DYNAMIC DIFFERENTIAL PRESSURE EFFECTS ON DRILLING OF PERMEABLE FORMATIONS

In the mathematical modeling of bit penetration rate for tri-cone roll er bits in permeable formations, virtually all of the current techniqu es assume that the differential pressure between the bottom-hole wellb ore pressure and the formation is a ''static'' value. This work shows that the appropriate differential pressure is a dynamic quantity, beca use for overbalanced drilling, fluid filtrate from the wellbore requir es a finite lime to flow into the formation, producing a changing pres sure gradient ahead of the bit. Moreover, this dynamic gradient is dir ectly dependent upon the rate of drill bit penetration, which is in tu rn dependent upon the dynamic gradient itself: Accordingly, coupled pe netration rate and dynamic gradient equations must be solved which fre quently result in the prediction of higher drilling penetration rates than when the static gradient is used. The appropriate dynamic differe ntial pressure equations are developed and applied to an example drill ing situation. It is shown that with water-based drilling fluids, for rock with permeability greater than a few microdarcies at virtually al l penetration rates, and for penetration rates less than 3 m/h (9.84 f t/h) at permeabilities greater than 1 mu d (microdarcy), the dynamic d ifferential pressure is significantly less than the static differentia l pressure. Accordingly, using the conventional static differential pr essure results in the prediction of penetration rates that are much to o low. Moreover, using measured penetration rates from the field, the conventional approach yields predicted in-situ rock strength that is m uch too high.