10,323
edits
Changes
Jump to navigation
Jump to search
Line 31:
Line 31: − Here it is important to remind the reader that in a lognormal frequency distribution, the ''mode'' (or most likely point) is positioned to the left, at the peak of the curve. The ''median'' (or 50% point) lies in the middle, separating the area under the curve into two equal parts, whereas the ''mean'' (or average) lies to the right of the median (see Figure 1). We shall be concerned mostly with the median and the mean in our estimates and calculations, generally discouraging use of the mode, as will be explained later.+ + + − + Line 49:
Line 51: − +
Uncertainties impacting reserves, revenue, and costs (view source)
Revision as of 16:56, 10 January 2014
, 16:56, 10 January 2014→Lognormality and log probability paper
Most geological and production parameters are not distributed according to a symmetrical or ''normal'' distribution, that is, they do not form a ''bell-shaped'' frequency curve. Instead, they tend to produce a frequency distribution skewed to the right, so that there are many small values and only a few large ones. Such patterns approximate a ''lognormal distribution,'' and they arise from multiplication of several factors to produce one geological parameter.<ref name=Kaufman_1963>Kaufman, G., 1963, Statistical decision and related techniques in oil and gas exploration: Englewood Cliffs, NJ, Prentice-Hall, 307 p.</ref> <ref name=Capen_1984>Capen, E. C., 1984, Why lognormal? in E. C.Capen, R. E. Megill, and P. R. Rose, ed., Prospect Evaluation: AAPG Course Notes: Tulsa, OK, AAPG, 8 p.</ref> <ref name=Megill_1984>Megill, R. E., 1984, An introduction to risk analysis, 2nd ed.: Tulsa, OK, PennWell Books, 274 p.</ref> Good examples include field sizes, production rates of wells in a field, [[porosity]]-feet (φh) of reservoirs, and effective well drainage area.
Most geological and production parameters are not distributed according to a symmetrical or ''normal'' distribution, that is, they do not form a ''bell-shaped'' frequency curve. Instead, they tend to produce a frequency distribution skewed to the right, so that there are many small values and only a few large ones. Such patterns approximate a ''lognormal distribution,'' and they arise from multiplication of several factors to produce one geological parameter.<ref name=Kaufman_1963>Kaufman, G., 1963, Statistical decision and related techniques in oil and gas exploration: Englewood Cliffs, NJ, Prentice-Hall, 307 p.</ref> <ref name=Capen_1984>Capen, E. C., 1984, Why lognormal? in E. C.Capen, R. E. Megill, and P. R. Rose, ed., Prospect Evaluation: AAPG Course Notes: Tulsa, OK, AAPG, 8 p.</ref> <ref name=Megill_1984>Megill, R. E., 1984, An introduction to risk analysis, 2nd ed.: Tulsa, OK, PennWell Books, 274 p.</ref> Good examples include field sizes, production rates of wells in a field, [[porosity]]-feet (φh) of reservoirs, and effective well drainage area.
[[File:Charles-l-vavra-john-g-kaldi-robert-m-sneider capillary-pressure 1.jpg|thumbnail|left|'''Figure 1.''']]
Here it is important to remind the reader that in a lognormal frequency distribution, the ''mode'' (or most likely point) is positioned to the left, at the peak of the curve. The ''median'' (or 50% point) lies in the middle, separating the area under the curve into two equal parts, whereas the ''mean'' (or average) lies to the right of the median ([[:Image:Charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_1.jpg|Figure 1]]). We shall be concerned mostly with the median and the mean in our estimates and calculations, generally discouraging use of the mode, as will be explained later.
[[File:Charles-l-vavra-john-g-kaldi-robert-m-sneider capillary-pressure 2.jpg|thumbnail|'''Figure 2.''']]
In combination with the cumulative probability curve, lognormality provides us with a very useful and powerful predictive tool. Accordingly, it is important to utilize (and understand) log probability paper. Although several forms are commercially available, the three-cycle type in which the probabilities extend from 0.01% to 99.99% is recommended (see Figure 2).
In combination with the cumulative probability curve, lognormality provides us with a very useful and powerful predictive tool. Accordingly, it is important to utilize (and understand) log probability paper. Although several forms are commercially available, the three-cycle type in which the probabilities extend from 0.01% to 99.99% is recommended ([[:Image:Charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_2.jpg|Figure 2]]).
Suppose you want to plot a distribution of field sizes from a basin or trend containing n number of fields.
Suppose you want to plot a distribution of field sizes from a basin or trend containing n number of fields.
# Remember that the absolute maximum and minimum values are not ''P''<sub>90%</sub> and ''P''<sub>10%</sub>!
# Remember that the absolute maximum and minimum values are not ''P''<sub>90%</sub> and ''P''<sub>10%</sub>!
# Although the values associated with any conventional probabilities (P<sub>90%</sub>, ''P''<sub>50%</sub>, and ''P''<sub>10%</sub>) can be read directly from the log probability paper, neither the mode nor the mean is so apparent. These parameters must be calculated.
# Although the values associated with any conventional probabilities (P<sub>90%</sub>, ''P''<sub>50%</sub>, and ''P''<sub>10%</sub>) can be read directly from the log probability paper, neither the mode nor the mean is so apparent. These parameters must be calculated.
# The mean (or average) is the single best numerical representation of the distribution and is determined approximately by ''Swanson's Rule of approximation'' (Megill, 1988)<ref name=Megill_1988>Megill, R. E., 1988, An introduction to exploration economics, 3rd ed.: Tulsa, OK, PennWell Books, 238 p.</ref> as follows:
# The mean (or average) is the single best numerical representation of the distribution and is determined approximately by ''Swanson's Rule of approximation''<ref name=Megill_1988>Megill, R. E., 1988, An introduction to exploration economics, 3rd ed.: Tulsa, OK, PennWell Books, 238 p.</ref> as follows:
:<math>\mathbf{Equation}</math>
:<math>\mathbf{Equation}</math>