavailable, and only process history data is used for fault detection. Typically detection is accomplished using statistical techniques which offers fast detection capabilities, but isolation and identification of faults are significantly more difficult. The main disadvantage of the model-free methods is the large labelled historic database that is required.
Kalman Filters Parity Space
Observers
Process History Based
Qualitative Model-based Causal models
Digraphs
Qualitative Physics Fault trees
Abstraction hierarchy
Structural
Functional
• Reduce the input space to a single dimension; • Allow for hierarchical monitoring; • Provide inherently multi-domain models.
Consider a generalised energy model of a unit operation (see Figure 3).
Fig. 3. Generalised energy model of unit operation
Diagnostic Methods Quantitative Model-based
Qualitative model-based methods make use of qualitative modelling techniques such as qualitative physics, or simple signed directed graphs and can be seen as a compromise between analytical rigour and ease of implementation. No single FDI technique will be equally applicable to all problem domains and Venkatasubramanian et al. (2003) argues that a hybrid approach will likely provide optimal FDI performance. If one considers hierarchical decomposition schemes the main advantages are an improvement in the performance of the classifier (less complex) as well as a decoupling of process units. The latter has been identified by Jardine et al. (2006) as a critical area for improvement. 2.3 Energy as modelling domain
FDD
FAULT ISOLATION
industrial chemical processes, the derivation of analytical models are widely considered to be either too complex or too costly to be feasible.
Qualitative
Qualitative Trend Analysis
Expert systems
Quantitative
Artificial Neural Networks
Statistical
Principal Component Analysis (PCA) Partial Least Squares (PLS)
Statistical Classifiers
Fig. 2. Diagnostic method classification
Since only a single parameter domain is concerned (energy) various unit operations can be coupled together to form a process. Additionally, a process can be simplified to a single model block with the various energy flows simply being the algebraic sum of each unit operation’s energy flows. Interestingly, by modelling the problem space in the energy-domain, model reduction is achieved whilst maintaining a large degree of similarity between the energy model and the physical process plant. 3. ENERGY-BASED FAULT DETECTION
The model-based methods require a model of the process. In the quantitative sphere, these models typically take the form of analytical or differential equations. Analytical models have the advantage of generally being more accurate, and the modelling fidelity can be adjusted according to the specific monitoring requirements. However, the major disadvantage of analytical models, as identified by Juslin et al. (2005) is the high degree of complexity inherent in the process, as well as the amount of time required to construct even a relatively simple model. For 354
Du Rand et al. (2009) developed a method that allowed condition monitoring of a nuclear-powered closed Brayton cycle, by monitoring the entropy s, and enthalpy h, at each point in the cycle. Effectively this transforms the measurement space into an energy domain. This transformation reduces the input space to only two dimensions, which is computationally more efficient, and allows a simple diagram (see Figure 4), referred to as the entropyenthalpy graph by Du Rand and Van Schoor (2012a), to
IFAC DYCOPS-CAB, 2016 June 6-8, 2016. NTNU, Trondheim, Norway Henri-Jean Marais et al. / IFAC-PapersOnLine 49-7 (2016) 353–358
be constructed (hereafter referred to as a signature) for each operating condition.
Fig. 4. Illustrative example of an h-s signature By comparing the signatures of various operating points, Du Rand et al. (2009) was able to determine whether errors occurred, as well as the magnitude of these errors (Du Rand and Van Schoor (2012b)). Du Rand’s technique is based on the thermodynamic properties of enthalpy and entropy. When one considers a thermodynamically open system the application of the first law of thermodynamics is cumbersome. To address this, a new quantity enthalpy h, which combines the internal energy of the working fluid u, and the work done on the fluid P v, into a single quantity, is introduced such that: h = u + Pv (1) where P is the pressure and v the volume of the fluid. It is simple to show that the heat transfer Q, for a closedsystem undergoing a constant pressure process can be expressed as: Q = m(h2 − h1 ). (2) For an ideal gas the equation of state is: P v = RT (3) where R is the gas constant and T the temperature, with P , and v as before. For an ideal gas it can be shown that the enthalpy h, is simply a function of the temperature of the gas, thus h = h(T ). This allows the enthalpy of the gas to be related to the specific heat cp of the gas by: dh = cp (T )dT. (4) Specific heat cp defines the amount of energy that is required to raise a specific amount of substance’s temperature by one degree, and is usually either provided at constant pressure or constant volume. In the case of constant pressure specific heat the pressure of the substance is kept constant, and for the constant volume case the volume is kept constant during the heating process. By making use of (2) and (4), and assuming constant specific heat cp , it is easy to show that: ∆h = cp (T2 − T1 ). (5) From (5) one can deduce that, for an ideal gas, a change in temperature will result in a similar change in enthalpy. By the first law of thermodynamics energy cannot be created or destroyed, but only changed from one form to another. The second law, provides the rate limits under which the first law holds, expressed as entropy s. For a compressible gas the associated change in entropy can be expressed as: T2 P2 ∆s = cp ln − R ln (6) T1 P1 355
355
where R is the gas constant which is equal to 8.314510 J/mol.K, and T1 , T2 , P1 , and P2 refers to the initial and final temperatures and pressures respectively. At this point a distinction must be made between reversible and irreversible processes. An irreversible process is one in which the process cannot be reversed without energy input from the environment. A typical example of an irreversible process is fluid flow in a pipe with friction considered. Pipe friction will reduce the amount of energy in the fluid, which cannot be recovered by reversing the fluid flow. Most real processes can be considered to be irreversible and as such enthalpy and entropy relations can be derived. Based on the preceding section (h, s) data points could be used to determine the thermodynamic state. Du Rand argues that since the normal irreversibility of the process can be calculated or estimated, any deviations from the normal state would be indicative of a fault. However, the system considered by Du Rand et al. (2009) was closed (physically and thermodynamically), and most petrochemical processes are open systems (meaning they exchange both matter and energy across system boundaries). Although a closed system can be considered as a collection of open systems, it is unclear how the open vs. closed nature of the process will affect the effectiveness of the h−s technique. Additionally, and perhaps more importantly, in the Brayton cycle considered by Du Rand and Van Schoor (2012a) no chemical variation takes place in the working fluid. This is most certainly not the case in a petrochemical process. 4. PLANT MODELLING In order to apply the proposed fault diagnostic technique of Section 3, a suitable model must first be developed. Autothermal reforming is the first operation in a gas-toliquids (GTL) process. Existing models of GTL processes were mainly techno-economically focused, or investigated specific chemistry intricacies. A more pragmatic modelling approach was taken with regards to the modelling of the autothermal reformer (ATR). Based on the available literature the key chemistry as well as practical operating points were identified, and some simplifying assumptions were made. Since the primary focus of this work is investigating the applicability of Du Rand’s energy-based FDI scheme to petrochemical process plants only steady-state conditions were considered. The primary reason for this is that dynamic systems poses a greater challenge from an FDI perspective. Thus, if the technique fails in the steady-state scenario it will also fail in the dynamic scenario. 4.1 Relevant chemistry The feedstock for a typical ATR is natural gas, a varying composition of hydrocarbons, sulphurous oxides (SOX ), and nitrous oxides (NOX ). Depending on the location of the natural gas reservoir the exact composition varies but, methane (CH4 ) typically constitutes the bulk fraction. In the work of Chan et al. (2005) eight reactions were identified for the ATR, of which four could be disregarded due to insignificant reaction rates. Panahi et al. (2011) only modelled three reactions in the ATR namely oxidisation
IFAC DYCOPS-CAB, 2016 356 Henri-Jean Marais et al. / IFAC-PapersOnLine 49-7 (2016) 353–358 June 6-8, 2016. NTNU, Trondheim, Norway
of methane, steam methane reforming, and the water-gasshift reaction (see below) which proved to be adequate. CH4 +
3 2
O2 ←−→ CO2 + 2 H2 O
CH4 + H2 O ←−→ CO + 3 H2
(7) (8)
CO + H2 O ←−→ CO2 + H2
(9)
4.2 Validated model
4.4 Fault conditions When considering the possible faults that could manifest in an ATR, an exhaustive search would be tedious and error prone. In order to avoid an exhaustive search, a distinction was made between different types of faults. The types of faults that were considered included faults that: • • • •
Directly affect physical properties of material streams; Induce gross model changes; Appear due to failed control systems; Are related to chemical composition variation.
For the purposes of this work, perfect sensors were assumed. This is in line with previous assertions made with regards to simplifying the application domain in an attempt to determine the suitability of a new technique, rather than exploring the limits of said technique.
Fig. 5. Model of the ATR in Aspen Hysys
R
The developed model is shown in Figure 5. The model was validated against the operating points provided in Table 1. In Figure 5, the feed gas, together with steam and oxygen is reacted in the reactor vessel. Flow rates of oxygen and carbondioxide is adjusted automatically to attain the required syngas characteristics. Table 1. ATR model parameters Parameter Inlet Temperature Outlet Temperature Operating Pressure H2 O:C ratio O2 :C ratio CO2 :CH4 ratio H2 :CO ratio
Expected Value
Simulated Value
Unit
675 1020 - 1030 30 ≈ 0.5 ≈ 0.5 ≈ 0.1 2-2.1
675 1025 30 0.5 0.53 0.12 2.001
◦C
◦C bar
Table 2. Summary of considered faults Fault No.
Fault description
F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F13
Temperature of feed stream is high (+5%) Temperature of feed stream is low (-5%) Pressure of feed stream is high (+10%) Pressure of feed stream is low (-10%) Flowrate of feed stream is high (+10 %) Flowrate of feed stream is low (-10%) Reformer bed fouled (5 bar pressure drop) Syngas leak (10% leak) CO2 valve stuck open (200 kgmol/h) CO2 valve stuck closed (0 kgmol/h) Feed stream contaminated with 10 % inert components Oxygen is contaminated with Nitrogen (10% contamination) Feed and Oxygen is contaminated (10% SO2, 10% N2)
5. RESULTS
4.3 Assumptions and operating point The following assumptions were made with regards to the modelling of the ATR vessel: • • • •
In addition to the common faults listed, a single multiple fault was considered. Primarily, this was simply included to assess whether or not the technique would be able to handle multiple faults. Multiple faults are typically not considered in FDI literature due to the likelihood of combinatorial explosion occurring with regards to the number of possible fault conditions. The list of faults considered in this work, together with a brief description and fault number is provided in Table 2.
Perfect mixing; No pressure drop; Adiabatic operation; Equilibrium reactor model.
Typical ATR vessels are designed such that near perfect mixing of the reagents is achieved, and the catalyst bed presents a minimal pressure drop to the flow of material. The reaction chemistry involved is such that chemical equilibrium is achieved during operation therefore Aspen R Hysys can employ an equilibrium criterion during the simulation process. Adiabatic operation implies that no energy is lost to the environment. While this is not achievable in practise, ATR vessels are designed as close to this point as possible. 356
5.1 Extended enthalpy-entropy method For the ATR system the graph-based approach followed by Du Rand and Van Schoor (2012b) could not be deployed. The (h, s)-graphs were based on the notion of a thermodynamically closed system. Thus, one would expect a cycle to have certain points that would be cycled through during the cycle’s operation. However, for an open system a similar argument does not hold. For this reason an alternative means of presenting the (h, s) data-pairs were devised. Initially, the ATR was operated under normal conditions (as per Table 1) so as to establish a baseline. This would be considered akin to determining the normal irreversibility of the system. For each fault condition, the resulting data was normalised with respect to the normal state. This provided a unitless quantity indicative of the magnitude
IFAC DYCOPS-CAB, 2016 June 6-8, 2016. NTNU, Trondheim, Norway Henri-Jean Marais et al. / IFAC-PapersOnLine 49-7 (2016) 353–358
of the deviation. To avoid false positives, due to rounding errors, a limit function was deployed. x ≥ 1 + threshold → x = 1 1 − threshold < x < 1 + threshold → x = 0 (10) x ≤ 1 − threshold → x = −1 was implemented. The threshold function is applied to the normalised data, with the results being transformed into a qualitative vector such that: (11) Fx = [h1 , s1 , h2 , s2 , ..., hn , sn ]. For each of the faults listed in Table 2, the resulting qualitative fault vector is presented in Table 3. Note that in Table 3 Input1 to Input4 correlates with the Feed, Steam, Oxygen, and Carbondioxide steams in Figure 5 respectively, and that Output refers to Syngas (in the same figure). Table 3. Mole-base qualitative vectors based on (h, s) data pairs Fault ID
Input1
Input2
Input3
Input4
Output
F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F13
-1 1 0 0 0 0 0 0 0 0 1 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
-1 1 -1 1 -1 1 1 -1 1 -1 1 -1 1
1 -1 -1 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 1 -1 1 1 0 1 -1 0 0 0
357
Table 4. Rate-base qualitative vectors based on (h, s) data pairs Fault ID
Input1
Input2
Input3
Input4
Output
F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F13
-1 1 0 0 1 -1 0 0 0 0 1 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0
-1 1 -1 1 1 -1 1 -1 1 -1 -1 1 1
1 -1 -1 -1 -1 1 -1 -1 1 -1 0 0 0
-1 1 -1 1 1 -1 1 -1 1 -1 1 0 1
1 -1 -1 1 1 -1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
-1 1 -1 1 1 -1 1 -1 1 -1 -1 1 1
1 -1 -1 -1 -1 1 -1 -1 1 -1 0 0 0
1 1 -1 1 1 -1 1 -1 1 -1 0 1 0
Constant specific heat One possible reason for the lack of isolability of the h − s technique is the assumption of constant specific heat. Typically, specific heat is a function of temperature. However, the only effect this would have on (5), is the introduction of an integral from the initial temperature to the final temperature, T2 cp (T )dT (12) ∆h = T1
which should only introduce minor variations. Indeed if one considers, for example pure Hydrogen gas (H2 ), the specific heat at constant pressure varies from 14.3117 kJ/kg.K at 300 K to 14.96137 kJ/kg.K at 1000 K. In a more realistic range of temperature variation the varying specific heat should not have a big effect.
6. PERFORMANCE ANALYSIS 6.1 Fault detection and isolation The lack of a zero vector in Table 3 indicates that the h − s technique can perform fault detection for the faults considered. For fault isolation, the situation is very different. There are some similar qualitative fault vectors in Table 3 (which have been suitably indicated). This shows that the h − s technique breaks down in terms of fault isolation. More specifically, those faults dealing with chemical composition variations (either in feedstocks or products) F9 -F12 are commonly affected. Not surprisingly, the multiple fault (which also dealt with chemical composition variations) could also not be isolated from other singular faults. 6.2 Shortfalls Molar quantities In Du Rand et al. (2009) molar quantities were used for the (h, s) data-pairs. It is thus not surprising that the technique fails to adequately isolate flowrate variations since flowrate variations is an extrinsic property. Attempting to determine an extrinsic property from only an intrinsic property is nonsensical. However, even when extrinsic properties were used in conjunction with the intrinsic properties, the technique failed to perform isolation (see Table 4). 357
Mixing of gasses When one considers the chemical composition variations of interest it typically excludes chemical reactions. The Gibbs energy G, of a mixture of two, ideal, non-reacting gasses is represented by: (13) G = n1 G1 + n2 G2 which combines the partial Gibbs energy of each species by their respective molar quantities ni . Considering that the partial Gibbs energy of an ideal gas can be represented by: Pi , (14) Gi = µ◦i + RT ln 1bar where µ◦i is the standard chemical potential of a species, and Pi the partial pressure of the species in question. By combining (13) and (14) the Gibbs energy of the system before mixing (assuming pressure of P ) is: Ginitial = n1 (µ◦1 + RT ln P ) + n2 (µ◦2 + RT ln P ). (15) After mixing each of the constituent gasses will exert a partial pressure on the other such that P1 + P2 = P and Gf inal = n1 (µ◦1 + RT ln P1 ) + n2 (µ◦2 + RT ln P2 ). (16) It is then simple to show that: ∆Gmix = Gf inal − Ginitial (17) P1 P2 + n2 RT ln ∆Gmix = n1 RT ln P P which simplifies to (18) ∆Gmix = nRT (x1 ln x1 + x2 ln x2 ) if Pi = xi P and (19) ni = xi n.
IFAC DYCOPS-CAB, 2016 358 Henri-Jean Marais et al. / IFAC-PapersOnLine 49-7 (2016) 353–358 June 6-8, 2016. NTNU, Trondheim, Norway
Since Gibbs energy is considered as a generating quantity in thermodynamics, the change in entropy (under constant pressure) can be expressed as: δG = −S. (20) δT P Substitution of (18) into (20) results in:
∆Smix = −nR(x1 ln x1 + x2 ln x2 ).
(21)
From (21) it is interesting to note that although mixing of the gasses will result in a change in entropy, the fractions of the mixture cannot be determined from the resulting change. Thus a molar fraction of 80:20 and one of 20:80 will result in the exact same change in entropy. Furthermore it is trivial to show that the change in enthalpy associated with the mixing of ideal gasses is: ∆Hmix = ∆Gmix + T ∆Smix , (22) ∆Hmix = 0. With reference to (22) the h − s technique will thus not be able to detect the mixing of perfect gasses from an enthalpy perspective. 7. CONCLUSION If one considers the performance of the h−s fault detection technique (as per Table 3) the results are less than stellar from an isolability perspective. Based on the fundamental equations for enthalpy and entropy it is not surprising that variations in temperatures and pressures could be accurately detected and isolated from another. Similarly, flow rate variations became detectable and isolable when the energy flow rate was considered (Table 4), but chemical composition variations remained a problem. Theoretically, assuming ideal gasses and an ideal equation of state it was shown in Section 6 that the h − s FDI scheme is severely limited in terms of detecting chemical composition variations. Insofar as the enthalpy is concerned ideal mixing has a zero net effect. Entropy fares slightly better but is only sensitive to variations in the fractional composition, and not the exact composition. Keeping in mind that the h − s technique was originally developed for a closed-loop system with a single working fluid the breakdown of the technique is not entirely surprising. It should be noted though that for industrialscale systems the reduction of the measurement space to fewer dimensions is highly advantageous. Additionally, the advantages afforded by the energy domain as far as it pertains to hierarchical FDI and process unit decoupling cannot be denied. What remains to be done then is to investigate whether or not Du Rand’s technique can be extended to provide suitable isolability performance for petrochemical processes. 8. ACKNOWLEDGEMENT This work is based on the research supported wholly or in part by the National Research Foundation (NRF) of South Africa under grant number 91093. Opinions expressed and conclusions arrived at are those of the authors and are not necessarily to be attributed to the NRF. 358
REFERENCES Almasi, A. (2011). Power plant condition monitoring. Power Engineering, 115(8), 60–63. Chan, S., Hoang, D., and Ding, O. (2005). Transient performance of an autothermal reformera 2-d modeling approach. International journal of heat and mass transfer, 48(19), 4205–4214. Chinneck, J. and Chandrashekar, M. (1984). Models of large-scale industrial energy systemsii: Optimization and synthesis. Energy, 9(8), 679–692. Du Rand, C.P., Van Schoor, G., and Nieuwoudt, C. (2009). Enthalpy–entropy graph approach for the classification of faults in the main power system of a closed brayton cycle htgr. Annals of Nuclear Energy, 36(6), 703–711. Du Rand, C. and Van Schoor, G. (2012a). Fault diagnosis of generation iv nuclear htgr components–part i: The error enthalpy–entropy graph approach. Annals of Nuclear Energy, 40(1), 14–24. Du Rand, C. and Van Schoor, G. (2012b). Fault diagnosis of generation iv nuclear htgr components–part ii: The area error enthalpy–entropy graph approach. Annals of Nuclear Energy, 41, 79–86. Foldvari, A. (2012). Risk-based condition monitoring and reliability-centred maintenance of industrial plants: Improved safety, reduced maintenance costs. Technical report, TUV Rheinland. Gertler, J. (1998). Fault detection and diagnosis in engineering systems. CRC press. Jardine, A.K., Lin, D., and Banjevic, D. (2006). A review on machinery diagnostics and prognostics implementing condition-based maintenance. Mechanical systems and signal processing, 20(7), 1483–1510. Juslin, K. et al. (2005). A companion model approach to modelling and simulation of industrial processes. VTT Technical Research Centre of Finland. Kothamasu, R., Huang, S.H., and VerDuin, W.H. (2009). System health monitoring and prognostics a review of current paradigms and practices. In M. Ben-Daya, S.O. Duffuaa, A. Raouf, J. Knezevic, and D. Ait-Kadi (eds.), Handbook of Maintenance Management and Engineering, 337–362. Springer London. Panahi, M., Rafiee, A., Skogestad, S., and Hillestad, M. (2011). A natural gas to liquids process model for optimal operation. Industrial and Engineering Chemistry Research, 51(1), 425–433. Peng, Y., Dong, M., and Zuo, M.J. (2010). Current status of machine prognostics in condition-based maintenance: a review. The International Journal of Advanced Manufacturing Technology, 50(1), 297–313. Venkatasubramanian, V., Rengaswamy, R., Yin, K., and Kavuri, S.N. (2003). A review of process fault detection and diagnosis: Part i: Quantitative model-based methods. Computers & Chemical engineering, 27(3), 293– 311. White, D.C. (2010). Save energy through automation. Chemical Engineering Progress, (1), 26. Yang, S., Xiang, D., Bryant, A., Mawby, P., Ran, L., and Tavner, P. (2010). Condition monitoring for device reliability in power electronic converters: A review. Power Electronics, IEEE Transactions on, 25(11), 2734– 2752.