Featured Research

from universities, journals, and other organizations

Math-based model for deep-water oil drilling

Date:
August 25, 2011
Source:
Society for Industrial and Applied Mathematics
Summary:
A new mathematical model has applications to the study of gas kicks in deep-water oil wells, which in worst-case scenarios can lead to blowouts.

Schematic of an oil rig.
Credit: Photo courtesy of Energy Information Administration, Office of Oil and Gas.

Oil 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, leading to disastrous events like the 2010 Gulf of Mexico Oil Spill.

The deeper the well, the higher the pressure, and the higher the risks associated with tapping oil from wells. During drilling, when the pressure applied to balance the hydrocarbon pressure in a well is not great enough to overcome that exerted by gas and fluids in the rock formation drilled, water, gas, oil, or other formation fluid can enter the hole. This is called a "gas kick," which in worst-case scenarios can lead to blowouts.

In a paper published earlier this month in the SIAM Journal on Mathematical Analysis, author Steinar Evjepresents new analysis of a mathematical model that has applications to the study of such gas kicks in deep-water oil wells.

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

"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," Evje goes on to explain.

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.

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 practices in order to minimize the possibility of oil well disasters, especially in deep-water wells. "The possibility of blowout occurrences needs to be mitigated in order to avoid human casualties, financial losses, and finally but not least, environmental damage," says Evje.


Story Source:

The above story is based on materials provided by Society for Industrial and Applied Mathematics. Note: Materials may be edited for content and length.


Journal Reference:

  1. Steinar Evje. Weak Solutions for a Gas-Liquid Model Relevant for Describing Gas-Kick in Oil Wells. SIAM Journal on Mathematical Analysis, 2011; 43 (4): 1887 DOI: 10.1137/100813932

Cite This Page:

Society for Industrial and Applied Mathematics. "Math-based model for deep-water oil drilling." ScienceDaily. ScienceDaily, 25 August 2011. <www.sciencedaily.com/releases/2011/08/110825124254.htm>.
Society for Industrial and Applied Mathematics. (2011, August 25). Math-based model for deep-water oil drilling. ScienceDaily. Retrieved April 18, 2014 from www.sciencedaily.com/releases/2011/08/110825124254.htm
Society for Industrial and Applied Mathematics. "Math-based model for deep-water oil drilling." ScienceDaily. www.sciencedaily.com/releases/2011/08/110825124254.htm (accessed April 18, 2014).

Share This



More Computers & Math News

Friday, April 18, 2014

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

Twitter Introduces Facebook-Style App Install Ads

Twitter Introduces Facebook-Style App Install Ads

Newsy (Apr. 17, 2014) Twitter hopes to make money on app install ads, which has proven to be a successful strategy for Facebook. Video provided by Newsy
Powered by NewsLook.com
Heartbleed Hack Leads To Arrest

Heartbleed Hack Leads To Arrest

Newsy (Apr. 17, 2014) A 19-year-old computer science student has been arrested in relation to a data breach of 900 social insurance numbers from Canada's revenue agency. Video provided by Newsy
Powered by NewsLook.com
Apple Rumored To Introduce Song ID Service In Next iOS Build

Apple Rumored To Introduce Song ID Service In Next iOS Build

Newsy (Apr. 17, 2014) Sources close to Apple told Bloomberg the company plans to introduce an integrated song identification service during the launch of its next iOS. Video provided by Newsy
Powered by NewsLook.com
Honda's New ASIMO Robot, More Human-Like Than Ever

Honda's New ASIMO Robot, More Human-Like Than Ever

AFP (Apr. 17, 2014) It walks and runs, even up and down stairs. It can open a bottle and serve a drink, and politely tries to shake hands with a stranger. Meet the latest ASIMO, Honda's humanoid robot. Duration: 00:54 Video provided by AFP
Powered by NewsLook.com

Search ScienceDaily

Number of stories in archives: 140,361

Find with keyword(s):
Enter a keyword or phrase to search ScienceDaily for related topics and research stories.

Save/Print:
Share:

Breaking News:
from the past week

In Other News

... from NewsDaily.com

Science News

Health News

Environment News

Technology News



Save/Print:
Share:

Free Subscriptions


Get the latest science news with ScienceDaily's free email newsletters, updated daily and weekly. Or view hourly updated newsfeeds in your RSS reader:

Get Social & Mobile


Keep up to date with the latest news from ScienceDaily via social networks and mobile apps:

Have Feedback?


Tell us what you think of ScienceDaily -- we welcome both positive and negative comments. Have any problems using the site? Questions?
Mobile: iPhone Android Web
Follow: Facebook Twitter Google+
Subscribe: RSS Feeds Email Newsletters
Latest Headlines Health & Medicine Mind & Brain Space & Time Matter & Energy Computers & Math Plants & Animals Earth & Climate Fossils & Ruins