Calculation of Pressures for Foams in Well Completion Processes
Authors: Buslov Ruslan , Towler Brian F. , Amian A.V. 
Published: December 2007

Abstract
A study of the flow and flow-back of two and three phase foams in well-bores is presented. Different schemes for relieving pressure during flow-back are discussed and the effects of liquid flow rate, aeration, and depth of the well on pressures and parameters of flow-back of foam (reduction of bottom hole pressure and volume of removed liquid) are presented and analyzed.
An iterative computation procedure is proposed for calculating well-bore pressures and other parameters of well completion. The proposed solution technique is not limited to a particular composition of foam or to a particular flow model. Changes in density, velocity, viscosity and pressures as foam moves inside the well are properly assessed. Slippage of the gas phase of the foam is also incorporated into the solution. A comparison of calculated and experimental results is presented to demonstrate the predictive capability of the proposed solution technique.

Introduction
Foam based fluids are widely used in many well operations where using the usual circulation agents such as water and mud creates serious problems in the near well bore formation. Such conditions have pointed toward the need for stimulation and circulation fluids, other than a hydrocarbon, which has a low water content. Foam has fulfilled that need because on a volume basis it is composed of a larger percentage gas than liquid.
In well completion it is very important to know what is the bottom hole pressure. Overestimated or underestimated bottom hole pressure can cause serious problems and additional expenses. Some methods of calculating foam properties do not take into consideration the fact that pressure changes along the well-bore. Parameters of foam are calculated at the maximum injection pressure and considered to be uniform. Hence the calculated bottom hole pressure and the measured one have different values.
Foam is composed of gas bubbles dispersed uniformly throughout a continuous liquid phase and cam be treated as a homogeneous fluid with both variable density and viscosity. Because foam quality, density, viscosity and flow rate vary over the length of the well-bore, it is necessary to use an iterative technique which takes these variations into consideration. The iterative technique used here is similar to the method Cullendar and Smith applied to pressures in gas wells wherein the well-bore was divided into segments. This permits changes in quality, density, velocity, viscosity, flow rate and pressure as foam moves inside the well-bore. Gas volume change corresponding to a new average pressure within each well-bore segment was calculated with the real gas law. Foam viscosity for each well-bore segment was calculated according to the equations proposed by Mitchell.
The proposed solution technique is not limited to a particular composition of foam or to a particular flow model. Changes in density, velocity, viscosity and pressures as foam moves inside the well are properly assessed. Slippage of a gas phase of a foam is incorporated into the solution. To calculate well operational parameters with foams as circulation agents we have to know what will be the behavior of foam inside the well and how properties of foam will change along the well-bore.
The behavior of foam inside the well-bore is different from other circulation agents. In the process of well completion we need to consider the energy of compressed bubbles. Using this energy we can decrease the bottom hole pressure 10 - 40 % compared to the bottom hole pressure at the end of circulation. Hence an experimental study of the flow and flow-back of a foam (which takes place after the pump and the compressor are shut down) is also presented in this paper. The reduction of bottom hole pressure during flow-back of foam depends on the method of relieving the pressure during flow-back: through tubing discharge, through annular discharge or through both simultaneously.
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