In most instances of the application of rock mechanics to oilfield problems the loading on the rock can be regarded as static or quasi-static. Furthermore the rock mechanical parameters that are used to quantify the rock response are obtained from static or quasi-static laboratory tests. Here we discuss an application in which the loading on the rock is large in amplitude and short in duration. We examine the creation of a perforation tunnel by a shaped charge jet. It is well known that a shaped charge jet travels at velocities in the range 1-7 km/s and that the jet tip exerts a pressure on the rock of the order of one million psi. Penetration of the rock and creation of the perforation tunnel last about 0.1 to 0.5 ms. The depth of penetration is one of the important perforating parameter for well productivity, particularly in hard formations, and its prediction and maximization are fundamental concerns. Recent mathematical models of the penetration process now include the effect of the rock strength through an ill-defined yield stress . We show that the results of these models provide good agreement with laboratory data when the yield stress is set proportional to the UCS with a constant of proportionality of about 20. Experimental data for jets shot into hard and soft concrete targets supports the predicted value of the yield strength, though we have severe reservations about the application of static parameters such as UCS in the context of this intense dynamic loading. Results from the models suggest that the rock strength severely limits the depth of penetration, which has implications for the design of shaped charges for use in hard rocks.
1. INTRODUCTION
In cased completions of oil and gas wells the wellbore is connected to the reservoir via perforation tunnels created by explosive shaped charges. The shaped charges are usually loaded into the wellbore inside a steel tube known as a "gun". When a shaped charge is detonated the metal liner collapses under the intense pressure created by the detonation of the explosive and forms a jet that is projected towards the target at a high velocity, see Fig 1. (In the oilfield the target consists of gun, water clearance, casing, cement sheath and rock.) Typically the speed of the jet at its tip is of the order of 7 km/s, while towards the tail of the jet speeds of the order of 1 km/s are more typical. The whole penetration process is completed in a few hundred microseconds. Usually the front part of the jet travels at a speed in excess of the sound speed in the rock. The associated bow shock wave can be discerned in the numerical simulations shown in Fig 2. The pressure on the target at the jet impact site is of the order of 1 million psi. At least in the early stages of penetration the impact pressure is sufficient to overcome the strength of the target. The target material in the neighborhood of the jet tip then flows, almost as if it were a fluid being penetrated by another fluid, displacing the target material radially and creating a cavity or tunnel in the target.
