The use of carbon sequestration and storage (CCS) is an appealing option to meet the ambitious objectives of the Paris Agreement. CO2 emissions can also be injected in active oil fields to perform enhanced oil recovery (EOR). We study a dynamic model of CCS and EOR of an economy subject to a cap constraint on the admissible atmospheric CO2 concentration. CCS can occur in inert reservoirs or in oil fields implementing EOR. We show that if the economy implements EOR it must do so at the beginning of the planning period and stop doing it strictly before being constrained by the carbon cap. When facing the constraint, CCS occurs only in inert reservoirs.