Numerical Modelling of Cuttings Transport With Foam in Horizontal Wells
Authors: Li Y. , Kuru E. 
Published: March 2010

Abstract
In this study, a one-dimensional unsteady-state two-phase mechanistic model of cuttings transport with foam in horizontal wells has been developed. A new critical deposition velocity correlation for foam-cuttings flow is introduced. The model is solved numerically to predict cuttings bed height as a function of the drilling rate, the gas and the liquid injection rates, the rate of gas and liquid influx from the reservoir, and the borehole geometry. Results of the sensitivity analyses study are presented.

Introduction
The Alberta Energy and Utilities Board defines underbalanced drilling (UBD) as "when the hydrostatic head of a drilling fluid is intentionally designed to be lower than the pressure of the formation being drilled, the operation will be considered underbalanced drilling(1)." The benefits of UBD include increased productivity by reducing formation damage, increased rate of drilling bit penetration, minimization or elimination of lost circulation, improved formation evaluation while drilling, reduction or elimination of differential pipe sticking, reduced stimulation requirements, and earlier production.
Foam is favourably used in UBD operations because of its variable density and good cuttings transport ability. Field application of the foamed drilling fluids is very often complicated because of the difficulties encountered in controlling their hydraulic properties. The complex flow mechanism involved in the circulation of foam makes a determination of the optimum combination of liquid and gas injection rates very difficult. Other questions also exist, such as how to predict the bottom-hole pressure and how to combine different controllable variables in order to obtain optimum cuttings transport performance and bit hydraulics.
In order to simulate the hydraulics of the foam drilling realistically, factors including foam rheological properties, drag coefficient of cuttings in foam, formation fluid influx, drillpipe eccentricity, and drilling rate need to be considered in any modelling study. An example of such a modelling study is presented in this article.
Okpobiri and Ikoku(2) developed a semi-empirical model for cuttings transport with air, mist, and foam in vertical wellbores. Harris et al.(3) suggested that foam-particle flow for hydraulic fracturing could be treated as a homogeneous flow. Medley and Liu(4) presented a one-dimensional steady-state foam flow model by modifying earlier models presented by Lord(5) and Sp?rker et al.(6) Drill cuttings and gas were considered as homogeneous internal phases of foam and the mixture properties were used to solve the steady-state mechanical energy balance equation. Owayed(7) developed a one-dimensional steady-state computational model for UBD by assuming a homogeneous flow of foam in a vertical well. The model included the effect of water influx into the wellbore during drilling. Valk? and Economides(8) established a method that combined the principle of volume equalization(9) with the method of constant-internal-phase(3) for foam-proppant flow. Guo et al.(10) presented an analytical model to estimate the bottom hole pressure when drilling with foam in directional wells. They recognized that the compressibility of foam could cause the cuttings concentration at a given depth to be different from the ones at the surface, rendering inappropriate calculations of the minimum required cuttings transport velocities.