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A new index for chemical process design considering risk analysis and controllability
Anton A. Kiss, Edwin Zondervan, Richard Lakerveld, Leyla Özkan (Eds.) Proceedings of the 29th European Symposium on Computer Aided Process Engineering June 16th to 19th, 2019, Eindhoven, The Netherlands. © 2019 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/B978-0-12-818634-3.50063-1
A new index for chemical process design considering risk analysis and controllability Nancy Medina-Herrera,a* Salvador Tututi-Avila,b Arturo Jiménez-Gutierrezc a
Universidad Autonoma de Nuevo León, Agronomy School, Francisco Villa s/n, Ex Hacienda el Canadá, General Escobedo, N.L, 66451, MEXICO
b
Universidad Autónoma de Nuevo León, Department of Chemical Engineering, Av. Universidad s/n, Ciudad Universitaria, San Nicolas de los Garza, NL, 66451, MEXICO
c
Department of Chemical Engineering, Instituto Tecnológico de Celaya, Av. Tecnológico s/n, Celaya, Gto. 38010 MEXICO
[email protected]
Abstract Safety and controllability are two important items that complement the economic analysis commonly done during a process design. Such factors are typically carried out once the process has been designed. Although some approaches have been proposed to include controllability properties from the design stage of the process, safety is still addressed after the design has been completed, so that safety devices are added to mitigate the consequences of potential accidents. Inherent safety is the most effective risk management approach, since actions can be taken to avoid accidents instead of mitigating their consequences. However, inherent safety is not a straightforward procedure, nor universal, and sometimes in conflict with other properties or parameters of the process. This manuscript describes a new index to account for inherent safety and controllability. The combination of a conditions number that accounts for controllability and a distance likely to cause death that emerges from the application of a quantitative risk analysis for the process was used as a basis. Three mathematical relationships were explored in the search for a suitable combination of such indices. The procedure was applied to a case study dealing with a distillation system design. Results show how the values obtained from the proposed index can give an initial assessment of the combined effect of risk and controllability as part of the design of a process. Keywords: controllability, design, inherent safety, risk analysis.
1. Introduction The concepts associated with inherent safety provide an effective tool for risk management. Inherent safety relies on the principles of elimination, minimization, moderation, substitution and simplification. The objective of inherent safety is to avoid risk instead of diminishing its consequences. The effectiveness of inherent safety depends on the stage of the plant life it is applied, being the design stage the most effective. The decisions based on inherent safety must be evaluated carefully, since inherent safety principles sometimes show conflicts among them. For instance, the minimization principle states that a process is safer when hazardous materials inventory is reduced, but dynamic performance might work against safety if inventory is reduced. Thus, it is important to assess safety in early stages of process design including this type of self-
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conflicting behavior. Recently, a comprehensive review of process safety indices has been published (Roy et al., 2016). From this collection, some highlighted indexes are discussed here. Dow Fire & Explosion Index (DF&EI) was the first proposed index to account for safety in the mid-60’s. There have been several works to assess inherent safety since it was defined in the 80’s. The first index related to inherent safety was proposed by Heikkila et al (1996). This index is similar to DF&EI and considers two main parts of the process: chemicals properties and process conditions. Khan and Amyotte (2004) have published an integrated inherent safety index, named I2SI. This index is more complex and considers process control within inherent safety. Most of the indices published so far are semi-quantitative, but many times weight factors are used to rank their importance. This semi-quantitative characteristic results in different processes with similar conditions so that material properties may get the same rating, which is not totally accurate. A quantitative risk analysis (QRA) has been shown as a proper tool to account for safety (Medina-Herrera et al., 2014). A QRA performs a more detailed study and provides a more exact risk measurement because probabilities and consequences are considered (AIChE, 2000). The Morari resilience index (MRI) can be used to discriminate among process alternatives; the larger its value, the more controllable the process is. Another important index is the condition number (CN) related to system sensitivity against input disturbances. Small values are desired. Another important index is the relative gain array number (RGANo) which gives information about the controlled and manipulated variables in the frequency domain; pairings with low RGANo values are preferred. All these indices provide a good basis to account for controllability, but a suitable approach to include both controllability and process safety is needed. In this work, we propose a quantitative approach for process design that accounts for inherent safety considering both risk and controllability. In terms of risk, we use a QRA approach to obtain a distance likely to cause death, which relates to material inventory. For controllability, we test two indices, namely the condition number and the relative gain array. From a set of design candidates, the indices are normalized, and three mathematical relationships between risk and controllability are explored.
2. Safety Indices Calculation 2.1. Design approach A set of initial designs ( P ) is considered to evaluate the performance of each design using the proposed indexes. Once the candidates are set, they are subjected to a combined controllability and QRA analysis. The approach is carried out using ASPEN Tech and MATLAB as software tools. In Aspen Plus steady state simulations are carried out, simulations are then exported to Aspen Dynamics, and the results are transferred to MATLAB, where indexes are computed. 2.2. Controllability analysis In terms of controllability, a singular value decomposition procedure is carried out, from which the condition number CNi is evaluated. Regularly, a matrix of gain is obtained for the process at zero frequency and a singular value decomposition analysis is carried out. In this work, we followed the methodology proposed by Gabor and Mizsey (2008) to
A new index for chemical process design considering risk analysis and controllability
375
make calculations using a linearized state-space model system of every candidate i. The linearized state space model can be obtained with the Control Design Interface module. The methodology also computes MRI and RGANo. 2.3. Quantitative risk analysis QRA was implemented to assess the risk of a chemical inside process, following the methodology described in Medina-Herrera et al. (2014). The methodology is based on frequency and consequences analyses. First, catastrophic scenarios are identified from potential failures within the system using a bow tie procedure, and frequencies are calculated from literature data on failures. Then, a consequence analysis is performed for every catastrophic scenario previously identified. In brief, the consequences analysis implies quantification of the amount of material released, dispersion calculations, characterization of the scenario, and finally quantification of consequences. The models for consequence analysis were taken from CCPS Guidelines for Quantitative Risk Analysis in Chemical Process (AIChE, 2000). After the application of QRA, DDi is obtained, which represents the distance of affectation such that there is a 50% chance of death in case of a catastrophic event. DDi was selected because it can be calculated as measurement of risk even when layout is not yet defined, in an early design stage. 2.4. Normalization After controllability and risk indices are individually evaluated, a normalization procedure is needed, since such indices have values with different orders of magnitude, and they also depend on the system of units. When the set P was evaluated and controllability and risk indicators were obtained for each candidate i, a normalization procedure was used taking as a basis the highest value of each index, DDi and CNi , within the set P, that is,
½ DDi i ° Maximum( DD ) ° ¾ i P CN i i ° CN N = Maximum(CN i ) °¿
DDNi =
(1)
As a result, the normalized indices are bound between zero and one, and they can be subject to numerical comparison on a consistent basis. 2.5. Basic mathematical relationships: Indices After the indicators are obtained with similar orders of magnitude, they can be used to rank process alternatives from controllability and risk considerations. Even when the relationship between such items is complex, we can establish that they are related to the process safety. Facing the lack of knowledge about the relationship between controllability and risk to assess safety, we followed the methodology by Ni et al. (2010) to create indices with two different inputs, and derived three basic mathematical relationships. As a result, a proposed safety index, SI, was developed, and three versions of such an index were created. The objective of testing three different relationships is aiding in the analysis to understand whether risk and controllability are additive, factored or follow a balanced relationship.
N. Medina-Herrera et al.
376
The first version SI1 is the addition of both criteria, distance likely to cause death ( DDN ) and condition number ( CN N ).
SI1 = DDN + CN N
(2)
The second version, SI 2 , is the product of both inputs,
SI 2 = DDN * CN N
(3)
For both additive and product relationships, the smaller the value of the index, the safer the process is. The third version we explore is a fraction given by the distance likely to cause death divided by the condition number (see Eq. (4)). In this case, a value close to one means that the process is balanced from both controllability and safety considerations, which may not necessarily be desirable. A value higher than one would indicate that risk is a more important criterion than controllability, and vice versa.
SI 3 = DDN / CN N
(4)
These three versions arise from the lack of knowledge on the relationship between risk and controllability. It deemed convenient to calculate and evaluate all three alternatives for an initial insight into behavior of the proposed index.
3. Case Study and Results The case study was taken from the CCPS Example of the guidelines for chemical process quantitative risk analysis (AIChE, 2000). The distillation system is a single column that separates n-hexane and n-heptane. The feed stream has 60,120 kg/h of a binary mixture with 58%wt of n-hexane. The purity specification for the top product is 0.9 on a weight basis, with a flowrate of 36,000 kg/h. The column has 16 equilibrium stages and the top pressure is 4.9 atm. The internal diameter calculated by ASPEN Plus was 2.7 meters. The residence time for sump was fixed at 6 minutes, and for reflux drum at 12 min using a 2D=L rule for tank dimensions. The QRA performed with the CCPS Guidelines has been used to analyze process risk. The objective of this example is to describe the methodology for the proposed index calculations along with the analysis of results. The hydraulic variables considered for this example were diameter and residence time for the reflux drum and sump. Such hydraulic variables affect both criteria, controllability and risk. In order to define the set of designs P , we took the CCPS design as the base case, which has a diameter of 2.71m and 12 and 6 min of residence time on the reflux drum and sump. Other designs were considered by varying the diameter from half the base diameter to three times that value, such that D = [0.5Dbase, 0.75Dbase, Dbase, 1.5Dbase, 2Dbase, 3Dbase] where Dbase=2.71m. As for the residence time, a range was fixed from 1 minute to 20 minutes, assuming equal values for both tanks. It should be noted that the base case assumes residence times of 12 and 6 minutes. When the diameter was varied, the designs were set with a residence time of 10 min for reflux drum and sump, and when residence time was varied, the diameter was kept fixed at 2.71m (in that case, the residence time was the same for reflux drum and sump).
A new index for chemical process design considering risk analysis and controllability
377
The results obtained are illustrated in Figure 1. We can observe that there is no significant difference using CN N or RGANoN for the controllability component. We also observe that for the range analyzed, the trend seems not to be linear. The index presents almost the same value from 0.5 times diameter to the base diameter; after that point, increasing the diameter has a more pronounced effect on the three forms of the safety index, which means that increasing the diameter to improve controllability conflicts with the safety parameter. The safest design is the base case, according to SI1 and SI 2 . The design with three times diameter (3D) is more balanced between controllability and risk, as given from the results of SI 3 , while for the base design controllability has a higher weight than risk ( SI 3 < 1 ), which means that changing the diameter is not recommended for an inherently safer process. In part b, we observe that the contribution of the two controllability indicators used here is similar for the three safety indices. It is important to notice that for this variation range (1min -20 min) the trend seems to be linear. From SI1 and SI 2 , a residence time of 1 minute is the safest option. From the results of SI 3 , the same trend is observed; decreasing residence time has a lower impact on risk with respect to the effect on controllability. Residence time has therefore an important effect on safety, as given from the risk evaluations conducted here.
Figure 1. CCPS case study Results of Proposed Indexes for analysis of (a) changes of diameter and (b) changes of residence times
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Conclusion A combined index that accounts for risk and controllability has been described. After normalizing the individual indices chosen for each item between zero and one, three types of relationships were explored. The results of the application to a case study taken from the CCPS publication showed that implementing the minimization principle of inherent safety can lead to a conflict with controllability properties, which calls for a careful consideration of risk and controllability during the design stage of a process. The approach given in this work attempts to contribute in that direction. It is worthy of mention that there is not a general guideline whether reducing inventory, which is called for from the minimization principle of inherent safety, is a correct policy when controllability is considered. The results of the application to the case study show this type of conflict. It is important to notice that this methodology has being implemented in case studies on steady state and it has not been implemented in an intrinsically dynamic system, such as a batch process. Further work is needed to consolidate these initial efforts towards the development of a useful index that combines risk and controllability and that can be used during the design stage of a chemical process.
References AIChE, A. I. of C. E. (2000). Guidelines for Chemical Process Quantitative Risk Analysis. (C. for C. P. Safety, Ed.) (2nd ed.). New York, New York. Gabor, M., & Mizsey, P. (2008). A Methodology To Determine Controllability Indices in the Frequency Domain. Industrial & Engineering Chemistry Research, 47(14), 4807–4816. Heikkilä, A.-M., Hurme, M., & Järveläinen, M. (1996). Safety considerations in process synthesis. Computers & Chemical Engineering, 20(Supplement 1), S115–S120. Khan, F. I., & Amyotte, P. R. (2004). Integrated inherent safety index (I2SI): A tool for inherent safety evaluation. Process Safety Progress, 23(2), 136–148. Medina-Herrera, N., Grossmann, I. E., Mannan, M. S., Jimenez-Gutierrez, A., & JiménezGutiérrez, A. (2014). An approach for solvent selection in extractive distillation systems including safety considerations. Industrial & Engineering Chemistry Research, 53(30), 12023–12031. Medina-Herrera, N., Jiménez-Gutiérrez, A., & Grossmann, I. E. (2014). A mathematical programming model for optimal layout considering quantitative risk analysis. Computers & Chemical Engineering, 68, 165–181. https://doi.org/10.1016/j.compchemeng.2014.05.019 Medina-Herrera, N., Jiménez-Gutiérrez, A., & Mannan, M. S. (2014). Development of inherently safer distillation systems. Journal of Loss Prevention in the Process Industries, 29, 225– 239. https://doi.org/http://dx.doi.org/10.1016/j.jlp.2014.03.004 Ni, H., Chen, A., & Chen, N. (2010). Some extensions on risk matrix approach. Safety Science, 48(10), 1269–1278. https://doi.org/http://dx.doi.org/10.1016/j.ssci.2010.04.005 Roy, N., Eljack, F., Jiménez-Gutiérrez, A., Zhang, B., Thiruvenkataswamy, P., El-Halwagi, M., & Mannan, M. S. (2016). A review of safety indices for process design. Current Opinion in Chemical Engineering, 14, 42–48. https://doi.org/10.1016/j.coche.2016.07.001
A new index for chemical process design considering risk analysis and controllability Nancy Medina-Herrera,a* Salvador Tututi-Avila,b Arturo Jiménez-Gutierrezc a
Universidad Autonoma de Nuevo León, Agronomy School, Francisco Villa s/n, Ex Hacienda el Canadá, General Escobedo, N.L, 66451, MEXICO
b
Universidad Autónoma de Nuevo León, Department of Chemical Engineering, Av. Universidad s/n, Ciudad Universitaria, San Nicolas de los Garza, NL, 66451, MEXICO
c
Department of Chemical Engineering, Instituto Tecnológico de Celaya, Av. Tecnológico s/n, Celaya, Gto. 38010 MEXICO
[email protected]
Abstract Safety and controllability are two important items that complement the economic analysis commonly done during a process design. Such factors are typically carried out once the process has been designed. Although some approaches have been proposed to include controllability properties from the design stage of the process, safety is still addressed after the design has been completed, so that safety devices are added to mitigate the consequences of potential accidents. Inherent safety is the most effective risk management approach, since actions can be taken to avoid accidents instead of mitigating their consequences. However, inherent safety is not a straightforward procedure, nor universal, and sometimes in conflict with other properties or parameters of the process. This manuscript describes a new index to account for inherent safety and controllability. The combination of a conditions number that accounts for controllability and a distance likely to cause death that emerges from the application of a quantitative risk analysis for the process was used as a basis. Three mathematical relationships were explored in the search for a suitable combination of such indices. The procedure was applied to a case study dealing with a distillation system design. Results show how the values obtained from the proposed index can give an initial assessment of the combined effect of risk and controllability as part of the design of a process. Keywords: controllability, design, inherent safety, risk analysis.
1. Introduction The concepts associated with inherent safety provide an effective tool for risk management. Inherent safety relies on the principles of elimination, minimization, moderation, substitution and simplification. The objective of inherent safety is to avoid risk instead of diminishing its consequences. The effectiveness of inherent safety depends on the stage of the plant life it is applied, being the design stage the most effective. The decisions based on inherent safety must be evaluated carefully, since inherent safety principles sometimes show conflicts among them. For instance, the minimization principle states that a process is safer when hazardous materials inventory is reduced, but dynamic performance might work against safety if inventory is reduced. Thus, it is important to assess safety in early stages of process design including this type of self-
374
N. Medina-Herrera et al.
conflicting behavior. Recently, a comprehensive review of process safety indices has been published (Roy et al., 2016). From this collection, some highlighted indexes are discussed here. Dow Fire & Explosion Index (DF&EI) was the first proposed index to account for safety in the mid-60’s. There have been several works to assess inherent safety since it was defined in the 80’s. The first index related to inherent safety was proposed by Heikkila et al (1996). This index is similar to DF&EI and considers two main parts of the process: chemicals properties and process conditions. Khan and Amyotte (2004) have published an integrated inherent safety index, named I2SI. This index is more complex and considers process control within inherent safety. Most of the indices published so far are semi-quantitative, but many times weight factors are used to rank their importance. This semi-quantitative characteristic results in different processes with similar conditions so that material properties may get the same rating, which is not totally accurate. A quantitative risk analysis (QRA) has been shown as a proper tool to account for safety (Medina-Herrera et al., 2014). A QRA performs a more detailed study and provides a more exact risk measurement because probabilities and consequences are considered (AIChE, 2000). The Morari resilience index (MRI) can be used to discriminate among process alternatives; the larger its value, the more controllable the process is. Another important index is the condition number (CN) related to system sensitivity against input disturbances. Small values are desired. Another important index is the relative gain array number (RGANo) which gives information about the controlled and manipulated variables in the frequency domain; pairings with low RGANo values are preferred. All these indices provide a good basis to account for controllability, but a suitable approach to include both controllability and process safety is needed. In this work, we propose a quantitative approach for process design that accounts for inherent safety considering both risk and controllability. In terms of risk, we use a QRA approach to obtain a distance likely to cause death, which relates to material inventory. For controllability, we test two indices, namely the condition number and the relative gain array. From a set of design candidates, the indices are normalized, and three mathematical relationships between risk and controllability are explored.
2. Safety Indices Calculation 2.1. Design approach A set of initial designs ( P ) is considered to evaluate the performance of each design using the proposed indexes. Once the candidates are set, they are subjected to a combined controllability and QRA analysis. The approach is carried out using ASPEN Tech and MATLAB as software tools. In Aspen Plus steady state simulations are carried out, simulations are then exported to Aspen Dynamics, and the results are transferred to MATLAB, where indexes are computed. 2.2. Controllability analysis In terms of controllability, a singular value decomposition procedure is carried out, from which the condition number CNi is evaluated. Regularly, a matrix of gain is obtained for the process at zero frequency and a singular value decomposition analysis is carried out. In this work, we followed the methodology proposed by Gabor and Mizsey (2008) to
A new index for chemical process design considering risk analysis and controllability
375
make calculations using a linearized state-space model system of every candidate i. The linearized state space model can be obtained with the Control Design Interface module. The methodology also computes MRI and RGANo. 2.3. Quantitative risk analysis QRA was implemented to assess the risk of a chemical inside process, following the methodology described in Medina-Herrera et al. (2014). The methodology is based on frequency and consequences analyses. First, catastrophic scenarios are identified from potential failures within the system using a bow tie procedure, and frequencies are calculated from literature data on failures. Then, a consequence analysis is performed for every catastrophic scenario previously identified. In brief, the consequences analysis implies quantification of the amount of material released, dispersion calculations, characterization of the scenario, and finally quantification of consequences. The models for consequence analysis were taken from CCPS Guidelines for Quantitative Risk Analysis in Chemical Process (AIChE, 2000). After the application of QRA, DDi is obtained, which represents the distance of affectation such that there is a 50% chance of death in case of a catastrophic event. DDi was selected because it can be calculated as measurement of risk even when layout is not yet defined, in an early design stage. 2.4. Normalization After controllability and risk indices are individually evaluated, a normalization procedure is needed, since such indices have values with different orders of magnitude, and they also depend on the system of units. When the set P was evaluated and controllability and risk indicators were obtained for each candidate i, a normalization procedure was used taking as a basis the highest value of each index, DDi and CNi , within the set P, that is,
½ DDi i ° Maximum( DD ) ° ¾ i P CN i i ° CN N = Maximum(CN i ) °¿
DDNi =
(1)
As a result, the normalized indices are bound between zero and one, and they can be subject to numerical comparison on a consistent basis. 2.5. Basic mathematical relationships: Indices After the indicators are obtained with similar orders of magnitude, they can be used to rank process alternatives from controllability and risk considerations. Even when the relationship between such items is complex, we can establish that they are related to the process safety. Facing the lack of knowledge about the relationship between controllability and risk to assess safety, we followed the methodology by Ni et al. (2010) to create indices with two different inputs, and derived three basic mathematical relationships. As a result, a proposed safety index, SI, was developed, and three versions of such an index were created. The objective of testing three different relationships is aiding in the analysis to understand whether risk and controllability are additive, factored or follow a balanced relationship.
N. Medina-Herrera et al.
376
The first version SI1 is the addition of both criteria, distance likely to cause death ( DDN ) and condition number ( CN N ).
SI1 = DDN + CN N
(2)
The second version, SI 2 , is the product of both inputs,
SI 2 = DDN * CN N
(3)
For both additive and product relationships, the smaller the value of the index, the safer the process is. The third version we explore is a fraction given by the distance likely to cause death divided by the condition number (see Eq. (4)). In this case, a value close to one means that the process is balanced from both controllability and safety considerations, which may not necessarily be desirable. A value higher than one would indicate that risk is a more important criterion than controllability, and vice versa.
SI 3 = DDN / CN N
(4)
These three versions arise from the lack of knowledge on the relationship between risk and controllability. It deemed convenient to calculate and evaluate all three alternatives for an initial insight into behavior of the proposed index.
3. Case Study and Results The case study was taken from the CCPS Example of the guidelines for chemical process quantitative risk analysis (AIChE, 2000). The distillation system is a single column that separates n-hexane and n-heptane. The feed stream has 60,120 kg/h of a binary mixture with 58%wt of n-hexane. The purity specification for the top product is 0.9 on a weight basis, with a flowrate of 36,000 kg/h. The column has 16 equilibrium stages and the top pressure is 4.9 atm. The internal diameter calculated by ASPEN Plus was 2.7 meters. The residence time for sump was fixed at 6 minutes, and for reflux drum at 12 min using a 2D=L rule for tank dimensions. The QRA performed with the CCPS Guidelines has been used to analyze process risk. The objective of this example is to describe the methodology for the proposed index calculations along with the analysis of results. The hydraulic variables considered for this example were diameter and residence time for the reflux drum and sump. Such hydraulic variables affect both criteria, controllability and risk. In order to define the set of designs P , we took the CCPS design as the base case, which has a diameter of 2.71m and 12 and 6 min of residence time on the reflux drum and sump. Other designs were considered by varying the diameter from half the base diameter to three times that value, such that D = [0.5Dbase, 0.75Dbase, Dbase, 1.5Dbase, 2Dbase, 3Dbase] where Dbase=2.71m. As for the residence time, a range was fixed from 1 minute to 20 minutes, assuming equal values for both tanks. It should be noted that the base case assumes residence times of 12 and 6 minutes. When the diameter was varied, the designs were set with a residence time of 10 min for reflux drum and sump, and when residence time was varied, the diameter was kept fixed at 2.71m (in that case, the residence time was the same for reflux drum and sump).
A new index for chemical process design considering risk analysis and controllability
377
The results obtained are illustrated in Figure 1. We can observe that there is no significant difference using CN N or RGANoN for the controllability component. We also observe that for the range analyzed, the trend seems not to be linear. The index presents almost the same value from 0.5 times diameter to the base diameter; after that point, increasing the diameter has a more pronounced effect on the three forms of the safety index, which means that increasing the diameter to improve controllability conflicts with the safety parameter. The safest design is the base case, according to SI1 and SI 2 . The design with three times diameter (3D) is more balanced between controllability and risk, as given from the results of SI 3 , while for the base design controllability has a higher weight than risk ( SI 3 < 1 ), which means that changing the diameter is not recommended for an inherently safer process. In part b, we observe that the contribution of the two controllability indicators used here is similar for the three safety indices. It is important to notice that for this variation range (1min -20 min) the trend seems to be linear. From SI1 and SI 2 , a residence time of 1 minute is the safest option. From the results of SI 3 , the same trend is observed; decreasing residence time has a lower impact on risk with respect to the effect on controllability. Residence time has therefore an important effect on safety, as given from the risk evaluations conducted here.
Figure 1. CCPS case study Results of Proposed Indexes for analysis of (a) changes of diameter and (b) changes of residence times
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N. Medina-Herrera et al.
Conclusion A combined index that accounts for risk and controllability has been described. After normalizing the individual indices chosen for each item between zero and one, three types of relationships were explored. The results of the application to a case study taken from the CCPS publication showed that implementing the minimization principle of inherent safety can lead to a conflict with controllability properties, which calls for a careful consideration of risk and controllability during the design stage of a process. The approach given in this work attempts to contribute in that direction. It is worthy of mention that there is not a general guideline whether reducing inventory, which is called for from the minimization principle of inherent safety, is a correct policy when controllability is considered. The results of the application to the case study show this type of conflict. It is important to notice that this methodology has being implemented in case studies on steady state and it has not been implemented in an intrinsically dynamic system, such as a batch process. Further work is needed to consolidate these initial efforts towards the development of a useful index that combines risk and controllability and that can be used during the design stage of a chemical process.
References AIChE, A. I. of C. E. (2000). Guidelines for Chemical Process Quantitative Risk Analysis. (C. for C. P. Safety, Ed.) (2nd ed.). New York, New York. Gabor, M., & Mizsey, P. (2008). A Methodology To Determine Controllability Indices in the Frequency Domain. Industrial & Engineering Chemistry Research, 47(14), 4807–4816. Heikkilä, A.-M., Hurme, M., & Järveläinen, M. (1996). Safety considerations in process synthesis. Computers & Chemical Engineering, 20(Supplement 1), S115–S120. Khan, F. I., & Amyotte, P. R. (2004). Integrated inherent safety index (I2SI): A tool for inherent safety evaluation. Process Safety Progress, 23(2), 136–148. Medina-Herrera, N., Grossmann, I. E., Mannan, M. S., Jimenez-Gutierrez, A., & JiménezGutiérrez, A. (2014). An approach for solvent selection in extractive distillation systems including safety considerations. Industrial & Engineering Chemistry Research, 53(30), 12023–12031. Medina-Herrera, N., Jiménez-Gutiérrez, A., & Grossmann, I. E. (2014). A mathematical programming model for optimal layout considering quantitative risk analysis. Computers & Chemical Engineering, 68, 165–181. https://doi.org/10.1016/j.compchemeng.2014.05.019 Medina-Herrera, N., Jiménez-Gutiérrez, A., & Mannan, M. S. (2014). Development of inherently safer distillation systems. Journal of Loss Prevention in the Process Industries, 29, 225– 239. https://doi.org/http://dx.doi.org/10.1016/j.jlp.2014.03.004 Ni, H., Chen, A., & Chen, N. (2010). Some extensions on risk matrix approach. Safety Science, 48(10), 1269–1278. https://doi.org/http://dx.doi.org/10.1016/j.ssci.2010.04.005 Roy, N., Eljack, F., Jiménez-Gutiérrez, A., Zhang, B., Thiruvenkataswamy, P., El-Halwagi, M., & Mannan, M. S. (2016). A review of safety indices for process design. Current Opinion in Chemical Engineering, 14, 42–48. https://doi.org/10.1016/j.coche.2016.07.001