Log Normal Distribution

For the Normal and related distributions such as the Log Normal, there is no exact calculation method available. In consequence all algorithms are based on numerical techniques that approximate the actual values. To the intrinsic error of the approximation algorithms you must add the effect of the inherent rounding errors of microprocessors floating point arithmetic. The propagation of both sources of errors leads to differences when comparing results computed by different applications.

PetroVR uses an interpolation table of 12,000 entries.

The log normal distribution input parameters are:

  • mean: Mean value of distribution.
  • sd: Standard deviation.
  • P90/P10 ratio: Ratio between the 90% and 10% percentiles.
  • percentiles: Enter 2 percentile points to define the curve. These are 10% and 90% by default.

You can define the distribution in one of three ways based on the available data:

  • Enter a mean and a standard deviation, letting PetroVR calculate the percentiles and ratio.
  • Enter a mean and a ratio, letting PetroVR calculate the deviation.
  • Enter both percentiles, letting PetroVR calculate the ratio, mean and deviation.

In each case the missing values will be updated automatically.

When defining a log normal distribution, there are two ways of providing the mean and the standard deviation. The more intuitive approach adopted by PetroVR is to input the mean and standard deviation of the log normal distribution (μ, σ). Other applications such as MS Excel read the input mean and standard deviation as those of the normal distribution in the exponent (μ', σ').

With the convention used in PetroVR, the three parameters value, mean and sd have the same unit (they belong to the same space). For instance, if the initial rate of a well is 5000 bpd, you could define a Log Normal distribution around it using 5000 bpd as the mean and, say, 500 bpd as the sd. The Excel convention forces the user to define the same distribution as Log Normal(8.51221802598965, 0.99751345119593e-1), which is not intuitive at all as it uses parameters that are in the logarithmic space (i.e., their units are ln(bpd)).

The same applies to the lognormal and inverseLognormal FML Probability Functions.