A steady-state model is presented to study the simultaneous flow of three phase gas-liquid-solid mixtures in conduits. The liquid phase can be comprised of a mixture of Newtonian (e.g. liquid hydrocarbon, water) and non-Newtonian (e.g. drilling mud) fluids. Gas can exist in a free state as well as dissolved in the liquid phase. The model accounts for possible injection of separate streams of gas, liquid hydrocarbon, and water into the conduit. The solid phase is assumed to be fully suspended in the multiphase flow mixture.
Component mass balances are written for the liquid hydrocarbon, water, non-Newtonian liquid, transported gas, injected gas, and solid. The set of balance laws is completed with a mixture momentum equation. Closure of the system of equations is effected by two drift flux equations, relations for fluid properties, mixtures, friction factor, wall shear stress, and component mass fractions. Solubility of gas is described by a black oil behaviour.
An iterative finite difference approximation scheme is used to solve the system of equations. The conduit is divided into segments. The set of equations is solved simultaneously over each segment, and progressively over the conduit.
The model is used to simulate an ubderbalanced drilling operation. The predicted bottom hole pressure compares well with that obtained fromPWD data. The results represent preliminary studies with the model and simulator and serves to identify additional work on a continuing collaborative effort to develop technology related to underbalanced drilling.