Most of the carbonates in the Tarim Basin in northwest China are low-porosity and low-permeability rocks. Owing to the complexity of porosity in carbonates, conventional rock- physics models do not describe the relation between velocity and porosity for the Tarim Basin carbonates well. We propose the porous-grain-upper-boundary （PGU） model for estimating the relation between velocity and porosity for low-porosity carbonates. In this model, the carbonate sediments are treated as packed media of porous elastic grains, and the carbonate pores are divided into isolated and connected pores The PGU model is modified from the porous-grain-stiff-sand （PGST） model by replacing the critical porosity with the more practical isolated porosity. In the implementation, the effective elastic constants of the porous grains are calculated by using the differential effective medium （DEM） model. Then, the elastic constants of connected porous grains in dry rocks are calculated by using the modified upper Hashin-Shtrikman bound. The application to the Tarim carbonates shows that relative to other conventional effective medium models the PGU model matches the well log data well.
