Sonic flow of liquid-gas mixtures at drill bit nozzles is believed to be responsible for some complications in underbalanced drilling (UBD), owing to pressure discontinuity and temperature drop at the nozzles. It is vitally important to avoid this flow condition in UBD by selecting optimal nozzle size and fluid flow rates. However, there is no method that can be used for prediction of the sonic flow condition.

This paper introduces an analytical model for calculating the critical pressure ratio when two-phase sonic flow occurs. The analytical model can be coded in a spreadsheet. The critical pressure ratio charts are also provided for field engineers. Use of the model and charts in selection of bit nozzle size and two-phase flow rates will reduce complications in UBD.


Underbalanced drilling (UBD) is defined as drilling operations where the drilling fluid pressures in the borehole are intentionally maintained to be less than the pore pressure in the formation rock in the open-hole section. The low borehole pressures are achieved by using lightened drilling fluids. The light fluids used in UBD are usually air, gas, foam, and aerated water. However, aerated oil, water, even weighted mud can be used for UBD in areas where formation pore pressure gradients are higher than hydrostatic pressure gradient of water.1

UBD provides benefits of minimizing lost circulation, reducing formation damage, increasing penetration rate, and improving formation evaluation, etc. The disadvantages of UBD include personnel and equipment safety issues, handling of produced formation fluids, wellbore damages (washout, collapse, and cuttings accumulation in the borehole), and high cost due to drilling complications. Although not well documented, some drilling complications, such as pipe sticking, are attributed to sonic flow at drill bit nozzles.

Sound wave and pressure wave are mechanical waves. When the fluid flow velocity in a nozzle reaches the travelling velocity of sound in the fluid under the in-situ condition, the flow is called sonic flow. Under sonic flow conditions, the pressure wave downstream of the nozzle cannot go upstream through the nozzle because the fluid medium is travelling in the opposite direction at the same velocity. In this condition, the upstream-pressure is not ffected by the downstream-pressure, i.e., a pressure discontinuity exists at the nozzle. Because of the pressure discontinuity, the increase in bottom hole pressure due to cutting accumulation, or mud ringing, in the annulus cannot be detected from the standpipe pressure gauge. Cuttings will continue to accumulate above drill bit until the drill string gets stuck.

Another complication associated with sonic flow is "ice-balling" of drill bit. Although this issue has not been well documented due to lack of direct measurements as evidence, it is apparently a fact in gas drilling with small nozzles at high gas injection rates. This issue tends to be proven by field observations. We have seen several cases where standpipe pressures went up rapidly with known reasons in gas drilling. After tripping out of the hole, nothing was found wrong with the drill bit. Having tripped in the hole with the same bit, the standpipe pressure went up again.

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