Summary
This paper presents a new numerical model of inflow to a well with a zone of damaged permeability. It is built on the principle of dividing the wellbore and damaged permeability zone into numerous segments. Simultaneous work of the segments is modeled with the method of velocity-potential theory. The model is applicable for wellbores of different trajectories including horizontal and multilateral wells. The model is focused on the extended application of results obtained during laboratory core testing that include a return-permeability (RP) profile of the core and cleanup parameters. The developed solution includes the effects of anisotropy, reservoir-boundary conditions, and a nonuniform distribution of formation damage in both radial and axial directions. The paper presents the new approach to include depth-variable distribution of damage in skin-factor models. The approach provides for the evaluation of pressure drop in a depth-variable damage zone by the resulting permeability that is defined by flow regime. Laboratory-obtained overall core permeability is associated with a linear flow, and when applied to a zone near the wellbore with radial or elliptic flow, it causes an error because of the depth-variable distribution of damage. The provided numerical simulations show that the impact of this factor on horizontal-well productivity is significant. The developed model is compared with existing analytical solutions of Furui et al. (2002) (FZH) and Frick and Economides (1993) (FE) for the case of a horizontal well with a cone-shaped damaged zone. The results show that a skin-factor transformation originally proposed by Renard and Dupuy (1991) for a case of a uniformly damaged well can be used successfully for the referred-to analytical solutions, which makes them applicable for wells with an elliptic drainage area. In this paper, we also suggest an approach whereby we relate the characteristics of the cleanup of the region near the wellbore to laboratory-testing conditions.
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