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Cuttings transport
Of the many functions that are performed by the drilling fluid, the most important is to transport cuttings from the bit up the annulus to the surface. If the cuttings cannot be removed from the wellbore, they will soon impede drilling.
Overview
In rotary drilling operations, both the fluid and the rock fragments are moving in the annulus. The situation is complicated by the fact that the fluid velocity varies from zero at the wall to a maximum at a point between the pipe outer wall and the wellbore wall. In addition, the rotation of the drillpipe imparts centrifugal force on the rock fragments, which affects their relative location in the annulus. Because of the extreme complexity of this flow behavior, drilling personnel have relied primarily on observation and experience for determining the lifting ability of the drilling fluids. In practice, either the flow rate or effective viscosity of the fluid is increased, if problems related to inefficient cuttings removal are encountered. The result is a natural tendency toward thick muds and high annular velocities. However, increasing the mud viscosity or flow rate can be detrimental to the cleaning action beneath the bit, and cause a reduction in the penetration rate. There may be a considerable economic penalty associated with the use of a higher flow rate or mud viscosity than necessary. Increasing the mud viscosity will not necessarily improve the cuttings transport efficiency in directional and horizontal sections as well. Usually, transport is usually not a problem, if the well is near vertical. However, considerable difficulties can occur when the well is being drilled directionally, because cuttings may accumulate either as a stationary bed at hole angles above about 50° or in a moving, churning bed at lower hole angles. Drilling problems that may result include:
 Stuck pipe
 Lost circulation
 High torque and drag
 Poor cement jobs
 Reduction in rate of penetration
 Faster bit wear
 Losing control of the bottomhole pressure
The severity of such problems depends on the amount and location of cuttings distributed along the wellbore.
Vertical wells
The problem of cuttings transport in vertical wells has been studied for many years, with the earliest analysis of the problem being that of Pigott.^{[1]} Several authors have conducted experimental studies of drillingfluid carrying capacity. Williams and Bruce were among the first to recognize the need for establishing the minimum annular velocity required to lift the cuttings.^{[2]} In 1951, they reported the results of extensive laboratory and field measurements on mud carrying capacity. Before their work, the minimum annular velocity generally used in practice was about 200 ft/min. As a result of their work, a value of about 100 ft/min gradually was accepted. More recent experimental work by Sifferman and Becker indicates that while 100 ft/min may be required when the drilling fluid is water, a minimum annular velocity of 50 ft/min should provide satisfactory cutting transport for a typical drilling mud. ^{[3]}, ^{[4]}
The transport efficiency in vertical wells is usually assessed by determining the settling velocity, which is dependent on:
 Particle size, density and shape
 Drilling fluid rheology, density and velocity
 Hole/pipe configuration
 Pipe rotation and eccentricity
Several investigators have proposed empirical correlations for estimating the cutting slip velocity experienced during rotarydrilling operations. While these correlations should not be expected to give extremely accurate results for such a complex flow behavior, they do provide valuable insight in the selection of drillingfluid properties and pumpoperating conditions. The correlations of Moore, Chien, and Walker and Mayes have achieved the most widespread acceptance.^{[5]}
Deviated wells
Since the early 1980s, cuttings transport studies have focused on inclined wellbores, and an extensive body of literature on both experimental and modeling work has developed. Experimental work on cuttings transport in inclined wellbores has been conducted using flow loops at the U. of Tulsa and elsewhere. Different mechanisms, which dominate within different ranges of wellbore angle, determine:
 Cuttings bed heights and annular cuttings concentrations as functions of operating parameters (flow rate and penetration rate)
 Wellbore configuration (depth, hole angle, hole size or casing/wellbore inside diameter (ID), and pipe size)
 Fluid properties (density and rheological properties)
 Cuttings characteristics (density, size, shape, bed porosity, and angle of repose)
 Pipe eccentricity and rotary speed.
Laboratory experience indicates that the flow rate, if high enough, will remove the cuttings for any fluid, hole size, and hole angle. Unfortunately, flow rates high enough to transport cuttings up and out of the annulus effectively cannot be used in many wells, because of limited pump capacity and/or high surface or downhole dynamic pressures. This is particularly true for high angles with hole sizes larger than 12¼ in. High rotary speeds and backreaming are often used when flow rate does not suffice
Particle slip velocity
The earliest analytical studies of cuttings transport considered the fall of particles in a stagnant fluid, with the hope that these results could be applied to a moving fluid with some degree of accuracy. Most start with the relation developed by Stokes for creeping flow around a spherical particle.^{[6]}
where
μ = Newtonian viscosity of the fluid, Pas;
d_{s} = particle diameter, m;
v_{sl} = particle slip velocity, m/s;
and
F_{d} = total viscous drag force on the particle, N.
When the Stokes drag is equated to the buoyant weight of the particle W,
Then, the slip velocity is given by
where
ρ_{s} = solid density, kg/m^{3};
ρ_{f} = fluid density, kg/m^{3};
and
g = acceleration of gravity, m/s^{2}
Stokes ’ law is accurate as long as turbulent eddies are not present in the particle’ s wake. The onset of turbulence occurs for ....................(4) where the particle Reynolds number is given by ....................(5)
For turbulent slip velocities, the drag force is given by
where f is an empirically determined friction factor. The friction factor is a function of the particle Reynolds number and the shape of the particle given by Ψ, the sphericity. Table 1 gives the sphericity of various particle shapes.
The friction factor/Reynolds number relationship is shown in Fig. 1 for a range of sphericity. The particle slip velocity for turbulent flow is given by
If we define a laminar friction factor, f = 24/Rep, then Eq. 7 is valid for all Reynolds numbers.
NonNewtonian fluids introduce new factors into particlesettling calculations. For a Bingham fluid, the particle will remain suspended with no settling if
where
τ_{y} is the fluid YP. Otherwise, because no other analytic solutions exist, an "apparent" or "equivalent" viscosity is determined from the nonNewtonian fluid parameters. For example, Moore used the apparent viscosity proposed by Dodge and Metzner for a pseudoplastic fluid.^{[4]}
where
μ_{a} = apparent viscosity, Pas;
K = consistency index for pseudoplastic fluid, Pas^{n};
n = power law index;
D_{o} = annulus OD, m;
D_{i} = annulus ID, m;
and
v = annulus average flow velocity.
Chien determines apparent viscosity for a Bingham plastic fluid shown in Eq. 10.^{[7]}
where μ_{p} is the plastic viscosity. The apparent viscosity models with most widespread acceptance are those of Moore.^{[8]}
Carrying capacity of a drilling fluid for vertical wells
The cuttings slip velocity is used to specify the minimum flow rate needed to clean the wellbore. This determination is not as straightforward as one might expect. In rotarydrilling operations, both the fluid and the rock fragments are moving. The situation is complicated further by the fact that the fluid velocity varies from zero at the wall to a maximum at the center of annulus. In addition, the rotation of the drillpipe imparts centrifugal force to the rock fragments, which affects their relative location in the annulus. Because of the extreme complexity of this flow behavior, drilling personnel have relied primarily on observation and experience for determining the lifting ability of the drilling fluid. In practice, either the flow rate or effective viscosity of the fluid is increased if problems related to inefficient cuttings removal are encountered. This has resulted in a natural tendency toward thick muds and high annular velocities. However, increasing the mud viscosity or flow rate can be detrimental to the cleaning action beneath the bit and cause a reduction in the penetration rate. Thus, there may be a considerable economic penalty associated with the use of a higher flow rate or mud viscosity than necessary.
As stated in the previous section, several investigators have proposed empirical correlations for estimating the cutting slip velocity experienced during the drilling process. While these correlations are not extremely accurate, they do give useful qualitative information about the cuttings transport process in vertical wells.
Five percent maximum concentration model for vertical wells
The following model was taken from Clark and Bickham.^{[9]} For vertical well conditions, Fig. 2 shows a schematic of the cuttings transport process in a YPL fluid under laminar flow conditions. The area open to flow is characterized as a tube instead of an annulus. This simplifies the wellbore geometry. The tube diameter is based on the hydraulic diameter for pressuredrop calculations.
Because drilling mud often exhibits a yield stress, there may be a region, near the center of the cross section, where the shear stress is less than the yield stress. There, the mud will move as a plug (i.e., rigid body motion). The plug velocity is v_{p}. The average cuttings concentration and velocity in the plug are c_{p} and v_{cp}, respectively. In the annular region around the plug, the mud flows with a velocity gradient and behaves as a viscous fluid. The average annular velocity of the mud in this region is v_{a}. In addition, for the cuttings in this region, the average concentration and velocity are C_{a} and v_{ca}, respectively.
Crosssectional geometry
First, let us define the basic wellbore geometry. The hydraulic diameter is defined as four times the flow area divided by the length of the wetted perimeter; namely,
For the wellbore annulus, the hydraulic diameter of the wellbore cross section is
where D_{h} is the wellbore diameter, and D_{p} is the drillpipe OD. The equivalent diameter is defined as
where A is the area open to flow. For the wellbore annulus, the equivalent diameter is
The plug diameter ratio is
Flow conditions
The mixture velocity is
where Q_{m} is the volumetric flow rate of the mud and Q_{c} is the volumetric flow rate of the cuttings, which depends on the bit size and the penetration rate. In addition, the mixture velocity can be calculated from the average plug and annulus velocities in the equivalent pipe; namely,
Cuttings concentration
The feed concentration is defined as
The average concentration, c, of cuttings in a short segment with length, Δz, and crosssectional area, A, can be calculated as
The cuttings concentrations in the plug and annular regions are assumed equal. This means that the suspended cuttings are uniformly distributed across the area open to flow. Obviously, this assumption has a major impact, and the actual distribution is probably a function of wellbore geometry, mud properties, cuttings properties, and operating conditions. Thus, we obtain
where
is the average settling velocity in the axial direction. The components of the settling velocities in the axial direction are
and
where
and
C_{D} is the drag coefficient of a sphere, τ_{y} is the yield stress of the mud, and μ_{a} is the apparent viscosity of the mud at a shear rate resulting from the settling cutting.
The value calculated using Eq. 20 is the minimum acceptable mixture velocity required for a cuttings concentration, c. Pigott^{[10]} recommended that the concentration of suspended cuttings be a value less than 5%. With this limit (c = 0.05), Eq. 20 becomes
where c_{o} < 0.05. This implies that the penetration rate must be limited to a rate that satisfies this equality. For nearvertical cases, the critical mudcuttings mixture velocity equals the value of Eq. 25. If the circulation rate exceeds this value, the suspended cuttings concentration will remain less than 5%. However, if the mud circulation velocity is less than the cuttings’ settling velocity, the cuttings will eventually build up in the wellbore and plug it. Back to top
Cuttings transport in deviated wells
A comprehensive cuttings transport model should allow a complete analysis for the entire well, from surface to the bit. The different mechanisms which dominate within different ranges of wellbore angle should be used to predict:
 Cuttings bed heights and annular cuttings concentrations as functions of operating parameters (flow rate and penetration rate)
 Wellbore configuration (depth, hole angle, hole size or casing ID, and pipe size)
 Fluid properties (density and rheology)
 Cuttings characteristics (density, size, bed porosity, and angle of repose)
 Pipe eccentricity
 Rotary speed
Because of the complexity, extensive experimental data were necessary to help formulate and validate the new cuttings transport models.
New experimental data
Largescale cuttings transport studies in inclined wellbores were initiated at the University of Tulsa Drilling Research Projects (TUDRP) in the 1980s with the support of major oil and service companies. A flow loop was built that consisted of a 40ft length of 5in. transparent annular test section and the means to vary and control
 The angles of inclination between vertical and horizontal.
 Mud pumping flow rate.
 Drilling rate.
 Drillpipe rotation and eccentricity.
Tomren et al.^{[11]} found marked difference between the cuttings transport in inclined wellbores and that of vertical wellbores. A cuttings bed was observed to form at inclination angles of more than 35° from vertical, and this bed could slide back down for angles up to 50°. Eccentricity, created by the drillpipe lying on the low side of the annulus, was found to worsen the situation. Analysis of annular fluid flow showed that eccentricity diverts most of the mud flow away from the low side of the annulus, where the cuttings tend to settle, to the more open area above the drillpipe. Okrajni and Azar^{[12]} investigated the effect of mud rheology on hole cleaning. They observed that removing a cuttings bed with a highviscosity mud, a remedy for the holecleaning problem in vertical wells, may in fact be detrimental in highangle wellbores (assuming a zero to low drillpipe rotation) and that a lowviscosity mud that can promote turbulence is more helpful. On the basis of this finding and on the previous study, hole cleaning was found to depend on:
 The angle of inclination
 Hydraulics
 Mud rheological properties
 Drillpipe eccentricity
 Rate of penetration
Becker et al.^{[13]} then showed that the cuttings transport performance of the muds tested correlated best with the lowendshearrate viscosity, particularly the 6rpm Fann VG viscometer dial readings.
By the mid1980s, a general qualitative understanding of the holecleaning problem in highly inclined wellbores had been gained. Because more directional and horizontal wells with longer lateral reaches were being drilled, the need for more and new experimental data created a demand for additional flow loops. In partnership with Chevron, Conoco, Elf Aquitaine, and Philips, TUDRP built a new and larger flow loop, with a 100ftlong test section of 8in. annulus, while construction of new flow loops was also done at HeriotWatt U., British Petroleum, Southwest Research, M.I. Drilling Fluids, and the Inst. Français du Pétrole. All the flow loops had a transparent part of the annular test section that allowed observation of the cuttings transport mechanism. These flow loops provided the necessary tools for collecting the badly needed experimental data.
Because of the new flow loops, a significant amount of experimental data was collected on the effect of different parameters on cuttings transport under various conditions. The observations made and subsequent analysis of the data collected provided the basis for work toward formulating correlations/models.
Larsen conducted extensive studies on cuttings transport, totaling more than 700 tests with the TUDRP ’ s 5in. flow loop. Tests were performed for angles from vertical to horizontal under critical as well as subcritical flow conditions. Critical flow corresponds to the minimum annular average fluid velocity that would prevent stationary accumulation of cuttings bed. Subcritical flow refers to the condition where a stationary cuttings bed forms. Analysis of the experimental data shows that when the fluid velocity is below the critical value, a cuttings bed starts to form and grows in thickness until the fluid velocity above the bed reaches the critical value. The critical velocity was reported in the range of 3 to 4 ft/sec, depending on the value of various parameters, such as:
 Mud rheology
 Drilling rate
 Pipe eccentricity
 Rotational speed
There were several new findings:
 Under subcritical flow conditions, a mediumrheology mud (PV = 14 and YP = 14) consistently resulted in slightly smaller cuttings beds than those obtained with the lowrheology (PV = 7 and YP = 7) or the highrheology (PV = 21 and YP = 21) muds. Calculation of the Reynolds number for the tests suggests that the flow regime for this mud is neither turbulent nor laminar but in the transition range.
 The small cuttings size used (0.1 in.) in the study was more difficult to clean than the medium (0.175 in.) and the large (0.275 in.) sizes (drillpipe rpm 0 to 50). The small cuttings formed a more packed and smooth bed.
 The height of the cuttings bed between 55 and 90° remained about the same, but there was a slight increase at about 65 to 70°.
 Significant backsliding of the cuttings bed was observed for angles from 35 to 55°.
Seeberger et al.^{[14]} reported that elevating the low shear rate viscosities enhances the cuttingstransport performance of oil muds. Sifferman and Becker^{[4]} conducted a series of holecleaning experiments in an 8in. flow loop. Statistical analysis of the data showed interaction among various parameters; thus, simple relationships could not be derived. For example, the effect of drillpipe rotation on cuttings transport depended also on the size of the cuttings and the mud rheology. The effect of rotation was more pronounced for smaller particles and for more viscous muds. Bassal^{[10]} completed a study of the effect of drillpipe rotation on cuttings transport in inclined wellbores. The variables considered in this work were:
 Drillpipe rotary speed
 Hole inclination
 Mud rheology
 Cuttings size
 Mud flow rate
Results have shown that drillpipe rotation has a significant effect on hole cleaning in directional well drilling. The level of enhancement in cuttings removal as a result of rotary speed is a function of a combination of:
 Mud rheology
 Cuttings size
 Mud flow rate
 The manner in which the drillstring behaves dynamically
New cuttings transport models
Larsen et al.^{[15]} developed a model for highly inclined (50 to 90° angle) wellbores. The model predicts the critical velocity as well as the cuttingsbed thickness when the flow rate is below that of the critical flow. Hemphill and Larsen^{[16]} showed that oilbased muds with comparable rheological properties performed about the same. Jalukar et al.^{[17]} modified this model with a scaleup factor to correlate with the data obtained with the 8in. TUDRP flow loop.
Zamora and Hanson,^{[18]} on the basis of laboratory observations and field experience, compiled 28 rules of thumb to improve highangle hole cleaning. Luo and Bern^{[19]} presented charts to determine holecleaning requirements in deviated wells. These empirical charts were developed on the basis of the data collected with the BP 8in. flow loop, and they predicted the critical flow rates required for prevention of cuttingsbed accumulation. The predictions have also been compared with some field data.
Mechanistic modeling
The existing cuttingstransport correlations and/or models have a few empirical coefficients, determined based on laboratory and/or field data. There is a need for developing comprehensive cuttings transport mechanistic models that can be verified with experimental data. Different levels of the mechanistic approach are possible and can be built on gradually. Ideally, a fluid/solids interaction model, which would be coupled and integrated with a fluidflow model to simulate the whole cuttingstransport process, is needed. Campos et al.^{[20]} recently made such an attempt, but much more work is needed to develop a comprehensive solids/liquid flow model.
Ford et al.^{[21]} published a model for the prediction of minimum transport velocity for two modes: cuttings suspension and cuttings rolling. The predictions were compared with laboratory data.
Gavignet and Sobey^{[22]} presented a cuttings transport model based on physical phenomena, similar to that published by Wilson,^{[23]} for slurry flow in pipelines that is known as the doublelayer model. The model has many interrelated equations and a substantial number of parameters, a few of which are difficult to determine. Martin et al.^{[24]} developed a numerical correlation based on the cuttingstransport data that they had collected in the laboratory and in the field.
Clark and Bickham^{[9]} presented a cuttingstransport model based on fluid mechanics relationships, in which they assumed three cuttingstransport modes: settling, lifting, and rolling—each dominant within a certain range of wellbore angles. Predictions of the model were compared with critical and subcritical flow data they had collected with the TUDRP ’ s 5 and 8in.flow loops. A prediction of the model was also used to examine several situations in which poor cuttings transport had been responsible for drilling problems. Campos et al.^{[20]} developed a mechanistic model for predicting the critical velocity as well as the cuttingsbed height for subcritical flow conditions. Their work was based on earlier work by Oraskar and Whitmore^{[25]} for slurry transport in pipes. The model’ s predictions are good for thin muds, but the model needs to be further refined to account for thick muds and pipe rotation. Kenny et al.^{[26]} defined a lift factor that they used as an indicator of cuttingstransport performance. The lift factor is a combination of the fluid velocity in the lower part of the annulus and the mudsettling velocity determined by Chien’ s correlation.^{[27]} Fig. 3 illustrates the basic flow configuration for mechanistic cuttings transport modeling. There are three distinct zones in this model:
 Stationary cuttings bed
 Moving cuttings zone
 “Cuttings free” mudflow zone
The cuttingsfree mud flow creates a shear force at the interface with the moving cuttings bed, which drags the moving cuttings zone along with it. In the moving cuttings zone, gravity forces tend to make the cuttings fall onto the fixed cuttings bed, while aerodynamic and gel forces tend to keep the cuttings suspended. At the interface between the moving cuttings zone and the stationary cuttings bed, fluid friction is trying to strip off cuttings, which are held by gravity and cohesive forces. The balance of these forces determines whether the cuttings bed increases or decreases in depth. The critical flow rate for cuttings transport leaves the cuttings bed unchanged. For effective hole cleaning, the desired flow rate exceeds the critical flow rate.
Field application
When the results of cuttings transport research and field experience are integrated into a drilling program, holecleaning problems are avoided, and excellent drilling performance follows. This has certainly been the case when engineers achieved two new world records in extendedreach drilling.
Guild and Hill^{[27]} presented another example of integration of holecleaning research into field practice. They reported troublefree drilling in two extendedreach wells after they lost one well because of poor hole cleaning. Their program was designed to maximize the footage drilled between wiper trips and eliminate holecleaning backreaming trips before reaching the casing point. They devised a creative way to avoid significant cuttings accumulation by carefully monitoring the pickup weight, rotating weight, and slackoff weight as drilling continued. They observed that cuttings accumulation in the hole caused the difference between the pickup weight and the slackoff weight to keep increasing, while cleaning the hole decreased the difference. By observing the changes in these parameters and by the use of other readily available information, they were able to closely monitor hole cleaning and control the situation.
Air, mist, and foam drilling
Air and mist drilling have several advantages over conventional drilling fluids. The principle advantages are:
 Higher penetration rates
 Longer bit life
 No lostcirculation problems
The usual disadvantages are:
 Control of fluid influx
 Control of highpressure zones
To realize these advantages, it is important to maintain adequate circulation. Determining the required volume flow rate to maintain this "adequate" circulation has always been difficult. The best available technique has been the chart developed by R.R. Angel.^{[28]} This chart allows the estimation of volume circulation rates for various hole sizes, drillpipe sizes, and penetration rates.
One difficulty with Angel ’ s result is that the equation giving the volume flow rate must be solved by trial and error. This difficulty is avoided by using the charts prepared by Angel, provided the case of interest is tabulated or can be estimated from similar cases. A second difficulty is that the drill cuttings are assumed to travel at the same velocity as the air. Angel notes that this is not a conservative assumption, and the analysis by Mitchell^{[29]} demonstrates that the predicted flow rates are 20 to 30% too low. The downhole temperatures used for Angel’ s chart are assumed to be 80°F at the surface, increasing 1°F per 100 ft of depth. There is no convenient way to convert to other temperatures. A final consideration is that the Angel charts do not apply to mist drilling. The addition of water to the air requires increases in both the volume flow rate and standpipe pressures to maintain the same penetration rate. Back to top
Compressible flow
The flow of a compressible fluid can often produce results that seem to go counter to common sense. For instance, consider the steady flow of air in a constant area duct. As with all fluids, there is a pressure loss because of friction, and the pressure decreases continuously from the entrance of the duct to the exit. Unlike the flow of incompressible fluids, the fluid velocity increases from the entrance of the duct to the exit. How could friction make the fluid speed up?
Two facts account for this acceleration:
 First, the gas pressure is proportional to the density (as in the ideal gas law P = ρRT). As the pressure of the gas decreases, the density must decrease also.
 Second, because the mass flow through the duct is constant, the product of density and velocity is constant. Thus, as the density decreases with the pressure, the velocity must increase to maintain the mass flow.
This example demonstrates a typical compressible flow characteristic—the interrelationship of pressure and mass flow. In air drilling, high velocities are needed at bottomhole to remove the cuttings. High velocities result in frictionpressure drops in the drillpipe and annulus, so higher standpipe pressures may be needed to keep the air flowing. Higher standpipe pressures result in higher gas densities, and, hence, result in lower velocities. Fortunately, most airdrilling operations do not result in the vicious circle situation previously described.
Cuttings transport and mist flow in vertical wells
The addition of the effect of cuttings and mist to the equations already developed require two changes. First, the effect of the cuttings and mist on momentum equation must be accounted for; and second, the forces exerted on the cuttings and mist must be determined. The principles of multiphase flow can be applied to both of these effects.
Two basic ideas are sufficient to develop the modified momentum equation. First, the mass flow rate of the cuttings is easy to determine; it is the product of the penetration rate, the hole area, and the density of the rock. Assuming that the cuttings velocity is known, a "density" for the cuttings mass flow rate can be determined.
This density represents the total mass of cuttings in a volume of the duct divided by the volume of the duct. The ratio of this density to the actual density of the rock is the volume fraction of the cuttings,
The remainder of the volume is filled by the air, with an air inmixture density defined as
With these definitions, the cuttings transport equivalents to the singlephase flow equations can be written as
and
Note that G and G_{s} are constant. The final missing piece is the relationship between the velocity of the air and the velocity of the cuttings. There is a large body of literature on the data necessary to determine this relationship. For example, in the petroleum engineering literature, there is the work of Gray.^{[30]} There is also a large amount of literature on terminal settling velocities for solid particles. Rewritten in terms of flow variables previously defined, this equation becomes
where
and
The term W_{s} is the buoyant weight of the cuttings. The term P is the aerodynamic force exerted on the cuttings by the air, with C_{D} the drag coefficient and δ the ratio of the average particle volume to its crosssectional area. Values of C_{D} can be found for various types of rock in Ref. 35, pages 172–174. The term δ was evaluated for an average cutting diameter of ^{3}/_{8} in. This size is considered to be typical of cuttings at the bit. Higher up the hole, these cuttings get broken into smaller pieces. Because there is no way of predicting the change in average particle size as the cuttings move up the annulus, the average diameter is held fixed at ^{3}/_{8} in. This assumption causes the model to overpredict the relative velocity between the air and the cuttings. This assumption is conservative because higher air velocities are now needed to lift the cuttings. The assumption used by Angel^{[28]} is that the particle velocity and the air velocity are equal, and he notes that this is not conservative.
The addition of mist to the flowing equations is much simpler than adding the cuttings. The water droplets in a mist are very small, and, as a result, the relative velocity between the air and the mist droplets is small. The usual assumption used in twophase flow analysis is that the air and mist move at the same velocity, and simulations using Eq. 36 verify this. Eq. 37, Eq. 38 and Eq. 39 are suitable to model mist flow with the following changes: the mass flow and density of the mist replace those for the cuttings, and the velocities of the mist and the air are set equal.
where c_{p} and c_{v} are the heat capacities at constant pressure and volume, respectively.
This cuttings model predicts highervolume flow rates than Angel ’ s model, which was expected because of the conservative nature of the cuttings model. The cuttings model also shows, however, that the flow rates specified by Angel are adequate to clean the hole, even though they do not satisfy the 3,000 ft/min requirement. The predicted temperatures are reasonably near the undisturbed geothermal temperature, which justifies the temperature assumptions used by Angel. Back to top
Foams
Foams consist of a continuous liquid phase, forming a stable cellular structure that surrounds and entraps a gas phase. Special chemicals, called surfactants, are used to capture the gas phase, at least for a desired period of time. Foams are considered to be dry or wet, depending on the gas content. Wet foams have spherical bubbles with a large amount of liquid between the bubbles, and dry foam bubbles are polyhedral in shape, with contact between the bubbles. In between these two extremes, geometrical structures having both curved and flat faces can exist. Foams are thermodynamically unstable systems because they always contain more than a minimal amount of gas solution interface (Herzhaft et al) ^{[31]}. This interface represents surface free energy, the amount of which can be estimated from knowledge of the surface tension and the interfacial area of the foam. Wherever a foam membrane breaks and the liquid coalesces, there is a decrease in surface free energy. Thus the decomposition of foam into its constituent phases is a spontaneous process. Since the solution phase is always denser than the gaseous phase, there is a strong tendency for the liquid to separate or drain from the main body of foam unless it is circulated or agitated in some way.
Foams can have extremely high viscosity. In all instances, their viscosity is greater than the viscosities of either the liquid or the gas that they contain (GRI ^{[32]}). At the same time, foam densities are much lower than the density of water. Foams are stable at high temperatures and pressures. So, by using foam as a drilling fluid, its high viscosity allows efficient cuttings transport and its low density allows underbalanced conditions to be established; thus formation damage is minimized. Foams are also preferred when water influx is a problem because they can handle large amounts of water.
Foams are being used in a number of petroleum industry applications that exploit their high viscosity and low liquid content. Some of the earliest applications for foam dealt with its use as a displacing agent in porous media and as a drilling fluid. Following these early applications, foam was introduced as a wellbore circulating fluid for cleanout and workover applications. In the mid1970s, N_{2}based foams became popular for both hydraulic fracturing and fractureacidizing stimulation treatments. In the late 1970s and early 1980s, foamed cementing became a viable service, as did foamed gravel packing. Most recently, CO_{2} foams have been found to exhibit their usefulness in hydraulic fracturing stimulation.
Regardless of why they are applied, these compressible foams are structured, twophase fluids that are formed when a large internal phase volume (typically 55 to 95%) is dispersed as small discrete entities through a continuous liquid phase. Under typical formation temperatures of 90°F (32.2°C) encountered in stimulation work, the internal phases N_{2} or CO_{2 }exist as a gas and, hence, are properly termed foams in their enduse application. However, the formations of such fluids at typical surface conditions of 75°F (23.9°C) and 900 psi [ 6205 kPa] produce N_{2} as a gas but CO_{2} as a liquid. A liquid/liquid twophase structured fluid is classically called an emulsion. The enduse application of the twophase fluid, however, normally is above the critical temperature of CO_{2} at which only a gas can exist, so we consider the fluids together as foams. The liquid phase typically contains a surfactant and/or other stabilizers to minimize phase separation (or bubble coalescence). These dispersions of an internal phase within a liquid can be treated as homogeneous fluids, provided bubble size is small in comparison to flow geometry dimensions. Volume percent of the internal phase within a foam is its quality. The degree of internal phase dispersion is its texture. At a fixed quality, foams are commonly referred to as either fine or coarse textured. Fine texture denotes a high level of dispersion characterized by many small bubbles with a narrow size distribution and a high specific surface area, and coarse texture denotes larger bubbles with a broad size distribution and a lower specific surface area. Back to top Because foams exhibit shearratedependent viscosities in laminar flow, they are classified as nonNewtonian fluids. In addition to shear rate, their apparent viscosities also appear to be dependent on quality, texture, and liquidphase rheological properties. Measured laminarflow apparent viscosities generally are larger than those of either constituent phase at all shear rates. When the liquid phase is thickened by addition of solids, soluble highmolecularweight polymers, or other viscosifying agents, we see production of even larger foam viscosities. While laminar flow is characterized by strictly viscous energy dissipation, turbulent flow is characterized more by kinetic than viscous energy dissipation. Density and velocity are the factors that establish kinetic energy, and reduced foam density may outweigh an increased viscosity contribution and produce a turbulentflow friction loss less than liquidphase friction loss. Soluble highmolecularweight polymers produce a form of turbulent drag reduction that is analogous to that which occurs in a nonfoamed liquid. In this case, a substantial dragreduction effect is evident when one compares the turbulentflow friction loss of foams with and without a gelled liquid phase.
Interactions between forces caused by surface tension, viscosity, inertia, and buoyancy produce a variety of effects observable in foams. These effects include different bubble shapes and sizes. Anomalous effects have been attributed to slippage as well as bubble size or texture. Buoyancy and inertia forces act on the foam and tend to destroy the discrete bubble structure, which makes the foam dynamically unstable. However, when work is performed on foam, as is the case when foam flows in a pipe, the bubble structure is being destroyed dynamically and then rebuilt, making the foam macroscopically act as a homogeneous fluid.
Beyer et al.^{[33]} developed foam flow equations from data collected in horizontal pipes. They observed slippage, applied Mooney ’ s method for flow data correction, and correlated the data with a Bingham plastic flow model. Blauer et al.^{[34]} concluded that foam behaves as a Bingham plastic without slippage in laminar flow. They equated the BuckinghamReiner equation to the HagenPoiseuille equation to determine an expression for effective viscosity for use in conventional Newtonian fluid laminar and turbulentflow frictionloss relationships.^{[35]} A critical Reynold’ s number of 2,100 was used to denote transition from laminar to turbulent flow. To the best of our knowledge, they present the only experimental turbulent foam flow data in the literature. Sanghani and Ikoku^{[36]} studied the rheological properties of foam flowing in an annulus and concluded that foam rheological behavior was best represented as a pseudoplastic fluid. They also stated that their data could be represented by a Bingham plastic model and a yield pseudoplastic model without large errors. Earlier investigators noted dragreduction effects in turbulent twophase flows when dragreducing additives were introduced into the liquid phase. These investigators, however, did not deal directly with foam flow but with such diverse twophase flow regimes as slug, plug, and annular mist. The importance of foam rheological properties has been recognized by investigators; however, very little agreement exists among them. Foam has been characterized as a Bingham plastic, a pseudoplastic, and a yield pseudoplastic. Slippage has been observed in some, but not all, cases. Unexplained anomalous effects were observed in many cases. Bubble size and shape have been considered and neglected. All these vastly different observations indicate that foam is a very complex fluid that could exhibit a number of characteristics. All investigators agree, however, that a rheological dependence on quality exists. That foams in general exhibit a yield stress is also well supported. Investigations have been conducted primarily with water as the liquid phase. Cuttings transport using foam in horizontal and inclined wellbores has been investigated in the past both experimentally and theoretically. A brief summary of critical work on cuttings transport with foam in horizontal and highly inclined wellbores is presented below.
Extensive experimental work was conducted that considered foamingagent selection and optimum concentration, salt/oil contaminants, rheological characterization of foams, development of a flow loop to test the foamcarrying capacity in highangle wells, definition of the test procedure and matrix, and analysis of the results (Martins and Lourenco ^{[37]}). After 60 bed tests were performed in a cuttingstransport flow loop, correlations were proposed to predict the cuttingsbed erosion capability in horizontal wells as functions of the foam quality and the mixture's Reynolds number.
Using the principles of mass and linear momentum conservation, a model consisting of three layers (motionless bed  observed in most experiments, moving foamcuttings mixture and foam free of cuttings) was presented (Ozbayoglu et al. ^{[38]}). As part of this study, cuttings transport experiments were conducted at inclinations of 7090 degrees for a wide range of foam flow velocities and ROPs. At a given flow rate and rate of penetration, bed thickness increases with an increase in foam quality. There is little effect of inclination angles within the considered range.
In another study, a onedimensional, unsteadystate, twophase mechanistic model of cuttings transport with foam in horizontal wells was developed (Li and Kuru ^{[39]}). In this model a new critical deposition velocity correlation for foamcuttings 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.
A critical foam velocity correlation has been proposed to predict the minimum foam flow rate required to remove or prevent the formation of stationary cuttings beds on the lowside of highly deviated and horizontal wells (Li and Kuru ^{[40]}). The effects of key drilling parameters (i.e. drilling rate, annular geometry, foam quality, bottomhole pressure and temperature) on the critical foam velocity were investigated.
Horizontal foamflow behavior in pipes and annular geometry under elevated pressures and temperatures was presented (Lourenco et al ^{[41]}). The study is empiricallybased and covers the effects of foam quality, foam texture, pressure, temperature, and geometry of the conduit on the rheological response of foams. This study is important since it is the first experimental work on foam flow under high pressure – high temperature conditions.
An experimental study of cuttings transport with foam at intermediate angles was conducted in the TULPAT flow loop using an anionic surfactant to determine the effects of inclination angle, foam quality, foam velocity and rate of penetration (ROP) on cuttings transport (Capo et al ^{[42]}). It is shown in this study that the transport of cuttings (in terms of cuttings concentration) improves when using foams of low quality. Also, inclination and rate of penetration (ROP) have a direct impact on insitu cuttings concentration.
Cuttings transport experiments were carried out at elevated pressures (100 to 400 psi) and temperature (80 to 170 °F) conditions on the TUACTF flow loop using foam and hydroxylethylcellulose polymer (HEC) mixtures with various liquid, gas and cuttings injection rates (Chen et al ^{[43]}). Two flow patterns, stationary cuttings bed and fully suspended flow, were observed during the cuttings transport tests. The flow patterns depend on polymer concentration, foam quality, and annular velocity.
The TUACTF was used to investigate the effects of pipe rotation, foam quality and velocity, and downhole pressure and temperature on cuttings transport and pressure losses in a horizontal wellbore (Duan et al ^{[44]}). Experiments were conducted with backpressures from 100 to 400 psi and temperatures from 80 to 160 °F. Pipe rotary speeds were varied from 0 to 120 RPM, with foam qualities ranging from 60 to 90% and foam velocities from 2 to 5 ft/sec. It was found that pipe rotation not only significantly decreases cuttings concentration in a horizontal annulus but also results in a considerable reduction in frictional pressure loss.
Effect of major drilling parameters on cuttings transport
Nazari et al.^{[45]} published a review on cuttings transport. Based on this paper, a summary of the influence of major drilling parameters on cuttings transport in deviated and horizontal wells are presented as follows:
 Mud flow rate – significant positive effect
 Increasing the annular velocity by increasing the flow rate decreases the cuttings bed height significantly.
 Mud rheology – moderate positive or negative effect depending on cuttings size, pipe rotation, hole inclination, and annular eccentricity
 Increasing the yield point to plastic viscosity ratio5 increases the carrying capacity6 in concentric annuli.
 Increasing apparent viscosity, yield point and initial gel strength increases the carrying capacity in low and medium annular velocity in concentric annuli.
 Cuttings roll in low viscosity mud is harder than in high viscosity mud.
 Newtonian fluid yields better cuttings transport than other fluids with same apparent viscosity.
 Higher ‘n’7 value causes higher lift force.
 Higher ’k’8 values for a mud system helps to keep the particles in suspension for longer periods of time.
 Mud rheology has moderate effect on small cuttings removal compared to large cuttings.
 Low viscosity mud is more effective in cuttings transport than high viscosity at the same flow rate.
 Hole angle – significant negative impact with increase in inclination
 Increase in hole angle from vertical to horizontal increases the hydraulic requirement for adequate hole cleaning.
 The increase reaches a plateau at approximately 65 degrees and slight decrease around 70 degrees to horizontal.
 The inclination of approximately 35 degrees or higher causes cuttings bed formation depending on several conditions.
 At approximately 3550 degrees of inclination the tendency of downward cuttings bed sliding is more likely to occur.
 Mud weight – small positive impact
 A small increase in mud density decreases the cuttings bed height.
 Increase in mud density with the same rheology has very small or no effect on hole cleaning.
 Mud type – small to moderate positive effect
 Cuttings bed sliding in the inclination range of 4060 degrees is more prevalent in oil based mud than water based mud. However it seems that the validity of this section results depends on the wettability of the formation.
 Oil based mud and water based mud having the same rheology generally perform the same in hole cleaning.
 In the inclination range of 4050 degrees, water based mud performs slightly better than oil based mud in cleaning the wellbore.
 Different mud types lead to different bed consolidation.
 Gelled drilling fluid in the well is a major hole cleaning problem and it could be reduced by choosing an oil based mud.
 New generation muds with high power index, n, at a low shear rate are effective in hole cleaning.
 Hole size – small to no effect for the same annular fluid velocity
 Lower velocities are required to remove the cuttings from holes with small sizes. In the case of the large annulus, it was often not possible to initiate cuttings rolling up the annulus, due to a rapid transition from cuttings suspension to stagnation when there was a slight decrease in the flow rate.
 Hole size effect has a negligible effect on hole cleaning assuming that the annular velocity is the same.
 Rotation speed – significant positive effect
 Rotation speed is more effective in inclined wells than vertical wells. However, a relation including both rotation and inclination has not been presented yet.
 In a small annulus the effect of rotation is more dominant than a large annulus.
 Near horizontal wellbores, low ROP and small cuttings are the most desirable conditions for using pipe rotation effectively.
 After drilling ceases, maintaining pipe rotation helps bed erosion and removes residual cuttings.
 Formation of Taylor vortices (after a specific rotational speed) assists in increasing the lift force in horizontal sections.
 Rotation enhances cuttings removal from the narrow side of an eccentric well.
 Rotation is also an effective element in removing small cuttings.
 Eccentricity  significant negative effect
 Annular eccentricity which is a result of inclination, weight on bit, etc, is influential in cuttings transportation.
 It is believed that it is more an internal state than an input.
 The best transportation occurs when the pipe is concentric.
 ROP – moderate negative effect
 Increase in ROP increase hydraulic requirement for effective hole cleaning.
 Drill bit type – unknown influence due to the regrinding of cuttings after they have been generated
 Bit type is not a dynamic input but it affects many drilling elements such as cutting size and ROP.
 Number of nozzles and their sizes is also optimized under the criteria of jet impact force or hydraulic horsepower.
 It seems that the combination of different nozzle sizes provide better cleaning.
 Drag coefficient, which is a good measurement of frictional force between solid and liquid phases, decreases by a higher number of bit nozzles (with the same diameter) and less flow rate.
 Cutting size – small negative or positive impact depending on several conditions
 Smaller cuttings are more difficult to remove.
Summary guidelines for efficient hole cleaning
Based on the results of many laboratories' research and various field experiences and observations, the following general guidelines are recommended. (See Hole cleaning)
 Design the well path so that it avoids critical angles, if possible.
 Use topdrive rigs, if possible, to allow pipe rotation while tripping.
 Maximize fluid velocity, while avoiding hole erosion, by increasing pumping power and/or using largediameter drillpipes and drill collars.
 Design the mud rheology so that it enhances turbulence in the inclined/horizontal sections while maintaining sufficient suspension properties in the vertical section.
 In largediameter horizontal wellbores, where turbulent flow is not practical, use muds with highsuspension properties and muds with high meterdial readings at low shear rates.
 Select bits, stabilizers, and bottomhole assemblies (BHAs) with minimum crosssectional areas to minimize plowing of cuttings while tripping.
 Use various holecleaning monitoring techniques including a drilled cuttings retrieval rate, a drilled cuttings physical appearance, pressure while drilling, and a comparison of pickup weight, slackoff weight, and rotating weight.
 Perform wiper trips as the hole condition dictates.
Nomenclature
a  =  acoustic velocity, m/s 
α_{vs} , b_{vs}  =  constants that include the viscometer dimensions, the spring constant, and all conversion factors 
A  =  flow area (see subscripts), m^{2} 
c  =  average concentration of cuttings overall 
c_{a}  =  cuttings concentration in annular region 
c_{o}  =  feed concentration of cuttings 
c_{p}  =  cuttings concentration in plug region 
C  =  compressibility 
C_{d}  =  discharge coefficients for the flow through an area change, dimensionless 
C_{D}  =  drag coefficient, dimensionless 
C_{e}  =  pressure drop correction factor for pipe eccentricity, dimensionless 
C_{p}  =  heat capacity at constant pressure, J/kgK 
C_{v}  =  heat capacity at constant volume, J/kgK 
d_{s}  =  particle diameter, m 
D  =  characteristic length in Reynolds number, m 
D_{e}  =  special equivalent diameter for yield power law fluid, m 
D_{eq}  =  equivalent diameter, m 
D_{hyd}  =  hydraulic diameter, m 
D_{h}  =  wellbore diameter, m 
D_{i}  =  inside diameter, m 
D_{o}  =  outside diameter, m 
D_{p}  =  drillpipe outside diameter, m 
D_{plug}  =  plug diameter, m 
F_{d}  =  total viscous drag force on the particle, N 
g  =  acceleration of gravity, m/s^{2} 
G  =  mass flow rate density of mixture, kg/m^{3–s} 
G_{s}  =  mass flow rate density of solids, kg/m^{3–s} 
h  =  specific enthalpy, J/kg 
h  =  total friction pressure drop, Pa/m 
He  =  Hedstrom number 
H_{s}  =  holdup of solid particles, volume fraction of solids 
k  =  absolute pipe roughness, m 
k  =  c_{p}/c_{v} 
K  =  consistency index for pseudoplastic fluid, Pas^{n} 
L  =  length of viscometer bob, m 
m  =  powerlaw exponent for HerschelBulkley fluids 
n  =  power law exponent for pseudoplastic fluids 
p_{n}  =  pressure in bit nozzle, Pa 
p_{r}  =  pressure in bit annular area, Pa 
P  =  pressure, Pa 
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=  aerodynamic force exerted on the cuttings by the air, N 
Q  =  heat transferred into volume, W 
Q_{c}  =  volumetric flow rate of the cuttings, m^{3}/s 
Q_{m}  =  volumetric flow rate of the mud, m^{3}/s 
r_{i}  =  inside radius of annulus, m 
r_{o}  =  outside radius of annulus, m 
Re  =  Reynolds number 
Re_{p}  =  particle Reynolds number 
R_{r}  =  r_{i}/r_{o} 
t  =  time, s 
T  =  absolute temperature, °K 
u  =  radial displacement, m 
v  =  average velocity, m/s 
v_{mix}  =  mixture velocity, m/s 
v_{sa}  =  average cuttings velocity in annular region, m/s 
v_{sp}  =  average cuttings velocity in plug, m/s 
W  =  buoyant weight or particle, N 
W_{s}  =  buoyant weight of the cuttings, N 
x  =  parameter in settling velocity equation 
y  =  parameter in settling velocity equation 
Y_{a}  =  parameter in settling velocity equation 
ΔP  =  pressure drop, Pa 
Δt  =  time increment, s 
Δv  =  change in velocity, m/s 
λ_{P}  =  D_{plug}/D_{eq} , the plug diameter ratio 
μ  =  Newtonian viscosity of the fluid, Pas 
μ_{a}  =  apparent viscosity, Pas 
μ_{p}  =  plastic viscosity, centipoise 
ρ  =  fluid density, kg/m^{3} 
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=  fluid inmixture density, kg/m^{3} 
ρ_{ƒ}  =  fluid density in solid/fluid mixture, kg/m^{3} 
ρ_{s}  =  solid density in solid/fluid mixture, kg/m^{3} 
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=  solid inmixture density, kg/m^{3} 
υ_{ƒ}  =  Poisson’
s ratio for the formation 
Subscripts
o = upstream, initial, or inlet
Superscripts
 = upstream properties
References
 ↑ Pigott, R.J.S. 1941. Mud Flow in Drilling. In API Drill. & Prod. Prac, 91.
 ↑ Williams, C.E. and Bruce, G.H. 1951. Carrying Capacity of Drilling Muds. Trans., AIME, 192: 111–120.
 ↑ ^{3.0} ^{3.1} Sifferman, T.R., Myers, G.M., Haden, E.L. et al. 1974. Drill Cutting Transport in Full Scale Vertical Annuli. J. Pet Tech 26 (11): 12951302. SPE4514PA. http://dx.doi.org/10.2118/4514PA.
 ↑ ^{4.0} ^{4.1} ^{4.2} Sifferman, T.R. and Becker, T.E. 1992. Hole Cleaning in FullScale Inclined Wellbores. SPE Drill Eng 7 (2): 115–120. SPE20422PA. http://dx.doi.org/10.2118/20422PA; Trans., AIME, 293.
 ↑ Walker, R.E. and Mayes, T.M. 1975. Design of Muds for Carrying Capacity. J. Pet Tech 27 (7): 893900. SPE4975PA. http://dx.doi.org/10.2118/4975pa; Trans., AIME, 259.
 ↑ Stokes, G.G. 1845, 1851. Transactions of the Cambridge Philosophical Society, 8, 9.
 ↑ Chien, S.F. 1971. Annular Velocity for Rotary Drilling Operations. Proc., SPE Fifth Conference on Drilling and Rock Mechanics, Austin, Texas, USA, 5–16.
 ↑ Moore, P.L. 1974. Drilling Practices Manual. Tulsa, Oklahoma: Petroleum Publishing Co.
 ↑ ^{9.0} ^{9.1} Clark, R.K. and Bickham, K.L. 1994. A Mechanistic Model for Cuttings Transport. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 2528 September. SPE28306MS. http://dx.doi.org/10.2118/28306MS.
 ↑ ^{10.0} ^{10.1} Bassal, A.A. 1995. A Study of the Effect of Drill Pipe Rotation on Cuttings Transport in Inclined Wellbores. MS thesis, U. of Tulsa, Tulsa, Oklahoma.
 ↑ Tomren, P.H., Iyoho, A.W., and Azar, J.J. 1986. Experimental Study of Cuttings Transport in Directional Wells. SPE Drill Eng 1 (1): 4356. SPE12123PA. http://dx.doi.org/10.2118/12123PA.
 ↑ Okrajni, S. and Azar, J.J. 1986. The Effects of Mud Rheology on Annular Hole Cleaning in Directional Wells. SPE Drill Eng 1 (4): 297308. SPE14178PA. http://dx.doi.org/10.2118/14178pa; Trans., AIME, 285.
 ↑ Becker, T.E., Azar, J.J., and Okrajni, S.S. 1991. Correlations of Mud Rheological Properties With CuttingsTransport Performance in Directional Drilling. SPE Drill Eng 6 (1): 16–24; Trans., AIME, 291. SPE19535PA. http://dx.doi.org/10.2118/19535PA.
 ↑ Seeberger, M.H., Matlock, R.W., and Hanson, P.M. 1989. Oil Muds in LargeDiameter, Highly Deviated Wells: Solving the Cuttings Removal Problem. Presented at the SPE/IADC Drilling Conference, New Orleans, 28 February3 March. SPE18635MS. http://dx.doi.org/10.2118/18635MS.
 ↑ Larsen, T.I., Pilehvari, A.A., and Azar, J.J. 1993. Development of a New Cuttings Transport Model for HighAngle Wellbores Including Horizontal Wells. Presented at the SPE Rocky Mountain Regional/Low Permeability Reservoir Symposium, Denver, 12–14 April. SPE25872MS.
 ↑ Hemphill, T. and Larsen, T.I. 1993. HoleCleaning Capabilities of OilBased and WaterBased Drilling Fluids: A Comparative Experimental Study. Presented at the SPE Annual Technical Conference and Exhibition, Houston, 3–6 October. SPE26328MS.
 ↑ Jalukar, L.S. et al. 1993. Extensive Experimental Investigation of Hole Size Effect on Cuttings Transport in Directional Well Drilling. Paper presented at the ASME Fluids Engineering Division Annual Summer Meeting, San Diego, California, USA, 7–12 July.
 ↑ Zamora, M. and Hanson, P. 1991. More Rules of Thumb to Improve High Angle Hole Cleaning. Pet. Eng. Intl.: 22.
 ↑ Luo, Y., Bern, P.A., and Chambers, B.D. 1992. FlowRate Predictions for Cleaning Deviated Wells. Presented at the SPE/IADC Drilling Conference, New Orleans, 18–21 February. SPE23884MS. http://dx.doi.org/10.2118/23884MS.
 ↑ ^{20.0} ^{20.1} Campos, W. et. al. 1994. A Mechanistic Modeling of Cuttings Transport in Highly Inclined Wells. ASME FED LiquidSolid Flows 189: 145–155.
 ↑ Ford, J.T., Peden, J.M., Oyeneyin, M.B. et al. 1990. Experimental Investigation of Drilled Cuttings Transport in Inclined Boreholes. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 23–26 September. SPE20421MS. http://dx.doi.org/10.2118/20421MS.
 ↑ Gavignet, A.A. and Sobey, I.J. 1989. Model Aids Cuttings Transport Predictions. J. Pet Tech 41 (9): 916–922; Trans., AIME, 287. SPE15417PA. http://dx.doi.org/10.2118/15417PA.
 ↑ Wilson, K.C. 1970. Slip Point of Beds in SolidLiquid Pipeline Flow. J. Hydrol. Division of ASCE 96, HYI, 1.
 ↑ Martin, M., Georges, C., Bisson, P. et al. 1987. Transport of Cuttings in Directional Wells. Presented at the SPE/IADC Drilling Conference, New Orleans, 1518 March. SPE16083MS. http://dx.doi.org/10.2118/16083MS.
 ↑ Oraskar, A.D. and Whitmore, R.L. The Critical Velocity in Pipeline Flow of Slurries. AIChE. J. 26 (4): 550.
 ↑ Kenny, P., Sunde, E., and Hemphill, T. 1996. Hole Cleaning Modelling: What's 'n' Got To Do With It? Presented at the SPE/IADC Drilling Conference, New Orleans, 1215 March. SPE35099MS. http://dx.doi.org/10.2118/35099MS.
 ↑ ^{27.0} ^{27.1} Guild, G.J., Wallace, I.M., and Wassenborg, M.J. 1995. Hole Cleaning Program for Extended Reach Wells. Presented at the SPE/IADC Drilling Conference, Amsterdam, 28 February2 March. SPE29381MS. http://dx.doi.org/10.2118/29381MS.
 ↑ ^{28.0} ^{28.1} Angel R.R. "Volumetric Requirements for Air and Gas Drilling, Gulf Publishing Company, 1958.
 ↑ Mitchell, R.F. 1983. Simulation of Air and Mist Drilling for Geothermal Wells. J. Pet Tech 35 (11): 21202126. SPE10234PA. http://dx.doi.org/10.2118/10234PA.
 ↑ Gray, K.E. 1958. The Cutting Carrying Capacity of Air at Pressures Above Atmospheric. Trans., AIME, 213: 180185. SPE874G.
 ↑ Herzhaft B., Toure A., Bruni F., Saintpere S. 2000. Aqueous Foams for Underbalanced Drilling: The Question of Solids. Presented at the SPE Annual Technical Conference and Exhibition, Dallas, 14 October. SPE62898MS. http://dx.doi.org/10.2118/62898MS.
 ↑ GRI. 1997. Underbalanced Drilling Manual. 2.272.130, GRI.
 ↑ Beyer, A.H., Millhone, R.S., and Foote, R.W. 1972. Flow Behavior of Foam as a Well Circulating Fluid. Presented at the Fall Meeting of the Society of Petroleum Engineers of AIME, San Antonio, Texas, USA, 8–11 October. SPE3986MS. http://dx.doi.org/10.2118/3986MS.
 ↑ Blauer, R.E., Mitchell, B.J., and Kohlhaas, C.A. 1974. Determination of Laminar, Turbulent, and Transitional Foam Flow Losses in Pipes. Presented at the SPE California Regional Meeting, San Francisco, California, USA, 45 April. SPE4885MS. http://dx.doi.org/10.2118/4885MS.
 ↑ Govier, G.W. and Aziz, K. 1987. The Flow of Complex Mixtures in Pipes. Huntington, New York: Robert E. Krieger Publishing Co.
 ↑ Sanghani, V. and Ikoku, C.U. 1982. Rheology of Foam and Its Implications in Drilling and Cleanout Operations. DOE/BC/1007947, US DOE Report, Washington, DC (June 1982).
 ↑ Martins A.L., Lourenco A.M.F., “Foam Property Requirements for Proper Hole Cleaning While Drilling Horizontal Wells in Underbalanced Conditions”, SPE Drilling & Completion, Volume 16, Number 4, pp 195200, December 2001
 ↑ Ozbayoglu M.E., Miska Z.S., Reed T., Takach N., “Cuttings Transport with Foam in Horizontal & HighlyInclined Wellbores”, SPE 79856, SPE/IADC Drilling Conference, 1921 February 2003, Amsterdam, Netherlands
 ↑ Li Y., and Kuru E., “Numerical Modelling of Cuttings Transport With Foam in Horizontal Wells”, Journal of Canadian Petroleum Technology, Volume 42, Number 10, October 2003
 ↑ Li Y., and Kuru E., “Prediction of Critical Foam Velocity for Effective Cuttings Transport in Horizontal Wells”, SPE 89324, SPE/ICoTA Coiled Tubing Conference and Exhibition, 2324 March 2004, Houston, Texas
 ↑ Loureno A.M.F., Miska Z.S., Reed T., Pickell M., Takach N., “Study of the Effects of Pressure and Temperature on the Viscosity of Drilling Foams and Frictional Pressure Losses”, SPE Drilling & Completion, Volume 19, Number 3, pp. 139146, September 2004
 ↑ Capo J., Yu M., Miska Z.S., Takach N., Ahmed R.M., “Cuttings Transport With Aqueous Foam at IntermediateInclined Wells”, SPE Drilling & Completion, Volume 21, Number 2, pp. 99107, June 2006
 ↑ Chen Z., Ahmed R.M., Miska S.Z., Takach N.E., Yu M.. Pickell M.B., Hallman J., “Experimental Study on Cuttings Transport With Foam Under Simulated Horizontal Downhole Conditions”, SPE Drilling & Completion, Volume 22, Number 4, pp. 304312, December 2007
 ↑ Duan M., Miska Z.S., Yu M., Takach N., Ahmed R.M., Hallman J., “Experimental Study and Modeling of Cuttings Transport Using Foam With Drillpipe Rotation”, SPE Drilling & Completion, Volume 25, Number 3, pp. 352362, September 2010
 ↑ Nazari T., Hareland G., Azar J.J., “Review of Cuttings Transport in Directional Well Drilling: Systematic Approach”, SPE 132372, presentation at the SPE Western Regional Meeting held in Anaheim, California, USA, 27–29 May 2010
Noteworthy papers in OnePetro
External links
University of Tulsa Drilling Research Projects (TUDRP)