Exploring the link between the flow zone indicator and key open-hole log measurements: an application of dimensional analysis

Dimensional analysis has been used as a tool for developing a non-linear empirical model giving the flow zone indicator (FZI) as a function of open-hole log measurements. Dimensional analysis confirms that interval transit time (Delta(t)), true resistivity (R-t), bulk density (rho(b)), the apparent water resistivity (R-wa) and the photo-electric absorption (P-e) are essential well-log measurements for estimating the FZI in sandstone formations. A unique power-law relationship has emerged between a dimensionless FZI group (lambda) and a dimensionless resistivity group (Omega) for distinct hydraulic flow units. Petrotyping, using either the discrete rock type (DRT) approach or the global hydraulic elements (GHE) approach, appears to provide a credible framework for comparative hydraulic flow unit description. Dimensionless groups permitted the analysis of the effect of several operational variables. The FZI increases with increasing bulk density, and with increasing interval transit time. On the other hand, the FZI decreases with increasing true resistivity (R-t). The relationship between the FZI and the photo-electric absorption is more intricate, though, since it depends on the value of the power-law exponent pi. Conventional log data from an oil well (well B), penetrating two distinct sandstone oil reservoirs in an onshore sandstone oilfield in the Middle East, were used to validate the dimensionless groups. For the field case presented, the FZI empirical model prediction capability does not appear to be diminished by the existence of a capillary transition zone. The FZI-based model, used for estimating permeability, represents an improvement in the prediction of permeability provided that reliable estimates of the FZI are available. Dimensional analysis proved to be a powerful modelling tool capable of revealing fine relationships that are invisible to exhaustive data mining techniques.