Abstract
Drilling hydraulics have considerable effect on the rate of penetration. Previous studies have examined this problem; however, the effects of differential pressure and reliability of pumping equipment usually were neglected. This paper gives a general description of hydraulic drilling parameters optimized when both these effects were considered. To derive the necessary conditions for optimal hydraulics a nonlinear programming method was applied.
Introduction
In the rotary drilling process the rock must be fractured at the bottom of the hole. To allow further fracturing and drilling progress, the cuttings must be removed from the bottom efficiently and transported toward the surface. For these purposes, both mechanical and hydraulic energy are brought from the surface to the rock face and should be applied in optimal manner. Previous work in drilling hydraulics has established that this has considerable influence on the rate of penetration as well as on other indicators of drilling efficiency. For that reason, this topic has been a subject of several investigations, both theoretical and experimental. Optimal hydraulics is the proper balance of hydraulic elements that satisfy some criterion of estimation (the objective function). For given drilling fluid properties, these parameters are flow rate (q) and equivalent jet bit nozzle diameter (de). Hydraulic quantities commonly used to characterize jet bit performance include hydraulic horsepower, jet impact force, jet velocity, and Reynolds number at the bit nozzles. However, all these hydraulic quantities are determined when the flow rate and equivalent nozzle diameter have been established. Briefly, the methods of optimal hydraulics program design can be divided in two groups:methods which depend on determining the bottomhole cleaning required, usually bit hydraulic horsepower, to balance the mechanical energy level, andmethods which assume maximization of an arbitrarily established criterion of estimation.
Methods in Group 1 have limited application during drilling program design since the required level of hydraulic horsepower, for given mechanical parameters (weight-on-bit and rotary speed combinations) in a particular formation interval, require field tests and thus they cannot be applied before drilling. This method is indicated in Fig. 1. Fullerton has balanced the mechanic and hydraulic energy by means of the "constant drilling energy" concept, valid for some formation types. The various criteria to be maximized in Group 2 are hydraulic horsepower, jet impact force, jet velocity, and Reynolds number. The basic work on this topic was published by Kendall and Goins. Methods for selecting proper nozzle sizes and flow rams are given for each criterion of estimation except the Reynolds number. The latter criterion is discussed by other authors, but they discussed optimal flow rates and equivalent nozzle diameter only for the constant pump pressure range. It was shown that using maximum Reynolds number at the bit nozzles as an objective function for optimal hydraulic program design gives the same result as for maximum jet impact force.
SPEJ
P. 425^
Investigation into the Water Jet Erosion Efficiency of Hydrate-Bearing Sediments Based on the Arbitrary Lagrangian-Eulerian Method