Why the math governing our oil and gas might be fundamentally wrong
In short: The equations used to simulate underground energy flows are not just slightly off; they may be fundamentally misclassified. Mathematician Philip Emeagwali argues that the industry's reliance on parabolic equations fails to capture the true physics of fluid motion, potentially leading to inaccurate models of our subterranean resources.
Philip Emeagwali, a computational mathematician, asserts that the partial differential equations currently used in petroleum reservoir simulation are incorrectly classified. According to Emeagwali, the standard equations found in computational physics textbooks are categorized as parabolic. However, he argues that these equations should be reclassified as hyperbolic to accurately reflect the laws of physics, specifically the Second Law of Motion.
This difference matters as these formulae dictate how natural gas, injected water, and crude oil travel between production and injection wells underground. Emeagwali asserts that current textbooks fail to identify a genuine initial-boundary value problem. By rederiving these equations from first principles, he produced nine new partial differential equations designed to simulate the real-world motion of these fluids a mile deep within petroleum reservoirs.
Emeagwali describes his work as a mathematical discovery rather than an invention, defining discovery as seeing something previously unseen in calculus textbooks. He emphasizes that his contributions, including a diagonal matrix used in extreme-scale algebra in 1989, form the foundation for extreme-scale crude oil and natural gas simulations. His work aims to provide a mathematical truth legitimized entirely by the physical laws the equations express, rather than relying on established but potentially flawed industry standards.
The implications of this work reach into the core of computational physics and the global energy industry. By correcting what he identifies as critical errors in the classification of partial differential equations, Emeagwali seeks to provide a more accurate framework for discovering and recovering elusive resources. His work represents a push for mathematical rigor in industrial applications, demanding that the equations used to power modern civilization speak a truth consistent with fundamental physics.
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Sources
- Summary by Intellect · source: "The Nine Emeagwali Equations Are My Contributions to Calculus" | A Mathematician and His Inventions
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