Underbalanced drilling holds several important advantages compared to conventional drilling technology. These include elimination of formation damage, faster penetration rate, ability for evaluation of reservoir productivity during the drilling process. As underbalanced drilling technology matures, it has also been used more and more. However, many aspects of underbalanced drilling technology remain poorly understood. The model presented in this paper seeks to understand the mechanisms involved in the transport of cuttings in underbalanced drilling.
The model simulates the transport of drill cuttings in an annulus of arbitrary eccentricity, and includes a wide range of transport phenomena including cuttings deposition and re-suspension, formation and movement of cuttings bed. The model consists of conservation equations for the fluid and cuttings components in the suspension, and the cuttings deposit bed. Interaction between the suspension and the cuttings deposit bed, and between the fluid and cuttings components in the suspension, are incorporated. Solution of the model determines the distribution of fluid and cuttings concentration, velocity, fluid pressure, velocity profile of cuttings deposit bed at different times.
The model is used to determine the critical transport velocity for different hydrodynamic conditions. Results from the model agree quite closely, qualitatively and quantitatively, with experimental data obtained from a cuttings transport flow loop at JNOC's Kashiwazaki Test Field in Japan. These results show the importance of slippage in the formation of the cuttings deposit bed. The model is useful in evaluating the minimum flow rate for effective cuttings removal in underbalanced drilling.
Rommetveit et al.  developed a numerical model for underbalanced drilling with coiled tubing. The main features of this transient, 1-D model included reservoir-wellbore interaction, alternative geometries for gas injection, rheology of different fluids, etc. The model consisted of seven mass conservation equations (for free produced gas, free injected gas, mud, dissolved gas, formation oil, formation water, and drill cuttings), and one overall momentum conservation equation. Simulation results showed that a lower gas injection rate was required in the case of gasified drilling fluid, compared with annular gas injection strategy. Gas-oil ratio of the reservoir production into the wellbore was found to have important effects on the ability to maintain downhole conditions underbalanced.
Liu and Medley  compared results generated from their computer model with results from Chevron's Foamup program and test data. Two different equations of state for foam were derived:
downward flow in the drillstring, and
upward flow in the annulus.
Wang et al.  pointed out the importance of monitoring and controlling down-hole pressure, as this affected reservoir fluids influx and hence, foam rheological properties. Field data from a Brazilian underbalanced well revealed that the equivalent circulating densities, which were needed in the numerical model, did not reach steady state and fluctuated by up to 50% during the time required to drill one section of pipe. It was postulated that changes in gas and liquid density, and void fraction, surface control of choke for two-phase flow, as well as disturbances due to drillstring connections and tripping operations caused the pressure fluctuations.
Wang et al.  in a follow-up study reported the application of their model to two field cases. Dynamic effects such as circulation start-ups and shut-downs, tripping, gas injection were included. In the first case, nitrogen gas was injected into the annulus as a means of controlling underbalanced conditions. The simulator over-predicted the bottom-hole pressure by 3.7%, compared to field measurement. In the second case, nitrogen foam was used as a drilling fluid in a naturally fractured reservoir exhibiting serious loss of circulation. It was found that the simulator over-predicted bottom-hole pressures, and the over-prediction increased with higher gas injection rates.
Langlinais, Bourgoyne and Holden  presented experimental data of annular frictional pressure drops for mud-gas mixtures flowing in vertical wells. The mixtures were composed of water-base drilling mud and nitrogen gas. Both the Bingham plastic and Power-Law models (for slot flow) showed deviation from measured data. Several different two-phase flow correlations were utilized to calculate the frictional pressure drop. The Hagedorn and Brown correlation, coupled with a power-law rheological model, and equivalent diameter was found to provide the best fit for the experimental data.