New Effective Stress Law for Predicting Perforation Depth at Downhole Conditions

Abstract

For natural completions, well productivity is proportional to the depth of the perforation tunnels. Perforation depth, in turn, is generally inversely related to the formation effective stress. Accurate productivity modeling, therefore, requires accurate knowledge of the relationship between the downhole stress environment and perforation depth.A comprehensive experimental effort was recently conducted to evaluate the penetration performance of shaped charges into stressed Berea sandstone cores. Rock confining stress (σ c ) and pore fluid pressure (P p ) were varied from ambient to 10,000 psi, to simulate a range of downhole stress environments. This current work featured a broader and more systematic investigation of the influence of pore pressure than previous studies.Our experiments yielded the expected inverse correlation between penetration depth and effective stress (σ eff ). However, the data suggest a new definition of effective stress. Historically, the perforating community has defined σ eff = σ c -P p , but a new treatment (σ eff = σ c -aP p ; a=0.5) better fits present data. Furthermore, this new effective stress law better fits published historical penetration results. Pore pressure's influence on penetration depth is therefore weaker than previously thought; for a given confining stress, increasing pore pressure does increase penetration, but to a lesser extent than conventional models would indicate. The present work suggests that all shaped charges would be similarly affected.These findings are relevant to penetration modeling, and in turn to well productivity modeling and prediction. Further implications are to laboratory testing, regarding scaling of parameters to accurately simulate field conditions. This work culminates an initial application of combined penetration mechanics and geomechanics analyses to the investigation of shaped charge penetration into geologic materials. Future work will address different rock types, additional poroelastic quantities, and dynamic effects as they contribute to pressure-induced strengthening of reservoir rock.

New Predictive Model of Penetration Depth for Oilwell-Perforating Shaped Charges

“…The actual behavior above 16,000 psi is unknown, but this coefficient cannot be negative. As previously reported in [27], a was found to be approximately 0.5 for an 8 ksi sandstone such as Berea. Using the prediction in Eq.…”

“…To first order, this approach assumes the ballistic pore pressure coefficient to be an intrinsic rock property. This simple one-charge/rock-combination-at-a-time approach was used in [27].…”

“…Additional research has revealed the industry's conventional understanding of the influence of pore pressure to be incomplete. The following definition of effective stress has been proposed [24,25,26,27]:…”

Study on the interaction mechanism between laser and rock during perforation

“…Behrmann et al [7] determined that the primary cause of wellbore damage in perforated completions was invasion of pulverized formation rock grains and the resulting low-permeability crushed zone. Grove et al [8] found that perforation depth was generally related to the formation effective stress and that increasing pore pressure increased penetration. Jan et al [9] concluded that creating a dynamic underbalance in the well that would deliberately induce flow into the wellbore for tunnel cleanup minimized this type of damage during the perforating process.…”

A Survey of Industry Models for Perforator Performance: Suggestions for Improvements

“…One relevant finding of this experimental work, which has been recently reported [24][25][26][27], is an improved definition of effective stress. The influence of pore pressure on penetration depth was found to be different than previously thought.…”