Integrating Pipe Fractional Flow Theory with Fully Compositional Wellbore Models

Multi-phase compositional wellbore flow is important in determining the flow and pressure drop in oil, gas, and geothermal wells. These effects become increasingly important in long laterals with multiple locations for fluid influx. Complex hydrocarbon phase behavior such as change in the number of phases, phase flipping, gas slippage can happen in the wellbore because of changes in pressure, temperature and inflow fluid rate and composition along the wellbore. This paper introduces a new wellbore model which integrates fully compositional fluid flow with an energy balance and pipe fractional-flow theory with multiple points of fluid entry along the wellbore. Four sets of governing equations: component mass conservation, momentum conservation (pipe fractional flow theory), composition conservation and energy balance are solved fully implicitly along the wellbore. This is then fully implicitly coupled with the flow and energy balance equations in the reservoir and fracture domains. The primary unknowns along the wellbore (total flow rate, hydrocarbon component composition, water saturation, pressure, and temperature) can then be obtained. Flash calculations are used to calculate the hydrocarbon phase saturation, density, viscosity, etc. and the flow rate of each phase is obtained from the fractional flow theory given the local flow rate and saturations. In the first case, we study the reservoir-wellbore flow in a gas condensate reservoir with 16 hydrocarbon components. As the pressure drops, an oil phase drops out of the single phase gas condensate, first in the wellbore and then in the reservoir. In a second case, we simulate CO2 flooding in a black-oil reservoir. Reservoir cooling is observed near the injection wellbore and an increased CO2 composition is observed in the produced oil from the production wellbore. In the third case, we study a low permeability volatile oil reservoir with 14 hydrocarbon components. Production from a hydraulically fractured horizontal wellbore is simulated considering the reservoir-fracture-wellbore flow. We observe that as the pressure drops in the wellbore, gas is liberated from the oil phase and this changes the wellbore pressure drop considerably. The lighter component compositions decrease with time while the heavier component compositions increase with time because of the liquid holdup effect. In the fourth case, we showcase a stand-alone wellbore model integrated with point sources. This paper fully integrates a pipe-fractional flow formulation with compositional wellbore flow, and an energy balance for the first time. This allows the model to be used directly with compositional reservoir simulators. The wellbore mesh is automatically generated and coupled with the reservoir/fracture mesh to allow for an integrated and seamless simulation from the reservoir to the surface facility. This model allows engineers to accurately account for the pressure drop and phase behavior within the wellbore when simulating the production/injection of complex fluids.