Statistical Analysis of Reservoir Data

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Statistical AnalysisofReservoir Data
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Statistical Models

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

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Normal Distribution

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

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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

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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

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Log Probability Paper

• Cumulative frequency for log normal distributions
  plot as straight line
• standard deviation from slope

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0
1s
2s
-1s
-2s
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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
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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

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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

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ExampleCalculation of VDP