APPENDIX

A Lagrangian co-ordinate system (j) is established in the material. These co-ordinates move with the medium and assume discrete values: 0, 1, 2 . . . j − 1, j, j + 1. . . . This co-ordinate system divides the material into zones whose mass remains constant. At zero time each co-ordinate has a unique Eulerian co-ordinate R,°; after n cycles the Eulerian co-ordinates are R". The following illustration shows the position of the mass points at to and fn:

is transformed into the Lagrangian co-ordinate system (j). Each stress component (2) in the above equation is a scalar function of position (R) and time (t). If the Eulerian co-ordinate (R) is considered to be a function of j and 1, then we can write:

ΟΣ
aj

ΑΣ R aR aj

Equation (A.2) is easily solved for ǝΣ/ƏR.

(A.2)

The time derivative of velocity simplifies considerably in the Lagrangian system since j is independent of time. In the Eulerian system, we have:

Using equations (A.2) and (A.4), we obtain the following first-order difference equations (superscripts denote cycle and subscripts denote Legrangian co-ordinate):

3. Stress

AVs+jn+b = Agn+b [3(R,n+b)2 μ,n+l 3(Rƒ+1®+k)2 Uƒ+1®+ik + Cs+qn+d]

Summary

Project Dragon Trail is a proposed nuclear experiment in the Mancos formation of the Douglas Creek gas area in western Colorado. As tentatively planned, the stimulation experiment will determine the effect of a 40 kiloton nuclear explosive on the gas producing capacity of the Mancos B zone. The shot would be fired at about 2700 feet. It could be carried out soon after Project Gasbuggy, the first proposed nuclear test in a gas reservoir, since the general Project Dragon Trail studies on technical feasibility and reservoir properties have been completed and submitted to the AEC. Arrangements have been made for CER Geonuclear Corporation to advise and assist Continental Oil Company in carrying out the experiment. Continental Oil Company is currently drilling and testing additional wells in the area to determine an optimum site location for a nuclear experiment. Upon the completion and analysis of the test data from these wells, and after acceptance of the Dragon Trail proposal by the AEC, Continental will drill and equip the device emplacement hole in the most acceptable location.

The Mancos B zone is well suited for a nuclear experiment. Because of its thickness, a large explosive can be tested; and because of the shallow depth, post-shot information wells can be inexpensively drilled, thus leading to a much more rigorous evaluation of nuclear effects and gas deliverability. This will lead to a more rapid commercialization of the method. Analyses of the test results on the Mancos B zone should be straightforward since the formation is uniform over a wide area, and its productive characteristics are well documented.