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A math-based model for deep-water oil drilling
Date:8/25/2011

issue becomes even more critical as many drilling operations today involve long and deep wells with corresponding high pressures and high temperatures," Evje explains. Regions along the well that are open to crevices and deformities in the rock formations present specific challenges, as it is critical to maintain well pressure at these positions within certain limits. Thus, in the case of inflow of gas from surrounding rock formations, it would be important to safely transport this gas out of the well.

The starting point for Evje's proposed mathematical model is a one-dimensional two-phase model, which is often used to simulate unsteady, compressible liquid and gas flow in pipes and wells. Unlike previously analyzed models, in this gas-liquid model, the two phases may have unequal fluid velocity and a generalized term to jointly represent liquid and gas pressure.

This allows a model that can describe the ascent of a gas slug (conglomerate of high pressure gas bubbles) due to buoyancy forces in a vertical well. A gas-kick situation is usually accompanied by such a flow scenario.

In order to compute reliable solutions, it is crucial to have a model that is well defined mathematically. Mathematical methods are applied in order to derive upper and lower limits for various quantities like masses and fluid velocities, which provide insight into the parameters that are important for the control of these quantities. In addition, they allow proof of the existence of solutions for the model in a strict mathematical sense. In this paper, the author demonstrates that under certain assumptions, a solution exists.

Conditions are assumed to be isothermal, and relevant physical mechanisms are factored into the model, such as frictional forces, hydrostatic pressure, force of gravity, and compression and decompression of gas.

Such mathematical analysis is essential to optimize and evaluate drilling operations and well-control practice
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Contact: Karthika Muthukumaraswamy
karthika@siam.org
267-350-6383
Society for Industrial and Applied Mathematics
Source:Eurekalert

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