We study dissolution in a chemically heterogeneous medium consisting of two minerals with contrasting initial structure and transport properties. We perform a reactive transport experiment using CO2-saturated brine at reservoir conditions in a millimeter-scale composite core composed of Silurian dolomite and Ketton limestone (calcite) arranged in series. We repeatedly image the composite core using X-ray microtomography (XMT) and collect effluent to assess the individual mineral dissolution. The mineral dissolution from image analysis was comparable to that measured from effluent analysis using inductively coupled plasma mass spectrometry (ICP-MS). We find that the ratio of the effective reaction rate of calcite to that of dolomite decreases with time, indicating the influence of dynamic transport effects originating from changes in pore structure coupled with differences in intrinsic reaction rates. Moreover, evolving flow and transport heterogeneity in the initially heterogeneous dolomite is a key determinant in producing a two-stage dissolution in the calcite. The first stage is characterized by a uniform dissolution of the pore space, while the second stage follows a single-channel growth regime. This implies that spatial memory effects in the medium with a heterogeneous flow characteristic (dolomite) can change the dissolution patterns in the medium with a homogeneous flow characteristic (calcite).