•An estimate for the steady convective flux for anisotropic media is developed.•Steady convective dissolution in anisotropic media scales as (kv/kh)1/2.•Steady convective dissolution in heterogeneous models scales in the same fashion.•This theoretical estimate can be used in upscaled models. Enhanced dissolution of CO2 into a saline aquifer due to convective mixing is an important physical process for the secure long-term storage of significant quantities of CO2. Numerical simulations have previously shown that the dissolution rate of CO2 into reservoir brine will stabilise after a certain time period, with only small oscillations about a long-term average. A theoretical estimate for this average long-term mass flux in an isotropic homogeneous reservoir has previously appeared in the literature. In this paper, an estimate for the steady dissolution rate in anisotropic homogenous porous media is developed using a simple theoretical argument. Detailed numerical simulations confirm that the steady dissolution rate scales as (kvkh)1/2 in an anisotropic homogeneous porous media, where kv and kh are the vertical and horizontal permeabilities, respectively. The scaling is also shown to be appropriate for heterogeneous models where vertical heterogeneity is introduced by including a random distribution of impermeable barriers.