Modelling elastic properties of impure chalk from South Arne Field, North Sea

In impure chalk, the elastic moduli are not only controlled by porosity but also by contact-cementation, resulting in relatively large moduli for a given porosity, and by admixtures of clay and fine silica, which results in relatively small moduli for a given porosity. Based on a concept of solids suspended in pore fluids as well as composing the rock frame, we model P-wave and S-wave moduli of dry and wet plug samples by an effective-medium Hashin-Shtrikman model, using chemical, mineralogical and textural input. For a given porosity, the elastic moduli correspond to a part of the solid (the iso-frame value) forming the frame of an Upper Hashin-Shtrikman bound, whereas the remaining solid is modelled as suspended in the pore fluid. The iso-frame model is thus a measure of the pore-stiffness or degree of cementation of the chalk. The textural and mineralogical data may be assessed from logging data on spectral gamma radiation, density, sonic velocity and water saturation in a hydrocarbon zone, whereas the iso-frame value of a chalk may be assessed from the density and acoustic P-wave logs alone. The iso-frame concept may thus be directly used in conventional log-analysis and is a way of incorporating sonic-logging data. The Rigs-1 and Rigs-2 wells in the South Arne field penetrate the chalk at the same depth but differ in porosity and in water saturation although almost the entire chalk interval has irreducible water saturation. Our model, combined with petrographic data, indicates that the difference in porosity is caused by a higher degree of pore-filling cementation in Rigs-1. Petrographic data indicate that the difference in water saturation is caused by a higher content of smectite in the pores of Rigs-1. In both wells, we find submicron-size diagenetic quartz.