Spatial averaging of hydraulic conductivity under radial flow conditions

• DOI: 10.1007/bf02065873
• Publication Date: 2005-08-13T19:40:12Z
• Authors: A. J. Desbarats
• Keywords: Log-normal distribution; Variogram

Steady-state radial flow in three-dimensional heterogeneous media is investigated using a geostatistical approach. The goal of the study is to develop a model of the relationship between corescale hydraulic conductivities measured at the wellbore and the conductivity of the surrounding drainage region as measured by a larger scale flow experiment such as a pump test. Conductivity at the point or core-scale is modeled as a stationary and multivariate lognormal spatial random function. Conductivity of the drainage region is obtained by a weighted nonlinear spatial average over the point-scale values within. This empirical spatial averaging process is shown to yield excellent approximations of true effective drainage region conductivities calculated using a numerical flow model. The geostatistical model for point-scale conductivity and the spatial averaging process are used to determine the first and second order ensemble moments of drainage region conductivity. In particular, an expression is derived for the conditional expectation of drainage region conductivity given point-scale values measured at the wellbore. The results are illustrated in a case study of a well from a sandstone oil reservoir where both core and transient-test conductivity data from the same interval are available for comparison.