| 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. |
| 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. | | 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. |
| 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]]). | | 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]]). |