Project Management in the Oil and Gas Industry

Table 2.7 Net present value including inflation.
Year
(1)
(2)
(3) = (1) × (2)
(4)
(5) = (4) × (3)
Net cash 
flow
Inflation 
rate
Net cash flow 
after inflation
Discount 
rate
Net present 
value
0
51785
1.0
51785
1.0
51785
1
20000
0.96
19231
0.95
18182
2
20000
0.92
18491
0.89
16529
3
20000
0.89
17780
0.85
15026
4
20000
0.85
17096
0.80
13660
Sum (NPV)
11612
Table 2.8 Row data.
340
298
422
340
305
356
320
382
297
267
355
312
340
366
349
311
306
368
382
404
326
350
322
448
350
358
384
346
365
303
398
306
298
339
344
378
282
320
360
360
367
341
326
325
352
384
Table 2.9 Frequency table.
Frequency
Average value
Group
ID
1
270
260–280
1
3
290
280–300
2
6
310
300–320
3
6
330
320–340
4
12
350
340–360
5
7
370
360–380
6
5
390
380–400
7
1
410
400–420
8
1
430
420–440
9
1
450
440–460
10
43
Total 

---

54 Project Management in the Oil and Gas Industry
0
5
10
15
270
Concrete strength, Kg/cm
2
Frequency
290
310
330
350
370
390
410
450
430
Figure 2.5 Frequency curve for concrete compressive strength data.
0
20
40
60
80
100
120
260
280
300
320
340
360
380
400
420
440
460
Concrete strength, kg/cm
2
Percentage less than concrete strengt
h
Figure 2.6 Cumulative distribution curve for concrete strength.
Table 2.10 Descending cumulative table.
Group no.
Test value
Reading value less 
than the upper limit
The percentage less 
than the upper limit
10
460
43
100
10
440
42
98
9
420
41
95
8
400
40
93
7
380
35
81
6
360
28
65
5
340
16
37
4
320
10
23
3
300
4
9
2
280
1
2
1
260
0
0

---

Project Economic Analysis 55
From the cumulative descending curve, one can find that 100 percent of 
the results of the samples have a strength less than 459 kg/cm
2
at the same 
time. In the results of previous tests, we find that the samples have results 
less than or equal to 280 kg/cm
2
, which is about two percent of the number 
of tested samples.
2.3.2 Probability Distribution of Variables 
Most civil engineering problems deal with quantitative measures in the 
familiar deterministic formulations of engineering problems. However, there 
is nothing deterministic at all, when you assume you have a reinforced con-
crete column in drawings mentioning that its section is 500 millimeters by 
500 millimeters. This means it will be this exact number when you measure 
the column. It is possible that there could be some deviation, which is allow-
able in the code. So, the column section dimensions are not deterministic.
The concept of mathematical variables and functions of variables have 
proven to be useful substitutes for less precise qualitative characteris-
tics. Variables, whose specific values cannot be predicted with certainty 
before an experiment, can be presented by the probabilistic models and 
distributions.
2.3.2.1 Normal 
Distribution 
Normal distribution is used to represent many natural phenomena, such 
as the lengths of people, and it is used in decision-making as it can present 
the inflation rate or the price of oil in the future. This distribution is widely 
used in metering equipment, as it represents the measurement error and 
the permeability of the soil and the spaces between the grains and satura-
tion as well as some economic data.
Equation: 
f x
e
x
( )
.
. (
) /
1
2
0 5
0 5
2
2
(2.12)
Mean:
x
x
n
i
(2.13)
where: 
x–  = arithmetic mean of sample data
x
i
= each individual value in sample 

---

56 Project Management in the Oil and Gas Industry
n = number of values in sample 
cm = class mark
nc = number of values in class, 
Standard deviation is given by
s
n
x
1
2
2
0 5
.
(2.14)
where is the standard deviation and is the arithmetic mean.
Normal distribution is the most commonly used probability distribu-
tion because it was found identical with the most natural phenomena. It 
was found that normal distribution is the best probability curve to present 
concrete strength from laboratory tests performed on the concrete in most 
countries of the world to present the concrete.
The characteristics of this distribution are as follows: 
• Normal distribution is the distribution symmetrically 
around the average and, more precisely, the arithmetic mean 
of the curve is divided into two equal halves 
• Normal distribution matches the arithmetic mean and 
median lines and mode value to find the most likely to occur.
The area under the curve is equal to one and the random variable as a 
result of concrete cube strength, for example, can take the values from
to – . So, this curve presents all the possible values of concrete strength.
As a result, each curve depends on the value of the arithmetic mean and 
standard deviation and any difference between the two parameters leads 
to a difference in the shape of the probability distribution. Therefore, the 
standard normal distribution is used to determine areas under a curve by 
knowing the standard deviation and arithmetic mean. Another variable, z, 
is obtained from the following equation: