Steinar Evje published a paper in the SIAM Journal on Mathematical Analysis with a new analysis of a mathematical model that has applications to study gas kicks in deep-water oil wells.

To explain a dangerous gas kick, consider the deeper the well the higher the pressures will be, and are higher the risks associated with tapping oil from very deep wells. During drilling when the pressure applied inside the sting of drill pipe to balance against the hydrocarbon pressure in a well is not great enough to overcome that exerted by gas and fluids in the rock formation, water, gas, oil, or other formation fluids can enter the drilling hole.

When the materials in the well overcome the pressure of the circulating drilling fluid the drilling fluid and the formation materials can “blow out” at the top of the well.  A “gas kick,” can in worst-case scenarios lead to blowouts as vividly seen in the BP 2010 Gulf of Mexico spill.

Oil Well Circulation Diagram. Click image for the largest view.

Well control is one of the most important processes during drilling operations. In deepwater drilling, controlling pressure in the oil well is crucial, as excessive pressures in the drilled hole can result in blowouts, as seen leading to disastrous events.

The use of mathematical models is important for the development of tools that can help simulate, and in turn, increase the control of deep-water well operations. Evje explained saying, “Various gas kick simulators are being developed for the purpose of studying well control aspects during exploratory and development drilling. Simulators have become an important tool for the development of new, more efficient and safer drilling methods.”

Evje continues, “A simulator for drilling operations is composed of a set of nonlinear coupled partial differential equations that describe the simultaneous flow of hydrocarbons in a well. This mathematical model represents a ‘virtual laboratory’ where the finer mechanisms related to a number of different physical effects can be studied in detail,”

Like all simulations getting to accuracy is the issue.  The main challenge presented in many of these models is the precise prediction of the pressure profile in addition to liquid/gas volumes and flow rates at various points along the oil well. “This 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.

Evje’s proposed mathematical model’s starting point 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.

Recognizing and planning in for the discrepancy allows for 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’s 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. Additionally, they allow proof of the existence of solutions for the model in a strict mathematical sense.

In this paper, Evje demonstrates that under certain assumptions, a solution exists.

In Evje’s model 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.

That kind of mathematical analysis is essential to optimize and evaluate drilling operations and well-control practices in order to minimize the possibility of oil well disasters, especially in deep-water wells.

Evje said, “The possibility of blowout occurrences needs to be mitigated in order to avoid human casualties, financial losses, and finally but not least, environmental damage.”

This work and the development that will follow will be ever more important as deep water located deep wells in the Gulf of Mexico and off the coast of Brazil tap into huge reserves under very high pressure and temperature.


1 Comment so far

  1. FMJ on May 29, 2014 5:35 AM

    The safety of deep sea drilling is one of the most important areas.
    In addition to monitoring the flow rate of the mud and the pressure measurements can analyze the characteristics of the mud. New electronic methods allow even the smallest changes in the speed of sound through the dissolved gases (a few percent saturation) and due to lower inflows of hydrocarbons are sure to measure and to warn.
    This also works with oil based mud.

    The digital measurement technology can measure foot securely changes the speed of 0.1 ft/m.

    Further details of the measurement technique, see below:

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