New pseudo-skin model for flow convergence to perforations in competent formations

Existing models for calculating pseudo-skin due to perforations give values that do not agree with observed values. In this paper we discuss a new analytical model that can be used for calculating pseudo-skin due to flow convergence to perforations. The model was developed by combining Bernoulli and Forchheimer equations. Geertsmaʹs (1974) correlation was introduced to account for the inertia coefficient β. d our model to calculate skin factors and productivity ratios (PR) for several perforation parameters. The results were compared with results obtained using existing models (Locke, 1981; Klotz et al., 1974; Hong, 1975; Harris, 1966). In terms of trend, results from all the models, including our model, agree. For example, the models show that the productivity index increases with increase in perforation length and shot density. Also, our model agrees with Lockeʹs (1981) finding that if all perforation parameters remain the same, a 90° phasing will give the maximum productivity while 0° phasing will give minimum productivity. tatively, results from our model differ (in some cases significantly) from results from other models. For example, some models predict that for 4 shots/ft (13 shots/m) and 90° phasing, a perforated well will have same productivity as an open-hole completion if the perforation depth is between 4 and 6 in (0.1016–0.1524 m). With our model we predicted that this equivalence will occur if the perforation depth is between 14 and 16 in (0.3556–0.4064 m). idated our model with field data from Brunei and experimental data published by Muskat and McDowell (1950) and Howard and Watson (1952). Our model applies to wells with perforations in competent (consolidated) formations and for modified Reynoldʹs number of up to 1000.