54 Journal of Canadian Petroleum Technology 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 forma- tion 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 pene- tration, 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 vari- able 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 proper- ties. The complex flow mechanism involved in the circulation of foam makes a determination of the optimum combination of liq- uid 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 opti- mum cuttings transport performance and bit hydraulics. In order to simulate the hydraulics of the foam drilling realisti- cally, factors including foam rheological properties, drag coeffi- cient of cuttings in foam, formation fluid influx, drillpipe eccen- tricity, 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 Spörker et al. (6) Drill cuttings and gas were considered as homogeneous inter- nal 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 well- bore during drilling. Valkó 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 cut- tings concentration at a given depth to be different from the ones at the surface, rendering inappropriate calculations of the mini- mum required cuttings transport velocities. Herzhaft et al. (11) investigated the solids-carrying capacity of foams experimentally, and concluded that efficiency of particles transport increases with the increase of foam quality. Recently, Martins et al. (12) presented an empirical model to predict cuttings bed height during the flow of foam in inclined and horizontal wells. In previous cuttings transport models (2-10) , authors assumed homogeneous flow of solids and foam. In homogeneous flow models, particles are considered uniformly dispersed in foam and slip velocity of solids is neglected in the calculation of pressure drop along the well. Assumption of homogeneous flow, however, implies that the drag force is infinite which leads to overestima- tion of the solids carrying capacity of the foam. In this article, a one-dimensional, unsteady-state model is developed to simulate cuttings transport with foam in horizontal wells. The model is not an ultimate solution for the hole cleaning problem with foam, however, it can be used as a tool to under- stand physical principles governing the cuttings transport phe- nomena and how different factors would influence the cuttings transport performance with foam. The following section explains the model development. Model Development A two-layer model is developed in order to study factors affect- ing cuttings transport with foam in horizontal wells. This approach has been originally used for modelling of slurry trans- port in pipes (13-15) . Several studies in petroleum drilling engineer- ing on cuttings transport modelling have also used the two-layer modelling approach (16-19) . Existence of layers in the form of sta- tionary beds and heterogeneous suspension of cuttings has been verified by many experimental studies (20-22) . A schematic view of a two-layer model for foam-solids flow in a horizontal well is shown in Figure 1. The upper layer consists of a foam-cuttings mixture with a low solids concentration, while the lower layer consists of a stationary bed of cuttings with foam Numerical Modelling of Cuttings Transport With Foam in Horizontal Wells Y. LI, E. KURU University of Alberta 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 geom- etry. Results of the sensitivity analyses study are presented. PEER REVIEWED PAPER (“REVIEW AND PUBLICATION PROCESS” CAN BE FOUND ON OUR WEB SITE)