Modeling formation resistivity changes due to invasion and deformation during initial leak-off test build-up

Leak-off tests (LOTs) are performed to determine the strength of a newly drilled formation below a cased interval and to characterize the upper bound of mud weight that can be safely used while drilling the next section, without risk of formation breakdown and lost circulation. In an LOT, drilling mud is pumped into the wellbore, causing the wellbore pressure to increase and exceed the formation pore pressure. During the initial LOT build up, excess pressure in the wellbore causes the surrounding rock to deform and mud filtrate to invade into the formation via porous flow. In this paper, change in formation resistivity around a wellbore during initial LOT build-up has been investigated. Invasion is modeled assuming two-phase radial Darcy flow and deformation using a 3D finite element model. Invasion may result in an exchange of conductive ions between water-based drilling mud and formation water both by diffusion in the direction favored by the concentration gradient of the ions and by convective transport. This process is incorporated into the model by solving the radial convection-diffusion equation for the aqueous phase using a finite difference method. Archie's law is used to determine the formation resistivity. Findings show that the direct effect of deformation on porosity, therefore on formation resistivity during an LOT, is negligibly small even when the formation rock is highly compressible with compressibility in the order of 10−3 psi−1. While salinity solely controls formation resistivity during an LOT conducted in a fully water-saturated interval, water saturation change and salinity change compete to produce a compound effect on formation resistivity of an oil-bearing zone where water saturation varies dynamically due to displacement of formation fluids. Unlike compressibility, the effect of permeability on formation resistivity response is found to be evident and readily observable. While analyzing the formation resistivity responses at various depths of investigation (DOIs), it is found that the effect of DOI on resistivity response can be useful in studying invasion and assessing formation damage during an LOT. In addition to this, through comparing time-lapse resistivity logs at multiple DOIs during an LOT with numerically synthesized resistivity responses, the model promises a novel approach towards determining the permeability of a freshly drilled and unaltered interval.