Project Management in the Oil and Gas Industry

Figure 2.23 Monte Carlo simulation.
Start
Sample random
variables
Recalculate
deterministic model
Calculate value and
other interest
parameter
Store values for this
trial
Simulation
trial results
Calculate
average, PV
Present
histogram
Sort
data
End
Repeat
iteration
for 8,000
to 10,000
times
Figure 2.24 Flow chart for Monte-Carlo simulation

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Project Economic Analysis 77
Generate
random
numbers for
input cells
Calculate
entire
spreadsheet
Display
results in an
output
chart
Run
Stop
Figure 2.25 Monte-Carlo simulation consequence.
The final output results in displays by software at the end of the simula-
tion and contains the statistical parameters of the variable Z, describing the 
limit state equation of the cost and time.
After all the trials are completed, this program will calculate and pres-
ent the mean, standard deviation, and the statistical parameters. Also, it 
can provide the frequency distribution of the value of the outcomes of Z 
and determine the probability of increasing the cost to the limit of the 
budget.
As shown in Figure 2.25, the input data for all the variable parameters is 
selected by choosing the probability, arithmetic mean, and standard devia-
tion or coefficient of variation. After running the simulation, the output 
will be a probabilities distribution curve. 

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78 Project Management in the Oil and Gas Industry
Then, run the random numbers as per the “Mid square Method” (Von 
Neumann and Metropolis, 1940s), which produces pseudo-random four 
digit numbers:
1. Start with a four digit seed number.
2. Square the seed and extract the center most four digits. (This 
is your sampling parameter.)
3. Use the sampling parameter as the seed for the next trial. Go 
to step two.
4. Random number generators usually return a value between 
zero and one.
For any software you use to perform the simulation for the cost, time, or 
other risk criteria, the process can be summarized as follows.
Any random variable less than one, in this case this number is assumed to 
be the cumulative curve value, and by knowing the probability distribution 
curve, then, by the software definition, the value of that variable corresponds 
to these random numbers, which correspond to the cumulative value and do 
that for all variables and put these values in the deterministic model.
From the deterministic model, obtain the value of the output and other 
parameters. Then, store the data for this trial and repeat these steps again 
for 8,000 and 10,000 times, so you have 10,000 output for the variable and 
can calculate the arithmetic mean and standard deviation. Then, draw the 
distribution or histogram curve and the cumulative curve.