Summary

Accurate prediction of shut-in and flowing bottomhole pressures (BHPs) in inclined holes presents a challenge in aerated-mud drilling. It is highly desirable to develop a simple and accurate hydraulics equation for this purpose. This paper fills the gap.

A closed-form hydraulics equation was developed in this study on the basis of recent experiments on multiphase flow in an inclined-well model. The newly developed hydraulics equation is a four-phase model that considers injected liquid, injected gas, formation-fluid influx, and cuttings entrained at the bottom of the hole during drilling. It degenerates to the Poettman and Bergman equation when terms for friction loss, cuttings weight, gas weight, and temperature variation are neglected.

The equation was first calibrated with the data measured from a full-scale research borehole. It was then tested with two field cases covering a deep (7,403 ft vertical depth) and a shallow (697 ft vertical depth) horizontal well drilled with aerated muds. The results show 3.42 and 0.8% error of the equation in BHP prediction for the deep and shallow wells, respectively. The equation was also compared with two commercial software packages (S1 and S2) using the measured BHP from another well. It indicates that the flowing BHP calculated by the equation is comparable to that from S1 and much more accurate than S2. Sensitivity analyses with Eq. 7 show that the gas-injection rate affects "static" pressure more than flowing pressure in the annular space for the tested data range. The sensitivity analyses also indicate very high equivalent circulating density (ECD) and low equivalent mud weight (EMW) in shallow depths near the surface.

Introduction

An aerated mud is a three-phase system consisting of gas (normally, air or nitrogen), liquid (normally, water or oil), and solid (cuttings). The liquid constitutes the continuous phase, with gas appearing as discontinuous bubbles. Aerated muds are defined as liquid/gas mixtures with densities ranging from 4.0 to 6.9 lbm/gal.

Aerated muds are used for near-balanced and underbalanced drilling operations, mostly to reduce formation damage.1,2 Good designs are key to the success of aerated-mud drilling operations. Severe wellbore damages and failures can result from poor designs. Pressures in the annular space during drilling and after a circulation break play vitally important rules in controlling borehole instability during aerated-mud drilling, especially in inclined holes. Because aerated mud is a compressible fluid, special care needs to be taken in hydraulics calculations, mainly because the frictional and hydrostatic pressure components influence each other through the pressure-dependent fluid density. Sophisticated numerical simulators are required to perform accurate computations. Both steady-state- and transient-flow simulators are available for aerated-mud-drilling hydraulics calculations.3–7 Unfortunately, the results from these simulators frequently conflict8 because of assumptions made in the mathematical formulations. It is, therefore, highly desirable to develop a simple and reliable hydraulics equation.

Assuming bubbly flow (flow of liquid/gas mixture in which the gas phase is dispersed into the continuous liquid phase in the form of small bubbles), a closed-form hydraulics equation that coupled the frictional and hydrostatic pressure components was developed in this study. The equation was calibrated with data from a full-scale research borehole and was tested with data from two field cases, covering deep [9,739 ft measured depth (MD)] and shallow (1,094 ft MD) horizontal wells drilled with aerated muds. The equation has also been compared with two commercial software packages using the measured BHP from another well. The comparison indicates that the flowing BHP calculated by the equation is comparable to that from the first simulator and more accurate than that of the second simulator. Sensitivity analyses with Eq. 7 show that the gas-injection rate has a more significant impact on the "static" pressure than on the flowing pressure in the annular space for the tested data range.

Mathematical Model
Assumptions.

The following assumptions are made:

  • Bubbly flow exists in the annular space.

  • No slipping effect exists between phases.

Bubbly flow is defined as the flow of a liquid/gas mixture in which the gas phase is dispersed into the continuous liquid phase in the form of small bubbles. Lage and Time's work5 indicates that bubbly flow exists when the in-situ gas/liquid ratio (GLR, dimensionless) is less than unity. It also shows that dispersed bubble flow occurs for superficial liquid velocities greater than 6 ft/sec and superficial gas velocities as high as 12 ft/sec. The research work by Sunthankar et al.9 on multiphase flow in an inclined well model confirmed the results of Lage and Time's in that bubbly flow exists in the annular space when the in-situ GLR is less than unity. It can be shown that the in-situ GLR is greater than 1 only in a small portion of borehole sections (near surface) in the aerated-mud drilling practice (EMW between 4.0 and 6.9). Apparently, the first assumption is more valid for deep wells. The second assumption, not justified in aerated-mud drilling, is used only for simplifying mathematical formulations. This assumption is relaxed, and corrections are made by calibrating the resultant equation with actual measurements, tuning the friction factor as a function of the GLR, as described in the next section.

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