200 likes | 522 Views
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
E N D
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
-2s -1s 0 +1s +2s
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, VDP: • 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, VDP: • step1--transform permeability data [Ln(k)] • step2--calculate s, the sample standard deviation, of the transformed data • step3--compute