SPATIAL SENSITIVITY FUNCTIONS FOR FORMATION-TESTER MEASUREMENTS ACQUIRED IN VERTICAL AND HORIZONTAL WELLS

摘要

We develop a conceptual and quantitative methodology to assess the three-dimensional (3D) spatial zone of response of formation-tester measurements acquired in vertical and horizontal wells. Spatial sensitivity functions are calculated numerically from the variation of pressure transient measurements due to perturbations of petrophysical properties at a given point in space and time. Calculations are performed under the assumption of two-phase fluid flow and consider both packer- and point-sources as well as pressure and fractional-flow monitoring probes. We examine perturbations of a range of petrophysical properties to calculate the sensitivity function, including permeability, porosity, and permeability anisotropy. Conventional single-phase spherical- and radial-flow asymptotic solutions often used in the interpretation of formation-tester measurements can lead to significant errors in the construction of the sensitivity maps. Such errors can bias the estimation of permeability and permeability anisotropy because of unaccounted capillary pressure and relative permeability effects. In addition, non-symmetrical flow barriers distort the spatial zone of response, whereas presence of supercharging limits the ability of formation-tester measurements to probe radially deep into the formation. Damaged and stimulated zones near the wellbore can also modify the spatial resolution properties of the acquired measurements and significantly reduce their radial length of investigation. For cases of rock formations penetrated by horizontal wells, the spatial zone of response of formation tester measurements can be highly non-symmetrical. The spatial sensitivity functions described in this paper could be used to design measurement acquisition and interpretation strategies that maximize spatial resolution and depth of investigation in complex geometrical situations that include two-phase flow phenomena.