Successful acid stimulation of long-horizontal-well intervals in carbonate reservoirs requires effective acid distribution along the entire reservoir length. Such treatments also require large volumes of acid and seawater/brine injection at sufficiently high injection rates to drive the acid wormholes deep into the reservoir. Under these flowing conditions, significantly large tubing friction loss is anticipated unless optimal friction reducer performance in the tubing is maintained throughout the pumping operation. Because prediction of wormhole penetration and corresponding skin factor depends on analysis of downhole-injection pressures at the reservoir face, it is crucial to properly account for these hydrostatic and friction changes prior to evaluation of wormhole length and skin factor. In this study, an integrated flow model has been developed to predict the wellbore-pressure profile and wormhole distribution by tracking the movement of the acid in the wellbore and the formation. The wellbore-flow model is based on steady-state, 1D, pressure-based nodal method. The segmented wellbore in the reservoir interval is then coupled with analytical transient reservoir-flow models. The wormhole propagation in the formation is calculated based on the modified Buijse-Glasbergen correlation and upscaling model developed in our earlier work. The resultant wormholing skin factor is calculated by simulating and updating the changing well injectivity along the entire injection interval at every timestep. The model developed in this work is applicable for both fully completed wells (i.e., radial flow) and selectively completed perforation-cluster wells (i.e., spherical flow) typically employed in carbonate reservoirs. Analysis of injection rates and pressures during acid treatment provides engineers with a way to determine the varying injectivity and tubing friction as stimulation proceeds. The model presented here can be used as a forward model for analyzing real-time treatment rate and pressure histories and can also be used to review past treatments to improve future treatment designs. Using actual field-stimulation data, we also discuss key elements to successful stimulation planning and the diagnosis of matrix-acid treatments to achieve effective wormhole coverage for horizontal completions in carbonate formations.
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