Statistical Analysis of Reservoir Data

Statistical Models Statistical Models are used to describe real world observations –provide a quantitative model prediction interpolation

Normal Distribution Example –porosity from cores or logs Two parameters: –mean –standard deviation Characteristics –symmetric –mean, median and mode occur at same value

Probability Paper Any two parameter model can be plotted as a straight line –cumulative frequency for normal distributions plot as straight line standard deviation from slope

Log Normal Distribution Example –permeability values from cores or logs Two parameters: –mean (of log(x)) –standard deviation (of log(x)) Characteristics –log(x) values have normal distribution –assymetric large “tail” toward large values mean, median and mode do not occur at same value

Log Probability Paper Cumulative frequency for log normal distributions plot as straight line standard deviation from slope

0 +1  +2  -1  -2 

Reservoir heterogeniety Usually permeabilities are “log- normally” distributed. That is, the logarithm of their values form a normal (bell-shaped) probability curve. This can be demonstrated by plotting permeabilities, arranged in order from smallest to largest, on a “log- probability” scale. Dykstra-Parsons permeability variation = From Craig

Reservoir heterogeniety Dykstra-Parsons Perm. Variation, V DP : step1--arrange perms in increasing order step2--assign percentiles to each perm number step3--plot on log-probability scale step4--compute

Reservoir heterogeniety Dykstra-Parsons Perm. Variation, V DP : step1--transform permeability data [Ln(k)] step2--calculate s, the sample standard deviation, of the transformed data step3--compute

Example—Calculation of V DP