Looking at the nature of Egypt, the country has two thirds of its oil in brownfields. Therefore, using techniques like hydraulic fracturing and horizontal drilling is unavoidable. Hydro-fracturing is not only implemented to stimulate brownfields production, but it is also used when it comes to unconventional oil and gas exploration. However, there are several uncertainties when it comes to the process.

During the fracking process, a huge amount of fluid made mainly from water, sand, and chemicals, is injected in a high pressure to stimulate the wells. Hence, it can sometimes go wrong. If the responsible operator did not study and plan carefully, hydro-fracturing can use a lot of water and affect the water level. Additionally, it can harm groundwater and the flow back can pollute rivers and streams. Therefore, it is highly recommended to use mathematical thinking and to plan ahead of the process.

 Monte Carlo Technique

The Monte Carlo simulation technique is a mathematical approach that is usually used to estimate the outcome of uncertain variables. It “is a stochastic method that generates random numbers to make a sample population of the system or different statistical state of variable parameters in order to achieve statistically different materials properties,” according to an article published on Science Direct.

Monte Carlo technique helps its user in drawing a realistic analysis of risks through specialized software. The technique is used in many fields including risk management, nuclear-based imaging systems, electrical conductivity in composites, pharmaceutical manufacturing, medical physics, and more.

When it comes to fields and systems like emission tomography, the Monte Carlo technique is considered the “gold standard for design,” imaging system assessment and optimization. It helps in optimizing the acquisition parameters and estimating the performance “to design reconstruction algorithms,” as discussed by IOPscience.

As the Monte Carlo technique has succeeded in many fields, papers discussed and suggested the ways in which it will be beneficial in predicting the uncertainties in the hydraulic fracturing process.

Using Monte Carlo in Fracking

Hydraulic fracturing operations can be affected by many factors including, fluid properties, pumping rate, proppant, rock properties, and reservoir fluid. Based on these factors, the process can have many uncertainties, which can lead to wrong predictions and unprofitable outcomes. Therefore, designing an uncertainty-based model has been suggested by scholars and geologists to be used in the hydraulic fracturing process.

The Monte Carlo technique, which is considered a numerical analysis of the variables, can be used to identify the main parameters affecting the hydraulic fracturing process. Hence, it can help operators mitigate the risks caused by these uncertain factors and achieve better results, according to Awad Ahmed Quosay’s paper, entitled ‘Hydraulic Fracturing: New uncertainty-based modeling approach for process design using Monte Carlo simulation technique’.

Using the Monte Carlo technique, operators can “apply uncertainty-based values on the designing analytical formulas,” Quosay discussed, suggesting more emphases to “be directed to rheological modeling of the fracturing fluid.” In his paper, he analyzed different parameters using the Monte Carlo numerical method. The numerical equations found out that some variables in one equation can affect another one despite the lack of direct relation. Therefore, designing an uncertainty-based model can help in enhancing the analytical model’s quality.

In order to achieve better results during the hydro-fracturing work, it is of great significance to consider the uncertainties around the process. Therefore, using mathematical approaches, like the Monte Carlo technique, is important. The numerical equations throughout the Monte Carlo method help the applier to identify the uncertain parameters and create a model to avoid or mitigate these uncertainties, leading to better performance and eventually high profit.