# Uncertainty Analysis in the Oil & Gas Industry- Why we keep underplaying uncertainty? Variables & Probability Distributions

In the last article, we looked at the current industry perception towards uncertainty analysis where we exposed some of the common biases we may have and how they may affect our decision making. We also considered some examples during the life of a field of decisions O&G professionals will face and the tools they have in order to quantify these risks. First however let’s try and define what uncertainty analysis is.

Uncertainty analysis can be defined as a comprehensive methodology to assess and evaluate several options considering both aspects of risk and uncertainty. So, what do we mean by risk? Well risk is the probability of the different outcomes from an event, for example when drilling a well we wither end up with a discovery or a dry hole (Figure 1).

Uncertainty by itself is just a statistical variation of a variable which may be for example petrophysical, geological or economical. Uncertainty analysis has three main properties which are the uncertainty type:

·        -  Technical
·        -  Economic
·        -  Modelling

The technical type may be subdivided into static and dynamic parameters such a permeability, porosity and Kr/Pc curves. The economical type is related to that of CAPEX & OPEX, whilst the modelling type is if it’s a continuous or discrete variable. A continuous variable has an infinite number of possible values with the opposite being a discrete variable.

The uncertainty statistical behavior whether it be:

·         - Deterministic (permeability, Opex)
·         - Discrete (Fault connectivity, production scenarios)
·         - Stochastic (geostatistical realizations, structural maps)

The uncertainty status in terms of if a variable is controllable or not:

·         - Controllable (well location, number of platforms)
·         - Uncontrollable (fault transmissivity, porosity maps, oil price, inflation)

Variables are divided into two main categories, numeric and categorical where numeric is subdivided into continuous and discrete whilst categorical is sub divided into ordinal and nominal variables as illustrated in Figure 2 below.

Variables are also termed as dependent and independent variables where the dependent variable is the outcome variable and is generally dependent upon another variable. The independent variable are all other variables which may impact the dependent variable.

Variables can be defined by probability distributions which are a representation of the probability of manifestation of said variable. Numerous probability distributions exist with the most common illustrated in Figure 3 below. The most important one of these distributions is the normal or Gaussian distribution which is characterized by the bell shape.

Each of these distributions take parameters which define them. For example, the normal distribution is defined by a mean and standard deviation value whilst a triangular distribution is specified by its low and high values. To determine what probability distribution a variable takes we have several methods such as:

·         - Analog data from other fields
·         - Logs & core information
·         - Statistical studies on the parameters involved
·         - Statistical tests such as the K-S and Chi squared methods

Some of the most widely used distribution in the oil & gas industry are the normal, log normal and triangular distributions (Figure 4). The normal distribution is used in representing variables such as production, cost and porosity whilst the log normal is famous for representing permeability.

This is a link to a shiny app I coded to give you an idea and more hands-on experience with these distributions. I have also embedded the app in this post at the bottom. The app will allow you to choose the probability distribution and define its input. Try entering the following parameters for porosity as a normal distribution:

·         - Sample size = 3000
·         - Number of bins = 35
·         - Sample mean = 0.25
·         - Standard deviation = 0.01

The next article in this series will look at introducing experimental design and Monte Carlo simulations. Author : Ahmed Muftah
SDM & EOR Specialist
Primera Reservoir

# References

Owen, Sean. "Common Probability Distributions: The Data Scientist's Crib Sheet - Cloudera Engineering Blog". Cloudera Engineering Blog. N.p., 2017. Web. 12 Mar. 2017