A Model for the Transport of Sand Grains From a Perforation During Underbalance Surge
Authors: Pearson J.R.A. , Zazovsky A.F. 
Published: December 2007

Abstract
A model of cleaning debris out of the perforation during underbalance surge has been developed. The model is based on the following assumptions:the perforation flow is a quasi-steady-state one and it is driven by the transient inflow of the pore fluid to the perforation tunnel andtransport of particles out of the perforation tunnel is accompanied by their settlement under gravity.
The criterion used for satisfactory perforation cleaning is that all particles lying within the perforation tunnel immediately after perforation are washed out from the tunnel during the (underbalance) surge. Subject to certain obvious restrictions, the model allows us to establish the dependence of the underbalance pressure necessary to obtain clean perforations on such parameters as rock permeability (which is consistent with known field and experimental data), pore fluid viscosity and the radius of the perforation tunnel.

Introduction
Perforation cleaning is a key phase of well completion, affecting final well productivity. It is widely accepted in the industry that not all perforations clean up completely; many of them are blocked and do not contribute to production. Two main causes of such inefficiency of perforations are well known:the accumulation of debris inside perforations that decreases their hydraulic conductivity andthe permeability damage near the walls of perforations caused by crushing and recompaction of the rock while perforating, sometimes followed by fines migration during post-perforating flow.
Perforating of weak rocks may be accompanied by the collapse of perforations leading to sand production problems. Previous work on cleanup has focused on the need to mobilize fines in the pores during surging.
This paper concentrates on the fluid mechanics of surge flow and transport of debris; we derive from our model the degree of underbalance (underbalance pressure) required to ensure that all debris is cleared from the perforation cavity by the initial surge flow from the formation into the well after perforation. Too small an underbalance will lead to debris remaining in the perforation cavity, thus providing a probable source of material for later sand production or damage to gravel packs. Too large an underbalance increases the danger of collapse of the rock surrounding the perforation cavity; in some cases, collapse leads to less than complete removal of damaged rock by the surge flow and hence to later sanding problems, or it can lead to total blockage of the perforation.
The dependence of this minimum underbalance pressure for complete cleaning on the cavity radius is successfully included in a dimensionless formulation. The enhancement of formation collapse because of surge flow is also considered briefly.
The model does not take account of the constriction of the perforation tunnel at its exit nor any interaction between particles in calculating the flow field and their trajectories.

Background
Underbalance perforating involves a series of sequential processes: gun firing and charge detonation; jet formation; shock-wave advancement in the wellbore fluid and bubble formation; jet penetration through casing, cement and reservoir rock; pressure relaxation inside the perforation tunnel to the local wellbore pressure; transient surge flow from reservoir into the perforation; and finally flow-rate stabilization followed by steady-state fluid production. Each process has its own characteristic time scale, which it is important to bear in mind when discussing underbalance perforating as a whole.
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