Abstract 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 equationsis 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 from PWD 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.
Introduction Drilling in an underbalanced mode may be applied to wellsto be drilled and completed in pressure depleted reservoirs, areas prone to differential sticking, areas where there are slough ing shales, reservoirs where loss circulation is common, low permeability reservoirs, reservoirs with hard rocks, areas with fluid disposal problems, and slim holes.
The advantages of using underbalanded drilling include increased rate of penetration, counter-current imbibition and reduction information damage, reduction in loss circulation, reduction in differential sticking, increased bit life, reduction in sloughing of hole, better gauged hole, better cementing jobs, investigation of reservoir in real time, and reduction of concerns on fluid disposal. The net result of these advantages isa reduction in costs.
The disadvantages of underbalanced drilling include difficult hydraulic calculations, corrosion problems with aeration methods, high costs associated with nitrogen and chemicals, inability to handle fluid influxes, inability to use conventional MWD tools, inability to re-circulatefoams, down hole and surface fires, hole erosion, additional cost associated with a closed system surface equipment, and cost associated with additional data acquisition equipment.
The following sections present a summary of a mathematical model, its numerical solution, and the initial results of the simulator applied to under balanced drilling
Model Development A complete description of the physical model and the governing equations canbe found in a report by Sharma and Kamp, and a subsequent paper by Kamp et al. A summary of the model is repeated here for completeness.