Interpretation of two-phase production logs (PLs) traditionally constructs borehole fluid-flow models decoupled from the physics of reservoir rocks. However, quantifying formation dynamic petrophysical properties from PLs requires simultaneous modeling of both borehole and formation fluid-flow phenomena. This paper develops a novel transient borehole/formation fluid-flow model that allows quantification of the effect of formation petrophysical properties on measurements acquired with production-logging tools (PLTs).
We invoke a 1D, isothermal, two-fluid formulation to simulate borehole fluid-phase velocity, pressure, volume fraction, and density in oil/water-flow systems. The developed borehole fluid-flow model implements oil-dominant and water-dominant bubbly flow regimes with the inversion point taking place approximately when the oil volume fraction is equal to 0.5. Droplet diameter is dynamically modified to simulate interfacial drag effects, and to effectively account for variations of slip velocity in the borehole. Subsequently, a new successive iterative method interfaces the borehole and formation fluid-flow models by introducing appropriate source terms into the borehole fluid-phase mass-conservation equations.
The novel iterative coupling method integrated with the developed borehole fluid-flow model allows dynamic modification of reservoir boundary conditions to accurately simulate transient behavior of borehole crossflow taking place across differentially depleted rock formations. In the case of rapid variations of near-borehole properties, frequent borehole/formation communication inevitably increases the computational time required for fluid-flow simulation. Despite this limitation, in a two-layer reservoir model penetrated by a vertical borehole, the coupling method accurately quantifies a 14% increase of volume-averaged oil-phase relative permeability of the low-pressure layer caused by through-the-borehole cross-communication of differentially depleted layers. Sensitivity analyses indicate that the alteration of near-borehole petrophysical properties primarily depends on formation average pressure, fluid-phase density contrast, and borehole-deviation angle. A practical application of the new coupled fluid-flow model is numerical simulation of borehole production measurements to estimate formation average pressure from two-phase selective-inflow-performance (SIP) analysis. This study suggests that incorporating static (shut-in) PL passes into the SIP analysis could result in misleading estimation of formation average pressure.