Inference of near-borehole permeability and water saturation from time-lapse oil-water production logs

The conventional interpretation of production logs (PL) acquired in time-lapse mode helps petrophysicists to detect the advancement of fluid contacts in the near-borehole region. Without inclusion of a dynamic reservoir model, conventional time-lapse interpretation remains limited to describing time variations of fluid inflow rates produced from or injected into fluid-producing rock formations. However, proper reservoir management requires quantifying depth variations of near-borehole properties (e.g., formation damage and fluid saturation) over time to construct reliable field-scale reservoir models. This paper develops a new-formation fluid flow model capable of simulating oil-water production measurements acquired from vertical and deviated boreholes. We implement an iteratively coupling flow algorithm to explicitly interface a borehole fluid flow model to a reservoir multiphase flow simulator. The specific application considered in this study invokes the coupled borehole-formation fluid flow model to estimate near-borehole permeability and water saturation from time-lapse oil-water production measurements. Borehole fluid flow simulation is based on an isothermal two-fluid formulation that applies separate mass and momentum conservation equations to the oil and water phases. When solving momentum conservation equations, we compute interfacial drag and buoyant forces based on the assumption of spherical oil or water droplets with negligible interfacial mass transfer. Subsequently, the spatial distribution of droplet diameter associated with the discontinuous fluid phase is dynamically modified to accurately account for variations of slip velocity across fluid-producing layers. Linkage of the borehole and formation fluid flow models is next carried out by introducing additional source terms into the borehole mass conservation equations. In a synthetic reservoir model supported by an infinite-acting aquifer, the coupled flow algorithm integrates production logs acquired in time-lapse mode to construct a near-borehole reservoir model that describes depth variations of skin factor over the elapsed time. Feasibility studies show that the estimated petrophysical properties can be adversely influenced by the large volume of investigation associated with PL measurements. Moreover, undetectable fluid production across low-permeability layers decreases the sensitivity of production logs to layer incremental flow rate, thus increasing estimation uncertainty. Despite these limitations, estimated fluid saturation and permeability across high-permeability layers are within 15% and 20% of the corresponding actual values, respectively. The developed interpretation algorithm additionally integrates well logs and production logs acquired in an oil-water field example to construct a PL-calibrated near-borehole reservoir model. Results enable (a) the differentiation of low-permeability layers from highly-damaged formations, (b) the identification of layers accountable for high water production, and (c) the quantification of the added value of remedial workover operations to isolate water-producing layers. In addition, the coupled model is used to study sensitivity of production logs to near-borehole petrophysical properties. We show that production logs are mainly sensitive to formations' absolute and relative permeabilities, water saturation, and pressure.