We present a method of estimating the distribution of permeability along the length of a liner-completed horizontal well from measurements of well flowing pressure at multiple points along the path of flow in the wellbore. We do not model the deployment mechanism of the sensors, although in principle this can be achieved with stinger completions.

The method applies to flow under constant-rate conditions and yields estimates of permeability along well trajectory in the principal directions normal to well path. Therefore, estimates of horizontal permeability perpendicular to well orientation and vertical permeability can be obtained for the gridblocks intersected by the well. Estimation accuracy, however, improves when the geometric mean of the normal permeabilities is obtained, as opposed to their individual values. This permeability group is what governs the influx into the wellbore. We neglect the effect of skin, but the method can be used to invert for a piecewise well index coefficient, that is proportional to the permeability group and inversely proportional to skin. Therefore, the method can generate the longitudinal profile of a parametric group that represents the quality of the formation and the integrity of completion.

The quality of the inversion is governed by the spatial density of measurements, accuracy of measurements, knowledge of wellbore hydraulics, and knowledge of the relative permeability characteristics of the formation. We obtain fair estimation of wellbore-gridblock permeability distribution for a five-node pressure configuration in a 2000 ft horizontal well experiencing 60 psi pressure drop (10,000 STB/day), given realistic bands of uncertainty associated with the governing parameters, including measurement drift, and errors in liner roughness, and relative permeability exponent. Also, the inversion can be rendered insensitive to knowledge of the reservoir permeability field through a far-field scaling technique. Therefore, good estimates of the near-wellbore permeability profile can be obtained with highly uncertain knowledge of the reservoir permeability field. This is important as the technique can be applied not only to early-time but also late-time data. We illustrate the application of the multipoint pressure method through a series of examples and discuss its potential as an interventionless method of well diagnosis, for estimation of both flux and permeability distribution in high-angle completions.

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