MONTE CARLO SIMULATION AS A TOOL TO SHOW THE
INFLUENCE OF THE HUMAN FACTOR INTO THE QUANTITATIVE
RISK ASSESSMENT
J.R. González Dan1, A. Guix1, V. Martí 2, Josep Arnaldos1, R.M. Darbra2*
1
Centre for Technological Risk Studies (CERTEC). Department of Chemical Engineering. Universitat
Politècnica de Catalunya-BarcelonaTech. Diagonal 647, 08028 Barcelona, Catalonia, Spain.
2
Grup de Tècniques de Separació i Tractament de Residus Industrials (SETRI). Chemical
Engineering Department. Universitat Politècnica de Catalunya-BarcelonaTech, Diagonal 647, 08028
Barcelona, Catalonia, Spain.
Abstract
The frequency of occurrence of an accident is a key aspects in the risk assessment field.
Variables such as the human factor (HF), which is a major cause of undesired events in process
industries, are usually not considered explicitly, mainly due to the uncertainty generated due to
the lack of knowledge and the complexity associated to it.
In this work, failure frequencies are modified through Monte Carlo (MC) simulation
including the uncertainty generated by HF. MC is one of the most commonly approach used for
uncertainty assessment based on probability distribution functions that represent all the
variables included in the model.
This technique has been also proved to be very useful in the risk assessment field. The model
takes into account the uncertainty and variability generated by several HF variables.
In order to test the model, it has been applied to two real case studies, obtaining new
frequency values for the different scenarios. Together with the consequences assessment, new
isorisk curves were plotted. Since the uncertainty generated by the HF has now been taken in
to account through MC simulation, these new values are more realistic and accurate. As a result,
an improvement of the final risk assessment is achieved.
Keywords: Uncertainty; Human Factor; Risk Assessment; Monte Carlo simulation; Safety.
*Corresponding author: [email protected] Tel +34 934010811, Fax: +34934011932.
2
1
INTRODUCTION
The assessment of safety in the chemical industry is not a simple task because it involves a
variety of aspects that have to be considered when analysing safety aspects such as the
processes, hazards or human errors including their interactions. In order to establish how safe
a chemical plant is, a parameter called risk has to be used. This concept can be quantified by
calculating and then combining (often multiplying) the frequency and the magnitude of all the
accidents that could occur in a specific plant, process or equipment (Casal, 2007).
The frequency of an accident scenario is commonly assessed by a generic failure frequency
approach and it is a key aspect in risk assessment. The values of generic frequencies that are
currently used in the chemical industry are based on historical data of accidents. The accuracy
of their calculations is based on the quality and reliability of the data used. The differences
between the sources of failure frequencies, such as the Reference Manual Bevi Risk
Assessments (BEVI) (RIVM, 2009), depends on the factors considered for their calculation and
on the way the situations have been classified.
Different variables are taken in to account for the creation of these values, aspects such as
the mechanical failures or the human factor are not explicitly detailed, and this creates
uncertainty in the frequency calculation. It is a common practice when handling uncertainties
to just ignore them or to use simple sensitivity analysis (Frey and Rubin, 1992). A decision
making process based on risk is more effective when an accurate characterization of uncertainty
has been conducted (Arunraj et al., 2013).The human factor is consider an important source of
uncertainty; this is commonly excluded because in order to quantify this factor it involves a
high level of complexity. However, the management of the human factors has been increasingly
recognized as playing a vital role in the control of risk.
The Health and Safety Executive (HSE, 2012), from United Kingdom, has created one of
the sources of generic frequencies, which recognizes that it is widely accepted that the majority
of accidents in the chemical industry are generally attributable to technical failures but also to
human factors. Thus, this factor may initiate or contribute to the accidents’ occurrence. Taking
this into account, it seems necessary to introduce the human factor in the frequency calculation.
To achieve this aim, the Monte Carlo simulation has been used. This technique is one of the
most commonly approaches used for uncertainty assessment and it is based on probability
distribution functions that represent the input variables. Therefore, the human factor is
introduced by the development of a frequency modifier based on the Monte Carlo Simulation.
The Monte Carlo (MC) frequency modifier varies the frequency by including the human
factor in their calculation in order to minimize the uncertainty involved. This allows obtaining
more accurate and realistic values of frequencies. After combining the new frequency with a
consequence assessment of the accidents, a comparison of the results with risk assessment
methods can be conducted. One of these methodologies that represents the risk through isorisk
contours is the Quantitative Risk Assessment (QRA), which takes into account the frequency
and consequence of the accidents.
2
HUMAN FACTOR
The human factor can be described in many ways. The HSE guidance states (HSE, 2005)
that a simple way to view the human factor is to think about three aspects: the job, the
individuals and the organization, and how they affects people’s health and safety-related
2
behaviour. A selection of the variables based on this classification was made in order to create
the model for this study based on previous studies (González et al., 2015a and 2015b) from the
authors. This selection considers that the overall human factor is composed of three different
factors representative of these basic categories: Organizational Factor, Job Characteristic Factor
and Personal Characteristic Factor. Each factor is characterized by the influence of the basic
variables shown in Figure 1 and explained next.
2.1 Organizational factor (α)
This factor refers to the conditions provided by the company to generate a safe environment.
This includes the communication between the different levels of the hierarchy, the incidents
reporting culture, the conditions the company sets to recruit external personnel and the
instructions that the organization gives to their employees in order to perform the job in the
safest way possible. It takes into account three variables: Contracting, Training and
Communication & Reporting.
2.2 Job Characteristic factor (β)
The Job Characteristics Factor refers to the conditions that the company provide to the
employees to perform their job and includes the quantity of work assigned to each employee,
the conditions that surround the workplace such as noise and air quality, the personal protection
equipment that the employees need for the development of their daily tasks (earplugs, helmets,
goggles) and the safety equipment of the plant (safety showers, labels). This factor takes into
account three variables: Workload management, Environmental conditions and Safety
equipment.
2.3 Personal Characteristics factor (γ)
The Personal Characteristics Factor relates to the cognitive characteristics of the employees,
their personal attitudes, skills, habits, attention, motivation and personalities, which can be
strengths or weaknesses depending on the task. One of those elements or their combination can
markedly influence the human error occurrence. This factor depends on two variables: The
Skills & Knowledge and the Personal Behaviour.
Figure 1: Variables for the representative equation.
In order to introduce these human factors into the frequency calculation, a frequency
modifier based on the Monte Carlo simulation is needed. Next, the methodology used in order
to accomplish this is explained.
3
3
METHODOLOGY
A human factor model has been developed based on the variables previously explained.
From these variables a representative equation has been designed, then, uncertainty ranges are
assigned to the variables. A process of iterations of these variables through Monte Carlo
simulation is conducted to obtain a mean value, which represents the frequency modifier value.
The basis of this work can be found in González et al. (2015b). All these steps of the
methodology are explained next.
3.1 Establishment of the representative equation of the model
Based on the statement of the HSE, it has been decided that the modifier varies from 1 – 1.5,
since HSE affirms that in the petrochemical industry the accidents attributed to human error
account up to 50% (HSE, 2005). This means that when there are no factors associated to human
activities that can cause an accident (best-case scenario); there will be no variation by the MC
modifier on the generic failure frequency, so its value will be equal to 1. In the worst case, when
all the adopted parameters representing the human factor assume the maximum value (largest
influence on the accident frequency), the frequency modifier will get the maximum value
equivalent to 1.5, in that case, the failure frequency can increase up to 50% of its initial value.
In a previous study (González et al., 2015a) using the proposed model of human factors
(Figure 1) and the Analytical Hierarchy Process (AHP), the weight of the different variables
was determined. For the “Training” variable of the organizational factor a weight of “0.60” was
found, “0.20” for the “Contracting” variable and “0.20” for the “Communication & Reporting”
variable (see Figure 1). For the rest of the variables the weight was the same. This was based
on a questionnaire replied to 40 international experts.
In order to obtain a representative equation of the model, which will be used for the Monte
Carlo simulation, a set of aspects were considered: the variables and their connections in the
model (Figure 1), their weights, the restriction of the value of the modifier (1.0 – 1.5) and the
possible values of each variable (0-10). Taking into consideration all this the following
equations were obtained for the factors:
Organizational factor: 𝛼 = (0.2)(𝑎) + (0.6)(𝑏) + (0.2)(𝑐)
Job characteristics factor:
𝛽=
Personal characteristics factor
(1)
𝑑+𝑒+𝑓
𝛾=
(2)
3
𝑔+ℎ
(3)
2
Where: a = contracting, b = training, c = communication & reporting, d = workload, e =
environmental conditions, f = workplace design, g = skills & knowledge, h = personal behavior.
Once the three individual equations are obtained, they are added (γ + β + α), obtaining
equation 4.
𝑥 = 𝛼 + 𝛽 + 𝛾 = (0.2 . 𝑎 + 0.6 . 𝑏 + 0.2 . 𝑐) + (
4
𝑑+𝑒+𝑓
3
) + (
𝑔+ℎ
2
)
(4)
Now since, the maximum value of each individual factor is 10, then:
𝑥 𝜀 [0,30]
(5)
If the frequency modifier is represented by f (x), then [F(x)]max is given when (x)min and
[F(x)]min when (x)max . With this information, two points of a straight line are obtained. After
considering all this, and using a lineal regression, the following equation was obtained:
F(x) = -0.0167·x + 1.5
(6)
In order to be able to work with this equation and make the iterations needed with Monte
Carlo simulation, an uncertainty range has to be assigned to each input “a” to “h” (Figure 1).
Depending the company assessed these values vary. In order to obtain them a process to assess
individual company is conducted and explained next.
3.2 Obtainment of the uncertainty ranges
In order to apply the model a precise performance of the assessed company is required. This
will give us the necessary information and it will be possible to assign uncertainty ranges to the
different elements related with the human factor. In order to do so, it eight questions were
defined for each variable based on national and international regulations. The company’s
representative has to answer by choosing among three different options in order to obtain an
uncertainty range for each of the variables. This evaluation method of the company’s
performance was already used in previous study (González et al., 2015). Figure 2 gives an
example of two of the eight questions of the poll for the training variable of the organizational
factor based on the documents “Occupation Health and Safety Assessment Series” (OHSHAS,
2007) and “International Labour Organization” (ILO, 2001).
1. Does the company have a training program for its employees?
(a) Yes
(b) Yes, but not implemented
(c) No
2. Does the company provides training to tis employees depending on the type
of work is carried out??
(a) Yes
(b) Usually
(c) Occasionally
Figure 2: Example of questions for the training variable
The three options belonging to each question represent a numeric value (a = 8, b = 5, c = 2).
The sum of the results for each variable (from the eight questions) is compared with a fixed
score range. These have been established in accordance with the HSE classification reported
for managing contractors (HSE 2011). Consequently, a range is going to be determined for each
variable (see Table 1): “Low”, “Medium” or “High”.
5
Table 1: Establishment of the uncertainty ranges.
Range
Value
Low
Medium
High
16-32
33-47
48-64
Uncertainty
range
0-3
4-6
7-10
An uncertainty range is assigned according to the range in which the result is found, which
is introduced in the Monte Carlo simulation model as explained next.
3.3 Uncertainty characterization through Monte Carlo simulation
The uncertainty can be described by probability density functions (PDF) in which the
distribution reflects the uncertainty of the model parameters. The Monte Carlo simulation
specifies a probability distribution for each sensitivity parameter.
This technique can be applied to one or more uncertain input variables at a time. The output
distributions will reflect the combined effects of this input uncertainty over the specified ranges.
The Monte Carlo simulation is not a new technique related to the risk assessment field, some
authors have used this technique in order to address the uncertainty in this kind of studies
(Faghigh-roohi et al., 2014; Smid et al., 2010; Stroeve et al., 2009).
An important part of the Monte Carlo simulation is the election of the probability density
function (PDF); this election depends on the assessed variable. In the risk assessment field the
most common PDF’s are: normal probability function (e.g. quantity released, temperature of
the substance), lognormal probability function (e.g. release duration) and the uniform
probability function for those variables that are more difficult to characterize.
Another aspect of the Monte Carlo simulation is that is based on the generation of multiple
trials or iterations in order to determine the expected value of a random variable. The simulation
is able to use many interactions depending the complexity of the system.
According Figure 1, for each variable different values are proposed (e.g. a = contracting with
values such as 2.51, 1.58, etc.) as it can be seen in Table 2. Then iterations will be carried out
to obtain the different outputs (e.g. α = organizational factor according to the initial values such
as 1.51, 2.54, etc.).
Table 2: Example of the construction of the iteration values.
a
b
c
Iteration
(Low) (Medium) (High)
number
0-3
4-6
7-10
1
2.51
4.54
7.05
2
1.58
5.12
9.45
3
0.99
4.02
8.21
:
:
:
:
6
α
1.51
2.54
1.99
:
Once the values of all the proposed iterations are acquired, the percentage values of
frequency modifier are plotted (Figure 3).
Figure 3. Example of obtention of the modifier
The mean value obtained after all the iterations is going to represent the MC frequency
modifier value. All this process can be done using several statistical softwares. For the case
studies explained next, the software used is “Minitab” (Minitab, 2010).
4
CASE STUDIES AND RESULTS
Two different case studies related to real chemical plants are presented. Companies A & B
represent facilities intended to store toxic products. The methodology proposed is applied for
both companies and their results are presented.
4.1 Company A
This company’s main activity is the reception, storage, dilution and distribution of several
chemicals spread over an area of 18000 m2. The solid products are stored in bags and the liquids
in atmospheric tanks. The plant has various facilities, regarding the storage of its products, the
company has a formaldehyde storage area containing four atmospheric tanks located within a
containment bund: three of 30 m3 and one of 45 m3. Another storage area for the acetic acid
containing two tanks of 35 m3. The company has 97 direct employees, 51 of whom are on fixed
shifts and the remaining on rotating shifts. The company has also sub-contracted staff in the
installation for specific operations.
An evaluation of the company was made by the company’s representative, accordingly to
the method proposed in section 3.2, in order to obtain the uncertainty ranges (see Table 3) in
order to be applied in to the Monte Carlo simulation.
7
Table 3: Uncertainty ranges for the variables of company A.
Company A
Variable
PDF
Total Uncertainty
score
range
25
0-3
Uniform
34
4–6
Uniform
40
4-6
Uniform
(a) Contracting
(b) Training
(c) Communication &
Reporting
(d) Workload
(e) Environmental
conditions
(f) Safety Equipment
(g) Personal behaviour
(h) Skills and Knowledge
40
4-6
Uniform
43
4-6
Uniform
31
28
25
0-3
0-3
Uniform
Uniform
0-3
Uniform
Once the uniform PDF is settled and the uncertainty ranges are established, the rest of the
required by the model values were obtained. In Table 4, the values of all the variables of the
model for the first five iterations of the company A are shown. The number of iterations done
in this case study was one thousand. Monte Carlo simulation was performed by using Crystal
Ball v 7.2 software (Oracle).
Table 4: Iterations of the variables of company A.
Iteration
number
1
2
3
4
5
:
1000
a
b
c
d
e
f
g
h
α
β
γ
1.27
0.53
1.21
1.57
2.33
:
0.15
4.22
4.51
5.88
4.91
4.55
:
4.83
4.12
5.69
4.33
4.83
4.27
:
5.05
4.22
4.14
4.80
4.66
4.86
:
4.35
5.36
5.98
4.03
5.65
4.58
:
4.61
1.20
0.75
2.01
0.83
2.40
:
0.33
0.93
2.78
1.71
1.10
1.82
:
2.23
2.61
2.56
0.33
1.76
1.30
:
2.47
1.27
0.53
1.21
1.57
2.33
:
0.15
4.22
4.51
5.88
4.91
4.55
:
4.83
4.12
5.69
4.33
4.83
4.27
:
5.05
As mentioned before, the software used in this study allows obtaining the value of the
mean of all the iterations accordingly to the PDF selected. This value represents the value of
the frequency modifier as it can be seen in Figure 4. For the company A the value of the modifier
is 1.34.
8
Figure 4: Obtention of the value of the frequency modifier for company A.
Once obtained the value of the modifier, the initial frequencies were changed. For this case
study, initial generic frequencies associated with the loss of containment events (LOCs) for
single containment atmospheric tanks were taken into account for this company; this
information was obtained from BEVI [2]. These initial frequencies are the ones commonly used
in traditional quantitative risk analysis (QRA) and they are generally corrected depending on
different factors (e.g. domino effect, working hours, etc.), according to the methodology
described in the guideline for quantitative risk assessment (CPR18E, 2013).
Table 5 shows the selected events, their initial frequency and the corrected frequency taking
in to account the number of the formaldehyde tanks and the domino effect generated from the
acetic acid.
Table 5: LOCs, initial and corrected frequencies for company A.
Code
Loss of containment events (LOC)
G.1
G.2
Instantaneous release of entire contents
Release of entire contents in 10 min. in a
continuous and constant stream
Continuous release of contents from a
hole with an effective diameter of 10 mm
G.3
Initial frequency
(year-1)
5x10-6
9
formaldehyde Acetic Acid
Corrected frequency
(year-1)
-5
2x10
2x10-5
5x10-6
2x10-6
2x10-5
1x10-6
4x10-6
4x10-4
For the formaldehyde tanks there is only one possible resulting accident, which is the toxic
dispersion. Regarding the acetic acid, the events can result in different kinds of final accidents
as can be seen in Figure 5.
Initial
Event
Immediate ignition
Delayed Ignition
VCE
P1
Consequences
Pool fire
Liquid
release
P4
VCE
+Pool fire
1- P4
Flash Fire
+Pool fire
P2
1- P1
1- P2
No consequences
Figure 5. Event tree for a release of acetic acid.
Using the probability data of the event tree associated to the selected event (CPR18E, 2013),
the final probability of occurrence for each accident it is obtained. In Table 6, the results of the
selected scenarios are presented: the final frequencies shown in Table 5, the value of the
modifier obtained by the Monte Carlo simulation and the final frequencies modified by the MC
frequency modifier.
Table 6: LOCs, QRA and modified final frequencies for company A
Substance
Table 5 Final
frequency
(year-1)
MC
Frequency
Modifier
Modified Final
frequency (year1
)
Toxic
Dispersion
2.00x10-5
1.34
3.68 x10-5
G.2
Toxic
Dispersion
2.00x10-5
1.34
3.68 x10-5
G.3
Toxic
Dispersion
4.00x10-4
1.34
5.36 x10-4
G.1
Pool fire
Flash fire
6.14 x10-6
5.94 x10-6
1.34
8.22 x10-6
7.95 x10-6
G.2
Pool fire
Flash fire
6.14 x10-6
5.94 x10-6
1.34
8.22 x10-6
7.95 x10-6
G.3
Pool fire
Flash fire
1.23 x10-4
1.19 x10-4
1.34
1.64 x10-4
1.59 x10-4
LOC Accident
G.1
Formaldehyde
Acetic acid
10
The magnitudes of the consequences (i.e. jet fire, BLEVE, etc.) is also another vital part of
the QRA which is necessary for the representation of the risk. Thus, the modifier not only
affects the frequencies of the accident, but also the overall risk. In order to compare the risk
obtained by this methodology, the consequences of the accidents were calculated. Table 7
shows the magnitude of the toxic dispersion in the particular case of an instantaneous release
for entire content (G1) of the formaldehyde tank from company A.
Table 7. Consequences data of the toxic dispersion for company A
LOC
General data
Product: Formaldehyde
Storage conditions:
- Temperature (ºC): ambient
- Pressure (bar abs.): atmospheric
Leak scenario data
Contained Leak: No
Dimensions of the deposit:
- Diameter (m): 2.9
- Height (m): 4.85
- Volume (m3): 30 (70% of capacity)
G1
ACCIDENT
Toxic Dispersion
Soil temperature (ºC): 14.3
Roughness (m): 0.1
Nature of ground: concrete
Moisture (%): 74
Temperature (ºC): 14.3
SOURCE DATA
Amount released (kg): 18.928
Pool area (m2): 158,2
DISPERSION DATA
Pool evaporation flow D/4,8 (kg/s): 0.0082
Pool evaporation flow F/1,5 (kg/s): 0.0031
Lethal area
Meteorology D/4,8
LC99 distance (L/W) (m): 8/3
LC50 distance (L/W) (m): 15/5
LC1 distance (L/W) (m): 27/9
Meteorology F/1,5
LC99 distance (L/W) (m): 28/5
LC50 distance (L/W) (m): 51/9
LC1 distance (L/W) (m): 92/16
In the same way, all the consequences for each loss of containment events considered and
for all the accidents listed in Table 6 were calculated. Thus, with the new modified frequency
values obtained and the magnitude of the consequences of all the accidents, the risk was
calculated. This risk is represented by isorisk curves plotted in a geographical map. These
curves were done using the RISKCURVES software (TNO, 2012).
In this case study the company conditions of the human factors were allocated in low
uncertainty ranges representing “poor conditions”, this originated a “high” value of the MC
frequency modifier (1.34). Thus, the isorisk curves corresponding to the Company A including
the new frequency varied from those of QRA.
Figure 6 shows four isorisk curves for this company: the continuous curves lines represent
the isorisk contours resulting from a QRA without the modified frequencies 10-5 year-1 in a
black line and 10-6 year-1 in grey colour. Whereas the non-continuous curves lines represented
the isorisk contours affected with the MC frequency modifier (10-5 year-1 in a black line and 106
year-1 in grey colour). For this company it can be observed an increase of both the isorisk
contours (10-5 year-1 and 10-6 year-1).
11
Figure 6. Isorisk curves for company A
4.2 Company B
The main activity of the second case study (company B) is the organic synthesis of basic
products in the pharmaceutical and veterinary industry. The facility has the necessary
equipment for the batch production of different chemical products. In comparison with the other
cases studies, this company has a bigger number of equipment and areas such as production,
services and storage areas, offices, laboratories etc. The focus area of this case study is the
methanol and acetone storage area containing eight cylindrical vertical tanks. The company has
211 direct employees with fixed and rotating shifts and sub- contracted staff.
In order to obtain the uncertainty range, the same evaluation method (section 3.2) was
conducted by the company’s representative. In Table 8, the results for company B are shown
including: the total score, the uncertainty range and the PDF selected.
Table 8. Uncertainty ranges for the variables of company B
Company B
Variable
Total
score
64
64
56
(i) Contracting
(j) Training
(k) Communication &
Reporting
(l) Workload
(m) Environmental
conditions
(n) Safety Equipment
(o) Personal behaviour
(p) Skills and Knowledge
12
PDF
Uncertainty
range
7 - 10
Uniform
7 - 10
Uniform
7 - 10
Uniform
61
7 - 10
Uniform
61
7 - 10
Uniform
58
46
46
7 - 10
4-6
Uniform
Uniform
4-6
Uniform
Following the same procedure for the first company, the values of all the variables of the
model for company B were obtained for one thousand iterations. In Table 9, the values of all
the variables of the model for the first five iterations of the company B are shown.
Table 9: Iterations of the variables of company B.
Iteration
number
1
2
3
4
5
:
1000
a
b
c
d
e
f
g
h
α
β
γ
7.92
8.53
8.50
7.64
8.78
:
7.44
7.34
9.39
7.73
8.20
8.86
:
7.28
8.21
8.93
7.20
7.05
9.41
:
8.51
8.36
9.18
8.79
9.49
8.53
:
9.99
9.09
7.13
8.93
8.45
8.69
:
7.84
9.40
8.95
7.09
9.77
7.33
:
8.39
5.07
5.27
4.41
5.70
4.92
:
4.37
5.47
5.49
4.40
5.80
4.88
:
4.64
7.92
8.53
8.50
7.64
8.78
:
7.44
7.34
9.39
7.73
8.20
8.86
:
7.28
8.21
8.93
7.20
7.05
9.41
:
8.51
Then, the mean value was obtained from all the iterations and accordingly to the PDF
selected (Uniform). This value represents the Monte Carlo frequency modifier for company B
and as seen in Figure 7 is 1.133. This value is low which makes sense because according the
performance of the company the uncertainty ranges are majority “low” which at the same time
represents a good performance of the human factors in the company.
Figure 7: Obtention of the value of the frequency modifier for company B.
Once the value of the modifier for this company was obtained (1.133), the initial frequencies
were changed. In this case, the LOCs selected were the ones derived from scenarios for single
containment atmospheric storage tanks, obtained from BEVI (RIVM, 2009). In this case, only
two initial events were taken into account (G.1 and G.2). The G.3 which is the continuous
release of contents from a hole with an effective diameter of 10 mm was discarded according
the F1-4 criteria rejecting an initiating event if it does not exceed the limit of the property
obtained from the Instruction 14/2008 SIE gathered in the technical guide used to perform
QRA's in Catalonia (Instrucció 14/2008 SIE, 2008).
13
As mentioned before, in order to represent the effect of the modifier, the calculations were
focus on the methanol and acetone storage area of the company. This area has three different
storage subareas: acetone (5 tanks), residual acetone (2 tanks) and methanol (1 tank). Table 10
shows the selected events, their initial frequency and the corrected frequency taking in to
account the number of tanks of each area and the domino effect.
Table 10: LOCs, initial and corrected frequencies for company B.
Acetone storage area
Loss of containment
events (LOC)
Code
G.1
G.2
Instantaneous release of
entire contents
Release of entire contents
in 10 min. in a
continuous and constant
stream
Residual acetone
storage area
Initial
Corrected
frequency frequency
(year-1)
(year-1)
Initial
frequency
(year-1)
Corrected
frequency
(year-1)
5x10-6
5x10-5
5x10-6
5x10-6
5x10-5
5x10-6
Methanol storage area
Initial
frequency
(year-1)
Corrected
frequency
(year-1)
2x10-5
5x10-6
1x10-5
2x10-5
5x10-6
1x10-5
For the methanol storage area, using the event tree in Figure 8, the possible resulting events
are the pool fire and the toxic dispersion. In the same way, regarding to the acetone storage
area, the possible final events are a flash fire and a pool fire.
Initial event
Ignition
Consequences
Yes
Pool Fire
No
Toxic dispersion
Liquid Spill
f
Figure 8: Event tree for a spill of flammables and toxic substances
Using probability data from bibliography (CPR18E, 2013) the final probability of
occurrence for each accident was obtained (Table 10). In Table 11, the results of the different
scenarios are presented including the modified final frequency corrected by the MC frequency
modifier obtained.
14
Table 11: LOCs, QRA and modified final frequencies for company B.
Area
LOC
Accident
G.1
Flash fire
Pool fire
Table 10
Final
frequency
(year-1)
1.40 x10-5
1.73 x10-5
G.2
Flash fire
Pool fire
1.40 x10-5
1.73 x10-5
G.1
Flash fire
Pool fire
5.61 x10-6
6.91 x10-6
1.133
6.70 x10-6
7.83 x10-6
G.2
Flash fire
Pool fire
5.91 x10-6
6.91 x10-6
1.133
6.70 x10-6
7.83 x10-6
G.1
Pool fire
Toxic dispersion
6.50 x10-7
9.35 x10-6
1.133
7.36 x10-7
1.06 x10-5
G.2
Pool fire
Toxic dispersion
6.50 x10-7
9.35 x10-6
1.133
7.36 x10-7
1.06 x10-5
Acetone
storage area
Residual
acetone
storage area
Methanol
storage area
MC
Modified Final
Frequency
frequency
Modifier
(year-1)
1.133
1.58 x10-5
1.96 x10-5
1.133
1.58 x10-5
1.96 x10-5
Table 11: LOCs, initial and corrected frequencies for companies A &B.
As mention before, the magnitude of the consequences needs to be obtained in order to
represent the overall risk. Thus, Table 12 shows the magnitude of the consequences for different
accidents such as the toxic dispersion and the pool fire, in the particular case of an instantaneous
release for entire content (G.1) of methanol from company B.
15
Table 12. Consequences data of the toxic dispersion for company B
LOC
General
Leak scenario data
Product: methanol
Contained Leak: Yes (Containment Area (m2)= 500)
Storage temperature (ºC): 14.3
Spill surface (m2): 500
Storage Pressure (bar abs.): atmospheric
Pool ratio (m): 12.6
Tank characteristics:
Roughness (m): 0.01
- Lenght (m): 4
Moisture (%): 74
- Volume (m3): 38
SOURCE DATA
Amount released (kg): 30.390
EVAPORATION DATA
Average flow of evaporation 4,8D (kg/s): 0.47
Average flow of evaporation 1,5F (kg/s): 0.19
G.1
ACCIDENT
Pool Fire
Toxic Dispersion
LETHAL AREAS
LC100 distance (m): 12.6
LC50 distance (m): 14.7
LC1 distance (m): 21.1
Meteorology 4,8D
LC99 distance (L/W) (m): 13/1
LC50 distance (L/W) (m): 13/1
LC1 distance (L/W) (m): 13/1
Meteorology 1,5F
LC99 distance (L/W) (m): 13/1
LC50 distance (L/W) (m): 19/1
LC1 distance (L/W) (m): 34/1
In the same way as before, the magnitude of consequences were obtained for each possible
accident and together with the new values of frequencies it was possible to represent the risk in
form of isorisk curves plotted in a geographical map.
Figure 9 shows different isorisk curves for the company B, as before, the continuous curves
lines represent the isorisk contours resulting from a QRA without the modified frequencies
whereas the non-continuous curves lines represented the isorisk contours affected with the MC
frequency modifier. The external continuous grey line represent the 10-6 year-1 curve and it is
equivalent after applying the MC modifier. This is because in this case the modification was
very light since this company had a good safety performance. Nevertheless, in the 10-5 year-1
isorisk curves, a difference in distance can be observed, although slightly, which is the noncontinuous black curve.
16
Figure 9: Iso risk curves for company B.
As it can be observed in both case studies, the final frequencies modified by the Monte
Carlo frequency modifier, are slightly higher than the previous ones. The reason of this increase
is the inclusion of the human factor into the calculation. This change on the frequency had a
repercussion in the overall risk represented by the isorisk curves obtained.
The results were quite different when comparing company A where the conditions of the
human factors were not good enough a high value of the MC modifier was obtained (1.34). In
company B, according to the assessment carried out, the good performance of the company has
originated a low value of the modifier (1.133).
Thus, company A registers a wider variation in distance on both isorisk curves (10-5 year-1
and 10-6 year-1). On the other hand, in the isocurves of company B with and without the MC
modifier are relatively similar, in any case, an increase is noted for the 10-5 year1 contour.
5
CONCLUSIONS
A frequency modifier based in Monte Carlo Simulation was created in order to introduce
the human factor in to the frequency calculation. These variables were represented as
probability density functions with a specific uncertainty range and they were treated with the
Monte Carlo simulation technique. The methodology was tested on two case studies
representing toxic substances storage facilities. The results of the new frequencies obtained
were higher than those derived from the generic databases.
These results are expected to represent more realistic values of the accident frequencies since
they include the influence of the human factor through the MC modifier. In order to compare
the results with QRA methodology using a consequence assessment, isorisk curves were created
for each case study.
An increase in distance of the isorisk curves were noticed when comparing with the QRA ones ,
this implies a more conservative approach which leads in to the improvement of safety measures
and therefore a reduction of potential accidents.
17
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