Page 200 - Hydrocarbon

Volumetric Estimation 187

3. the variance of the sum of distributions is the sum of the variances:
2
2
s ¼ s þ s 2 b
c
a
Products (say c i ¼ a i b i , where a i and b i are distributions)
4. the product of the distributions tends towards a log-normal distribution
5. the mean of the product of distributions is the product of the means:

m ¼ m m
c
a b
For the final rule, another parameter, K, the coefficient of variation, is introduced,
s
K ¼
m
2 2
6. the value of (1+K ) for the product is the product of the individual (1+K )
values:

2
2
2
ð1 þ K Þ¼ð1 þ K Þð1 þ K Þ
c a b
Having defined some of the statistical rules, we can refer back to our example of
estimating UR for an oil field development. Recall that
N 1
UR ¼ Area Thickness fS o RF
G B o
From the probability distributions for each of the variables on the right hand
side, the values of K, m and s can be calculated. Assuming that the variables are
independent, they can now be combined using the above rules to calculate K, m and
s for UR. Assuming the distribution for UR is log-normal, the value of UR for
any confidence level can be calculated. This whole process can be performed on
paper, or quickly written on a spreadsheet. The results are often within 10% of
those generated by Monte Carlo simulation.
One significant feature of the parametric method is that it indicates, through the
2
ð1 þ K Þ value, the relative contribution of each variable to the uncertainty in the
i
2
result. Subscript i refers to any individual variable. ð1 þ K Þ will be greater than 1.0;
i
the higher the value, the more the variable contributes to the uncertainty in the
result. In the following example, we can rank the variables in terms of their impact
on the uncertainty in UR. We could also calculate the relative contribution to
uncertainty (Figure 7.12).
The purpose of this exercise is to identify what parameters need to be further
investigated if the current range of uncertainty in reserves is too great to commit to
a development. In this example, the engineer may recommend more appraisal wells
or better definition seismic to reduce the uncertainty in the reservoir area and the
N/G, plus a more detailed study of the development mechanism to refine the
understanding of the RF. A fluid properties study to reduce uncertainty in B o
(linked to the shrinkage of oil) would have little impact on reducing the uncertainty