Statistical Analysis of Reservoir Data

1. Statistical AnalysisofReservoir Data

2. Statistical Models • Statistical Models are used to describe real world observations • provide a quantitative model • prediction • interpolation

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

4. 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

5. 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

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

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8. 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

9. 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

10. 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

11. Example—Calculation of VDP