The principle of a matrix acidizing treatment in carbonated reservoir is to bypass damaged near wellbore zone by creating empty channels called wormholes. The success of the stimulation depends on the ability of an operator to control the unstable process producing those wormholes. Length, size and density of these channels depend on numerous parameters from injection rate to rock properties. Significant efforts have been made in both experimental and numerical studies to optimize stimulation procedures. Today, core-scale numerical models can successfully reproduce the dissolution process, but they are limited in their ability to simulate wormholes at the wellbore scale. Large-scale models are based on semiempirical approaches.

We present in this paper a new simulator for matrix acidizing, built to simulate full acid treatment while considering every mechanism involved in the dissolution process at all physical length scales. It is based on a dual porosity model written at the wellbore scale, and derived from a volume averaging of the Dar?y-scale equations describing acid-rock local equilibrium dissolution. This model can reproduce different types of dissolution patterns, from compact to uniform through dominant wormhole patterns, and it accounts for wellbore-scale heterogeneities. An application of the simulator is presented in this paper. For a given damaged well, we first illustrate the interaction between the wormholing dynamics and the formation heterogeneities. Then we study the optimization of the treatment design, which is function of fluid placement and flow rate. For a set of acidizing parameters, we extract the resulting specific skin factors along the well from simulations. The skin values of each layer are then introduced in a reservoir simulator to calculate the well productivity. An objective function using this productivity change is minimized by an inversion algorithm, to converge toward optimum values of the treatment parameters.

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