Hole-cleaning Model Evaluates Fluid Performance In Extended-reach Wells

Terry Hemphill
Baroid Drilling Fluids Inc.
Houston

The model characterizes hole-cleaning efficiency in the eccentric annuli of extended-reach well bores, evaluates fluid performance while drilling, and predicts fluid rheological properties and pump output levels for optimum cleaning in prewell planning.

Based on the concept of lift factors, the model has been validated by field data and actual drilling conditions. To be useful, hole-cleaning simulations should be modeled under existing or expected conditions. Unrealistic input parameters will yield questionable or unusable results.

For oil-based and synthetic-based fluids, mud-rheological input used in the modeling process should be based on downhole conditions, not surface conditions.

Hole-cleaning problems do not necessarily occur near total depth, but can occur further uphole where hole enlargement or various casing diameters reduce mud velocities. Simulation of cleaning efficiency at several points in the annulus can determine areas of inadequate cleaning.

Theoretical foundations

The following elements are used in the model:

• Herschel-Bulkley rheological modeling of drilling fluids

• Annular-velocity modeling for eccentric drill pipe cases

• Particle-settling velocity modeling for static and dynamic cases

• Vertical-plane lift factors underneath eccentric drill pipe.

The model exclusively deals with the small area which lies underneath the eccentric drill pipe (Fig. 1 [14,893 bytes]). This is where cuttings accumulate during rotation in high-angle well bores.

In this model, the drill pipe's position in the eccentric annulus during rotation is unknown. To compensate for this, a certain level of drill pipe eccentricity is input to cover situations when the rotating drillstring is lifted off bottom. Because there is an infinite number of eccentricities at any given angle of deviation, additional complications include a skewed annulus. In high-angle situations where drill pipe is rotated, a drill pipe eccentricity level of 0.5 is normally used.

Rheological modeling

A number of mathematical steps are used in the model. First, fluid-rheological properties must be adjusted for downhole conditions. For water-based muds, this is generally not required, but is necessary for oil-based and synthetic-based fluids because their properties change dramatically with temperature and pressure.

Rheological properties of downhole oil-based and synthetic-based fluids can be determined from high-pressure, high-temperature (HPHT) viscometer measurements performed in the laboratory.

If these measurements are unavailable, then downhole properties can be predicted using rheological models constructed from extensive HPHT viscometer tests performed on fluids of the same base fluid type.

In these computer models,² the fluid rheological properties are measured at a surface temperature of 120° F. (49° C.) with a conventional six-speed viscometer. They are modified for effects of downhole temperature and pressure, both of which can affect fluid performance significantly.

From the predicted downhole viscometer dial readings, the Herschel-Bulkley rheological model is used exclusively to characterize fluid properties.³ Fluid behavior across the shear-rate spectrum for laminar flow is accurately described by three parameters:

1. Fluid-flow index or fluid-behavior index, n

2. Consistency index or plastic viscosity, K

3. Yield stress, t₀.

Only one value for each of the three parameters is used in the rheological model and for hydraulic calculations. According to current recommendations for drilling mud hydraulic calculations, multiple values of n and K are not required for different cases, which holds when the power-law rheological model is used.⁴

Two commonly found parameters used in other hole-cleaning models are avoided.

First, true yield stress (TYS) calculations are not used because the calculations implicitly assume the fluid-flow index n=1. TYS is commonly calculated by:

where: 0 is the viscometer reading.

Only Newtonian and true Bingham plastic fluids exhibit values with n=1. Water-based muds commonly exhibit n values much less than 1.0, with normal values of 0.40-0.65. Oil-based and synthetic-based fluids usually exhibit higher values of n, normally with values of 0.80-0.85.

As the n values deviate from 1.0, calculations of TYS become more prone to error. In addition, calculations involving TYS are used to approximate yield stress only, and do not give any information regarding plastic-viscosity and flow-index values.

Second, the low shear-rate viscosity (LSRV) term can be misleading in that it only refers to viscosity. However, viscosity is a result of the sum of plastic viscosity and yield stress, divided by the shear rate of interest.

Therefore, the LSRV measurements specify nothing concerning how much of the viscosity is due to plastic viscosity and how much is derived from the yield stress term.

In addition, this parameter is not used in hole-cleaning simulations because it is usually measured at very low shear rates (0.06 sec^-1). According to the latest work on irregularly shaped particle-settling velocities, these shear rates are much less than those experienced by falling cuttings during the settling process.

Annular velocity modeling

With predicted downhole rheological parameters including hole and drill pipe geometry, pump output, and assumed drill pipe eccentricity, the point velocities in the eccentric annulus are modeled using slot-flow approximation techniques.⁵

The calculations are done in a manner similar to that presented in 1990.⁶ The model implicitly assumes that when there is no flow underneath the eccentric drill pipe, cuttings removal is highly inefficient.

Accordingly, the hole-cleaning model calculates the average fluid velocity in a 90° arc immediately underneath the drill pipe (Fig. 1), or a 45° arc each side of the vertical hole.

Particle-settling velocity

The particle-settling velocity underneath eccentric drill pipe is calculated for static conditions using the methodology first presented in 1994,⁷ and later adopted by the API as the recommended procedure for drilling fluids.

Because hole-cleaning in deviated well bores occurs under dynamic conditions, the effect of fluid shear-rates positioned in the narrow gap underneath the eccentric drill pipe is included in the particle-settling velocity calculations.

Lift factors

The three hole-cleaning modules consisting of downhole rheological parameters, average velocity underneath eccentric drill pipe, and narrow-gap, particle-settling velocity are linked together through the use of lift factors.

The calculated lift factors represent ratios between the net upward velocity of the drilling fluid as it moves underneath the eccentric drill pipe (V_up), and the net downward velocity of the particle as it settles underneath the drill pipe (V_down).

These calculations are similar to general transport ratios in vertical well bores where fluid velocities moving upward along the drill pipe are normally greater than drilled rock cutting-settling velocities.

However, fluid velocities can sometimes be very small or even zero when the drill pipe is eccentric and when the fluid mechanics prevent flow underneath the drill pipe. In these cases, the vertical component of velocity is controlled by the cosine of the angle of deviation.

It is necessary to change the divisor when it is zero. The two general equations for calculating lift factors become:

As a result, a lift factor of +1 (V_down = 0), represents perfect cleaning underneath the eccentric drill pipe, and -1 (V_up = 0) represents the worst case scenario with rapid cuttings accumulation.

A lift factor of 0 (V_up = V_down) represents the case where the fluid velocity underneath the eccentric drill pipe is pushing the particle upward and equals the particle-settling velocity. This means that the particle remains suspended in a vertical plane underneath the eccentric drill pipe and is not accumulating into a bed of cuttings.

While it is best to have highly positive lift factors for efficient cleaning, in cases of highly deviated well bores (70-90° from vertical), a lift factor of zero is often acceptable.

In these high-angle situations, there can be very little net upward velocity, and the best option is to at least have the net upward velocity approximate the particle-settling velocity.

Lift factors of -1 denote little-to-no mud velocity moving upward under the eccentric drill pipe and represent a free fall of drilled cuttings and severe bed-cuttings accumulation.

Cleaning problems are predicted when lift factors remain at -1 for an extended period of time. Action in the form of increased pump output, major changes in fluid rheological properties, and/or increased drill pipe rotation should be taken into account in order to avoid excessive torque, packing-off, or stuck pipe problems.

Field applications

Two recent field applications of the hole-cleaning model in the North Sea have been described.⁸ The first example pertains to an extended-reach well that held the world record for horizontal displacement.

The second case pertains to the use of the cleaning model during the drilling operation. This well currently holds the world record for both hole size drilled at high angles and for casing run lengths in the extended-reach well.

Statfjord C-02 revisited

The Statfjord C-02 provides an excellent test case because the cleaning ability of the ester-based fluid in terms of surface rheology had previously been documented.9

The extended-reach sections of Statoil's Statfjord C-02 were drilled with an ester-based invert emulsion.¹⁰

The following items were employed in the reanalysis of data:

Downhole rheological predictions used a mathematical model based on surface information utilized for the Statfjord C-02 ester-based drilling fluid system.²

The model assumed a drill pipe eccentricity of 0.5 and an average cuttings diameter of 0.25 in (0.6 cm).

Simulation inputs for actual hole angles were used in the 121/4-in. and 81/2-in. intervals.

Daily drilling-report data including pump rates and other drilling parameters were utilized in the model.

The lift factors underneath the eccentric drill pipe were calculated with these various input parameters. There were reports of efficient hole-cleaning using the ester-based drilling fluid in this interval.

However, there were problems related to the high angles of deviation (64-83° from vertical) and the exceptionally long horizontal displacement.

(Fig. 2 [45,462 bytes]) shows that around 5,000 m, downhole torque began to rapidly rise, and by 5,400 m, rose above the torque model predictions calculated from the highest friction factor for the ester-based mud system. At that time, penetration rates ranged from 200 to 500 m/day.

Elevated downhole torque levels continued during drilling to approximately 5,600 m. Persistent hole-cleaning problems were recognized, and as a result, penetration rates were reduced to 80-200 m/day until completion of the interval.

While drilling, initial pump rates were 711 gpm and reached a maximum of 811 gpm at 4,900 m. They remained near that level until completion of the interval. At these rates, average annular velocities ranged between 171 and 192 fpm. Hole cleaning in this interval was aided by increased circulation time and drill pipe rotation.

Hole-cleaning efficiency in this interval, characterized by lift factors underneath the eccentric drill pipe, showed that cleaning efficiency was acceptable in the first half of the interval, but was deficient in the latter part.

After 5,000 m, the lift factors became negative and steadily dropped to -1 by 6,000 m measured depth (MD). In this interval, the model correctly predicted hole-cleaning problems beginning around 5,000 m, despite increased pump output.

The precipitous drop in the lift factors from 5,000 m to total depth (TD) was caused by a declining plastic viscosity beginning at 4,900 m MD. Afterward, t₀ levels were raised and the downhole values were maintained at 13-15 lb_f/100 sq ft in response to observed hole-cleaning and torque problems. As a result, the opposite reaction occurred to what was expected.

The drop in plastic viscosity at 4,900 m led to increased particle-settling velocity and a slightly increased mud velocity underneath the eccentric drill pipe. As a result, hole-cleaning efficiency fell.

The subsequent increase in t₀ had a negative effect of nearly choking-off the mud-flow underneath the eccentric drill pipe, thereby reducing V_up.

As a result, accumulation of cuttings increased and problems with erratic downhole torque became more frequent. Hole-cleaning problems continued but were alleviated by reducing penetration rates and increasing circulating time.

With the reduced cuttings load on the downhole system, torque levels returned to acceptable levels and the interval was slowly drilled to TD.

(Fig. 3 [15,861 bytes]), (Fig. 4 [15,887 bytes]), and (Fig. 5 [15,694 bytes]) show the calculated lift factors for the 121/4-in. interval plotted against the predicted downhole values of n, K, and t₀ respectively.

The results for the ester-based drilling fluid system clearly demonstrated the link between cleaning efficiency and mud properties in relation to downhole conditions experienced in this interval. With the large number of variables involved in the modeling process, confidence factors of 95% were not possible. However, the resulting trends shown in the figures are still useful.

The trends indicate that positive lift factors occurred in the 121/4-in. interval when downhole:

• The n values were around 0.81-0.83 or less.

• K values were around 134-140 equivalent (eq) cp (0.28-0.282 lb_f/100 sq ft secⁿ) or more.

• The t₀ values were approximately 8.4 lb_f/100 sq ft or less.

The results show that for the ester-based drilling fluid system, highly elevated values of K and t₀ under downhole conditions do not automatically produce enhanced hole cleaning.

There is a middle ground where the balance between encouraging mud-flow underneath the eccentric drill pipe and providing sufficient suspension of drilled cuttings must be met. To achieve this balance, all mud parameters including n, K, and t₀ must be considered.

81/2-in. hole interval

Pump rates used in this interval ranged between 355 and 411 gpm for average annular velocities in the open hole of 184-213 fpm. With the higher average fluid velocities in the open hole, as compared to those in the 121/4-in. interval, hole cleaning was not a problem while drilling.

In fact, downhole torque levels remained below the operator's best model predictions. (Fig. 6 [14,190 bytes]) shows the calculated lift factors for this interval drilled at a deviation of 84-78° from vertical.

Except for the initial 200-300 m of the interval, calculated lift factors remained at or near zero, a level considered acceptable for hole-cleaning efficiency at very high angles of deviation.

In this interval, downhole n, K, and t₀ levels fluctuated in more narrow ranges than those of the 121/4-in. interval. As a result, the use of trends similar to those in Figs. 3-5 are not meaningful.

However, the average values of the downhole rheological parameters are important, with calculated values of n = 0.88, K = 86 eq cp, and t₀ = 6.2 lb_f/100 sq ft, respectively. A comparison of the downhole rheological parameters that helped produce efficient hole cleaning in the 121/4-in. and 81/2-in. intervals show that they are not necessarily identical or close in numerical value.

Well bore geometry, fluid density, and pump output also affect results and can shift the optimum ranges in fluid rheology for good cleaning performance.

With identification of specific mud-property ranges for n, K, and t₀, hole-cleaning efficiency as described by lift factors can be optimized on future wells with similar profiles and pump outputs.

Sleipner A-2

The original drilling profile of the Sleipner A-2 was similar to the Statfjord C-02. However, a 16-in. bit was used instead of a 121/4-in. bit. Because there were concerns of running 133/8-in. casing in a 16-in. hole, the bit diameter was increased to 171/2 in. A schematic of the Sleipner A-2 well path is shown in (Fig. 7 [17,662 bytes]).

Prewell modeling of hole-cleaning efficiency in the 171/2-in. interval showed constant and highly negative results. With only two mud pumps on the rig, average annular velocities of 90 fpm were predicted in the 171/2-in. interval and lift factors of -1 resulted.

With low pump rates, no amount of fluid rheological optimization could produce adequate lift factors in the modeling process. Equally negative lift factor values of -1 were calculated earlier using a bit diameter of 16 in.

While drilling the 171/2-in. interval, the hole-cleaning model was run daily. Predictions were made during a period of high initial penetration rates, based on calculated lift factors of -1.

The drilling-fluid rheological properties were maintained in the ranges that would promote flow underneath the eccentric drill pipe while providing adequate suspension properties.

Within a day or two, hole-cleaning problems appeared in the form of elevated torque levels and problems during short trips. A third pump was then put on line, but there still was no improvement in hole cleaning. The lift factors remained at -1.

Because the operator paid close attention to rapid torque fluctuations and hole-cleaning problems, reaction times were immediate and no incidents of stuck pipe and avalanching cuttings occurred during this interval.

Nonetheless, the interval was successfully drilled to 3,361 m, a world record at that time for a 75°, 171/2-in. hole. After drilling operations were completed, 133/8-in. casing was cemented with no cuttings problems.

121/4-in. hole interval

In this interval, pump output levels were only slightly higher than those used in the Statfjord C-02 (740-832 gpm). Average annular velocities in the open hole were 171-192 fpm. During this interval, the hole-cleaning model was utilized on a more constant basis.

After modeling the fluid rheological properties for downhole temperature and pressure, the data were input into the hole-cleaning model, and lift factors were calculated at an average hole angle of 75°.

Experience gained from the Statfjord C-02 well was applied towards the Sleipner A-2. There was improved control of fluid plastic viscosity (K) and yield stress (t₀) parameters during the drilling of this interval, and lift factors were generally more positive.

Compared to the 121/4-in. interval of the Statfjord C-02, hole-cleaning efficiency characterized by the cleaning model improved in the 121/4-in. interval.

(Fig. 8 [17,887 bytes]) shows that lift factors underneath the eccentric drill pipe fluctuated between 0.4 and -0.5, and there were no calculated values of -1. Drilling records indicated efficient hole cleaning, and except for downhole tool failures, the interval was drilled without any problems.

Drilling report comments correlated directly with the highly negative lift factors, including comments of steering problems, few cuttings out, decreased penetration rates, and high torque.

The calculated lift factors are plotted against the predicted downhole values of n, K, and (₀ in (Fig. 9 [14,657 bytes]), (Fig. 10 [14,944 bytes]), and(Fig. 11[14,871 bytes]), respectively. The figures show that the ranges of the various rheological parameters were more tightly controlled than those in well C-02, and proves that improved rheological control of fluid parameters can provide more efficient hole cleaning.

Uphole model predictions

The model was also used to gauge hole-cleaning efficiency at 3,000 m and 1,650 m, positioned farther up the annulus inside the 133/8-in. casing where temperatures and pressures were reduced.

Surface-fluid rheological data were first adjusted for the predicted temperature and pressure conditions, and then the hole-cleaning model was run. The results indicated that no hole-cleaning problems were predicted by the model (Fig. 12 [19,562 bytes]). Upon drilling the interval to TD, a 95/8-in. liner was cemented.

81/2-in. hole interval

In the 81/2-in. interval, no major hole-cleaning problems were predicted. Pump output levels were 497-507 gpm, and annular velocities in the open hole were 256-263 fpm. The calculated lift factors underneath the eccentric drill pipe are shown in Fig. 13 [18,340 bytes]). Lift factors calculated under conditions existing at total depths, or bit depth, ranged between 0.55 and 0.25. These are significantly higher than the near-zero values for the Stafjord C-02. No wide fluctuations in lift factor values were calculated, again indicative of improved control of downhole rheological parameters under the given operating conditions.

Uphole model predictions

Fig. 13 also shows simulations of hole cleaning further up the annulus at 7,000 m and 5,340 m MD. Cleaning inside the 95/8-in. liner at 7,000 m indicated few problems and generally increased cleaning efficiency. At this point, downhole rheological predictions indicated increased values of K and moderately lower values of t₀.

However, cleaning problems were predicted farther up the hole inside the 133/8-in. casing at 5,340 m. Because of the increased annular diameter, annular velocities were reduced. As a result, cuttings build-up was predicted by the model and was observed on the well. It was for this reason that the fluid downhole yield-stress levels were at times higher than those in the 121/4-in. interval.

References

1. Kenny, P., Sunde, E., and Hemphill, T., "Hole-Cleaning Model: What Does the Fluid-Flow Index Have To Do With It?" JPT, November 1996 (original paper IADC/SPE 35099 "Hole-cleaning modeling: What's "n" Got To Do With It?" presented at the 1996 Drilling Conference in New Orleans).

2. Hemphill, T., "Prediction of Rheological Behavior of Ester-Based Drilling Fluids Under Downhole Conditions," SPE 35330 presented at the 1996 SPE International Petroleum Conference and Exhibition of Mexico in Villahermosa, Mar. 5-7, 1996.

3. Hemphill, T., Pilehvari, A., and Campos, W., "Yield-power law model more accurately predicts mud rheology," OGJ, Aug. 23, 1993, pp. 45-50.

4. "Recommended Practice on the Rheology and Hydraulics of Oil-Well Drilling Fluids," API Recommended Practice 13D, Third Edition, pp. 20-21, June 1, 1995.

5. "Flow Visualization," Baroid Drilling Fluids Graphics software.

6. Haciislamoglu, M., and Langlinais, J.,"Non-Newtonian Fluid Flow in Eccentric Annuli," ASME Journal of Energy Resources Technology, Vol. 112, pp. 163-69, 1990.

7. Chien, S.F., "Settling Velocity of Irregularly Shaped Particles", SPE Drilling & Completion, pp. 281-89, December 1994.

8. Kenny, P., and Hemphill, T., "Hole-cleaning Capabilities of an Ester-Based Drilling Fluid System," SPE Drilling & Completion, pp. 3-9, March 1996.

9. Hemphill, T., and Pogue, T., "Field Applications of ERD Hole Cleaning Modeling," SPE/IADC paper 37610, presented at the 1997 Drilling Conference in Amsterdam, Mar. 4-6, 1997.

10. Alfsen, T., Heggen, S., Blikra, H., and Tjtta, H., "Pushing the Limits for Extended Reach Drilling: New World Record From Platform Statfjord C, Well C2," SPE 26350 presented at the 68th Annual Technical Conference and Exhibition in Houston, Oct. 3-6, 1993.

Copyright 1997 Oil & Gas Journal. All Rights Reserved.