Thermal-Gradient & Porosity Well-Log Fluctuation Relation as Guide to in Situ Advective Flow Structure

Abstract

A quantitative physical relation ....T .. Pe (T–T0)/h .... connects spatial fluctuations in thermal gradient ..T and formation porosity T .. recorded over a 750m interval in a Colorado USA tight-gas formation well. The terms of the proportionality factor are Peclet number Pe, well interval h, and temperature T along the well interval. The relation between thermal gradient and formation porosity follows from a second spatial fluctuation relation, .... .. ..log(..), widely observed for wellcore porosity and the logarithm of well-core permeability .. in clastic rock and documented for the tight-gas formation. Insertion of the second fluctuation relation into the expression for advective heat transport, Q .. - C.... (T – T0) for fluid mass heat-capacity C.. and advective flow speed .. determined by formation permeability, leads directly to the first relation. We suggest that it is of interest to determine if advection-driven fluctuation relation ....T .. Pe (T– T )/h .... between thermal gradient and formation porosity, or its buoyancy-driven convective equivalent, is observed in geothermal reservoir upflow and/or downflow. If the relation is satisfied in a given well, well-log porosity data measured in production wells can be assumed to be a key physical variable in determining reservoir flow structure via 0 .... .. ..log(..) without the added expense of obtaining core. If the relation is not satisfied in a given well, this may be due to geological structures intervening in the in situ flow paths. Finally, if spatial fluctuations in geothermal field porosity are similar to fluctuations generally observed in clastic reservoirs, then porosity well-logs can, again potentially, provide clear broadband (multiple-scale-length) permeability structure constraints with which to anchor stochastic models of reservoir flow structure for production simulation.