Biot Critical Frequency Applied as Common Friction Factor for Pore Collapse and Failure of Chalk with Different Pore Fluids and Temperatures

Abstract

A fluid effect towards higher strengths for oil saturated chalk compared to water saturated chalk has previously been identified and labeled the water weakening phenomenon, but has not been further characterized physically until now. The hypothesis of this paper is that the Biot critical frequency can be used to explain this behavior on the pore scale and be extrapolated to the macroscale failure and pore collapse properties. A large set of previously published laboratory test results on chalk was collected. The data spans three different chalk types which were tested at temperatures from 20°C to 130°C with the following pore fluids besides dry chalk: fresh water, synthetic seawater of different chemical compositions, methanol, glycol, formamide, decane and crude oil of varying viscosity.The Biot critical frequency determines the transition from where an applied sound velocity is dominated by viscous forces to where it is dominated by inertial forces, i.e. when the pore fluid motion lags behind the applied frequency. It is therefore a measure of the internal surface friction between solid and fluid and is interpreted as a friction factor. The Biot critical frequency incorporates the porosity, permeability, fluid density and fluid viscosity, where the latter is highly temperature dependent. All these parameters are usually determined during laboratory tests and the fluid viscosity and density may be found in tabulated references. Besides the fluid effect there is an effect from the applied strain or stress rate on both the strength and yield properties. This phenomenon couples with the critical frequency through the use of a previously published study on the rate dependence.The data show that the Biot critical frequency can be used as a common friction factor and is useful in combining laboratory results. It is also inferred that the observed water weakening phenomenon may be attributed to the friction between solid and fluid. The scope for the applicability of the Biot critical frequency as a friction factor is in analysis of the compaction of chalk fields where the effect of different fluids and temperatures is relevant. IntroductionThe weakening effect of water in chalk is significant for North Sea reservoir subsidence and several experimental studies have focused on the subject. This paper reviews the results from these test series in order to match the theoretical considerations and find the governing physical properties. Gutierrez et al. (2000) found higher friction for oil saturated chalk (42˚) than water saturated (38˚) in simple tilt tests on a large test series on chalk samples submerged in either oil or water. The chalk studied is Lägerdorf chalk from a quarry in northwest Germany. While the solid-solid friction is one location for the friction forces in the submerged simple tilt test, the fluid-solid friction should thus be considered as well. This causes our focus on fluid-solid friction as a possible mechanism for weakening when assuming no alteration of the chalk surface and consequently no change i...