Gas-Blowout Control by Water Injection Through Relief Wells-A Theoretical Analysis
Authors: Lehner F. , Williamson A.S. 
Published: December 2007

A gas blowout may be brought under control by injecting water into the formation through relief wells. By avoiding direct contact between relief well and blowout well, this technique reduces the inflow of gas by creating sufficient backpressure in the formation itself. It guarantees a feasible, successful relief-well injection rate, no matter how large the lifting capacity of the blowout well may be. A constraint condition on relief-well injection pressures is found that ensures killing of the pressures is found that ensures killing of the blowout. The minimum number of relief wells then follows from injection-pressure limitations. The positions of the relief wells are kept arbitrary in positions of the relief wells are kept arbitrary in the analysis, but the results indicate that their landing points should be close to the blowout well and that direct communications with the latter (e.g., by formation fracturing) should be avoided. The analysis yields no information as to shutoff times or cumulative injection requirements. These must be found from a separate study, which could be guided by the results presented in this paper.

Introduction
Control over a blowout may be gained by any technique that blocks the escaping reservoir fluid either in the wellbore or in the formation. The method most frequently used is wellbore blockage the recapping of a wild well, for example, or the drilling of a relief well to establish direct connection with the wild-well borehole, followed by the injection of heavy mud at a rate greater than the lifting capacity of the blowing well. There are, however, reservoirs in which blowout conditions may become too severe to allow successful surface operations and also reservoirs in which bottom-hole pressures exceed the pressure that could be pressures exceed the pressure that could be balanced by feasible mud injection rates. Complications that rule out surface operations may also arise when the uncontrolled production from one formation "blows in" at another lower-pressure formation. In such cases the only safe and effective remedy may be to inject water into the formation through relief wells deliberately aimed off the wild-well landing point. This restricts the escape of reservoir fluid by a pressure buildup resulting from the flow of water through the formation, and by the continuous narrowing of the passageways open to the escaping reservoir fluid between spreading water-saturated volumes. When all passageways are closed off by the water, the wild well is under "dynamic" control and may produce a large fraction of the water that is being continuously injected it final plugging operation is still necessary to gain permanent control over the well. The termination of permanent control over the well. The termination of relief-well water injection must then be timed carefully, particularly when dealing with an overpressured gas reservoir.We are concerned here with only the reservoir engineering aspects of bringing a well under "dynamic control by continuously injecting water through relief wells. In considering such an operation, the most important matters to be decided are the following:1. The number of relief wells and their location with respect to the blowout well,2. The water injection rate, and3. The total quantity of water injected at shut-off.In the following we present a simple formula for estimating the minimum successful water-injection rate. The minimum number of relief wells required is then obtain from injection pressure limitations. Using this result, it is possible to determine the optimal strategy for locating relief wells. No information is obtained on cumulative injection requirements or shut-off times. This lies beyond the scope of simple analysis; but such a study -which would probably be undertaken on a computer could clearly be shortened by using the results of this paper as a screening tool.

ANALYSIS OF A TWO-DIMENSIONAL PROBLEM
In formulating the interrelation of the most important parameters governing the conditions for shut-off, we are forced to idealize.We assume that the fluid flow is two-dimensional in a plane homogeneous reservoir of uniformly thick layers.
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