Weighted Percentiles Approach for P10, P50, P90, and Pmean

Introduction:

Below is a basic outline of the Weighted Percentiles used in the AFA KOLDUN module(s). Although the mathematics includes NP Volume, the volume of oil/gas after petroleum economics, AFA algorithms have not enabled this feature.

Given:

EUR Array with percentiles, P₁₀, P₅₀, P₉₀, and P_mean

Peak Gas Rate Array with percentiles with P₁₀, P₅₀, P₉₀ and P_mean

NP Volume Array with percentiles with P₁₀, P₅₀, P₉₀ and P_mean

where:

EUR = Expected Ultimate Recovery

Peak Gas Rate = highest gas rate observed during forecast

NP Volume = Volume of hydrocarbon produced after volume discounted cash flow analysis.

1. Calculate Normalized Percentiles

This is basically feature scaling that is used to bring all values in the range of [0,1], or also known as unity-based normalization. Essentially, we are transforming all variables into a similar scale, and ideally ensures all features contribute equally to the model.

Generic Equation for Normalized Variables

where:

y = i…n, or P₁₀, P₅₀, P₉₀ or P_mean

A = EUR, Peak Rate, NP, or other variable.

P90

P50

P10

Pmean

2. Calculate Normalized Values

3. Calculate PX/Rate/Distance

Note that the below values change with each simulation run. “i“ refers to the the simulation run, not the time step.

4. Find the Distributions using Minimum from Step 3.

Find nearest curve which has minimum for each array. Alternatively, just use the minimum curve.