During the drilling process, the physical and rheological properties of a drilling fl uid have to be controlled accu- rately to ensure the fl uid’s appropriate performance. These properties are regularly tested and recorded on the
Effect of Pressure and Temperature on the Viscosity of Water
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 Pressure, psia Viscosity, cp 50°F 100°F 150°F 200°F 250°F 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 50 100 150 200 250 300 Temperature, °F Viscosity, cp 14.7 psi 2,000 psia 4,000 psia 6,000 psia 8,000 psia 10,000 psia
Drilling Fluids 109 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0 2,000 4,000 6,000 100°F 150°F 200°F 300°F 8,000 10,000 Pressure, psi V iscosity , cp 12,000 14,000 16,000 18,000 20,000
Fig. 3.12—Viscosity of diesel oil as a function of pressure and temperature (Annis 1974). Reprinted courtesy of ExxonMobil. 60 50 40 30 20 10 0 5 10 15 Solids, wt%
Wyoming bentonite High-yield drilling clay
V
iscosity
, cp
25
20 30 35 40 45 50
Low-yield drilling clay
drilling-mud report, which is presented by the API (API Spec. 13B-1 2009). The drilling-fl uid technicians carry out the fi eld tests at the wellsite where the mud properties are routinely monitored.
Because the chemical tests conducted upon the water phase are only semiquantitative, the control of the water’s ionic balance is quite complicated. Thus, a persistent question arises: How accurate are the test results? From a chemical standpoint, most of the chemical test results are suffi cient for interpretation of drilling-fl uid behavior. But, occasionally, no chemical balance is present and the interpretation of those results does not point to the actual problem.
A water-based mud is composed of a three-phase system: water, active solids, and inert solids. The active solids (hydrophilic) such as hydratable clays react with the water phase by dissolving chemicals and by providing vis- cosity to the mud. On the other hand, the inert solids (hydrophobic) such as sand and shale do not react with the water and chemicals to any signifi cant degree. Basically, the inert solids make diffi cult the analyses and control of the solids in the drilling fl uid (i.e., inert solids produce undesirable effects).
3.7.1 Properties of Drilling Fluids. There are many physical and chemical properties of drilling fl uids that are useful to know or even critical to determine. The physical properties of a drilling fl uid, the density, and the rheo- logical properties are examined continuously to optimize the rotary-drilling process. These properties contribute to preventing an infl ux of formation fl uid, providing wellbore stability, providing hydraulic energy at the drilling bit, removing drilled solids (cuttings) from the well and suspending them during static periods, and permitting segregation of solids and gas at the surface. The chemical properties of a drilling fl uid provide the chemical effects associated with formation damage, rheological-property changes, and cuttings-transport issues.
3.7.2 Testing for Density. The mass per unit volume of a drilling fl uid, density, is commonly reported either in pounds per gallon (lbm/gal), in kilograms per cubic meter (kg/m3), grams per cubic centimeter (also called spe- cifi c gravity [SG]), or in hydrostatic gradient, lbm/in2/ft (psi/ft) or psi/1,000 ft. The mud density and the depth of the well control the hydrostatic pressure exerted by a static drilling-fl uid column. The mud density prevents infl ow of formation fl uid into the well and collapse of the open hole and the casing. To prevent infl ow, the hydrostatic pressure of a mud column must exceed the formation or pore pressure. However, excessive mud weight can cause lost circulation and considerably affect the rate of penetration.
The mass per unit volume (density or mud weight) of the drilling fl uid is determined by the use of the mud bal- ance. A typical pressurized mud balance is illustrated in Fig. 3.14. It is important to note that fresh water weighs 8.34 lbm/gal. Therefore, to calibrate a mud balance, fresh water must be used. If brine is used, the calibration will be incorrect unless one knows precisely the salt concentration and can determine the actual weight of the calibra- tion fl uid.
Drilling Fluids 111
3.7.3 Testing for Flow Properties. The fl ow properties of the drilling fl uid play a very important role in the suc- cess of the rotary-drilling operation and they must be controlled if the fl uid is to perform its various functions properly.
Viscosity. The resistance to flow of a fluid and the resistance to the movement of an object through a fluid are usually stated in terms of the viscosity of the fluid. Experimentally, under conditions of laminar flow, the force required to move a plate at constant speed against the resistance of a fluid is proportional to the area of the plate and to the velocity gradient perpendicular to the plate. The constant of proportionality is called the viscosity. In the oil field, the following terms are used to describe the drilling-fluid viscosity: funnel viscosity, apparent viscosity, plastic viscosity, and effective viscosity. Viscosity is the rheological property of the drilling fluid that indicates its resistance to flow. Viscosity is defined as the ratio of shear stress to shear rate:
.
P W
J
,
. . . (3.9)where t is the shear stress, g. is the shear rate, and m is the viscosity. The shear rate is the velocity gradient or fl uid velocity/length. The shear stress is the force over an area exerted on the fl uid (t = force/area), and m is the constant of proportionality, or viscosity, of the fl uid. Viscosity, in the drilling industry, is expressed in centipoise (cp), where 1 cp = 0.01 poise = 0.01 dyne-sec/cm2 = 0.01 g/cm-sec. The shear rate (g., sec–1) of a fl uid is defi ned as the velocity change divided by the width of a canal through which it is moving in laminar fl ow. The shear stress (t, lbm/100 ft2) is the force per unit area needed to move a fl uid at a given shear rate. When the proportionality be- tween shear stress and shear rate is independent of shear rate, the fl uid is called Newtonian, and many common fl uids have this behavior. However, most of the drilling fl uids are characterized as non-Newtonian fl uids, where the proportionality is shear-rate dependent.
Testing for Viscosity. A simple test for viscosity at the wellsite is the Marsh-funnel test. The Marsh funnel, shown in Fig. 3.15a, is a cone-shaped tool with a small bore tube on the bottom end through which drilling mud fl ows due to gravity action. The resulting value is not a true viscosity value but a relative comparison one. The qualitative measurement indicates how thick the drilling mud sample is measuring a timed rate of fl ow. This vis- cosity is the number of seconds it takes for 1 quart of drilling mud to fl ow through the funnel. For example, the fl uid would be described as a “43 viscosity fl uid” if its fl owing from the funnel reaches the 1-quart line in 43 seconds. However, no useful engineering information can be derived from this test.
The shear stress-shear rate relationship of a drilling mud is determined by conducting tests in a concentric viscom- eter (Fig. 3.15b). This consists of concentric cylinders, one of which rotates (usually the outer one). A sample of fl uid is placed between the cylinders and the torque on the inner cylinder is measured, as illustrated in Fig. 3.16. Assuming an incompressible fl uid, with fl ow in the laminar-fl ow regime, the equation of motion can be solved for t to give:
2 1 2 t M r L W S , . . . (3.10)
where Mt is the torque,r1 is the radius of the bob, and L is the length of the cylinders. In a concentric viscometer, torque Mt is measured at different rotational speeds of the outer cylinder.
Shear stress is then calculated from Eq. 3.10 and shear rate is given by:
S Z J 2 2 2 2 2 1 4 r r r
,
. . . (3.11) where r2 is the inside radius of the outer cylinder and w is the angular velocity of the outer cylinder. A number of commercially available concentric-cylinder rotary viscometers are suitable for use with drilling muds. They are similar in principle to the viscometer already discussed. All are based on a design by Savins and Roper (1954)—a two-speed viscometer that enabled the determination of the parameters of a fl uid model called a Bingham plastic model. A Bingham plastic fl uid model assumes that no fl ow occurs for shear stresses below τY, called the yield point. For shear stresses above the yield point, a Bingham plastic fl uid behaves as a Newtonian fl uid with viscos- ity μp, called the plastic viscosity. The formula for the Bingham plastic model is given byY p
W W P J. . . . (3.12)
Fig. 3.17 shows the result of a typical viscometer test, with the Bingham-plastic curve shown as a solid line and the actual fl uid response shown as a dashed line. We can see that the Bingham plastic model does not fi t this fl uid very well except for high shear rates, and that the true yield point falls well below the calculated yield point. For this reason, many other fl uid models have been devised, which will be studied in Chapter 5. For our current pur- poses, we will only consider the Bingham plastic model, but note that the viscometer results can be used in other ways. Viscometers are built so that
· 1° dial reading = 1.067 lbf/100 ft2 = 5.109 dynes/cm2 shear stress · 1 rev/min = 1.703 reciprocal seconds, shear rate
Therefore, the plastic viscosity and yield point are calculated very simply from two dial readings at 600 rev/min and 300 rev/min, respectively.
, T600 T300 PV . . . (3.13) YP = θ300 − PV, . . . (3.14) r r T 2 1 Rotor sleeve Bob Fluid ω
Drilling Fluids 113
where PV is plastic viscosity and YP is yield point. The units of plastic viscosity come out conveniently as centi- poise (cp). Yield point results are reported using the units lbf/100 ft2. Apparent viscosity μ
a may be calculated from the Savins and Roper (1954) viscometer reading as follows:
. 300 a T P Z
. . . (3.15)
ma = t/g = 5.109/1.703 poise/degree per rev/min = 300 cp/degree per rev/min = 300 q/w, where q is the dial read- ing at w rev/min. Apparent viscosity is usually reported at the 600 rev/min reading.
Notice that real fl uids are not ideally any of the models shown above, but generally are close to one model or another. The selection of the model may be motivated by a particular fl uid velocity of interest. Using a direct reading concentric-cylinder rotary viscometer, a more meaningful measurement of rheological properties is ob- tained. This rotational cylinder and bob instrument is largely known in the drilling industry as a V-G meter. In 1951, Melrose and Lilienthal (Rogers 1963) developed this multispeed viscometer for laboratory or fi eld use in measuring the rheological properties. The rotational viscometer is capable of providing plastic viscosity, apparent viscosity, yield point, and gel strength.
Although most models operate at six different speeds, only two dial readings are converted to the rheological parameters plastic viscosity and yield point—the 300- and 600-speed readings. The shear speed—that is 300 rev/min and 600 rev/min—is the rotational speed on a standard oil-fi eld viscometer on which the shear rate is measured. The V-G meter is called a direct reading viscometer because at a given speed, the dial reading is a true centipoise viscosity. For example, the dial reading (511 sec–1) at 300 rev/min (q
300) represents the true viscosity.
Plastic Viscosity. For a plastic fl uid, the plastic viscosity is the shear stress in excess of the yield stress that will induce a unit rate of shear. In other words, it is that part of the fl ow resistance in a drilling fl uid mainly produced by the friction of the suspended particles and by the viscosity of the liquid phase (IMCO 1981). It is given by Eq. 3.13. Recommended ranges of plastic viscosity are given in Fig. 3.18 as a function of mud density.
Yield Point. The yield point of clay in fresh water is defi ned as the number of barrels of 15-cp mud that can be obtained from 1 ton of dry material. Above 15 cp, small additions of clay have a signifi cant effect on viscosity. The yield point is given by Eq. 3.14. Recommended ranges of yield point are given in Fig. 3.19 as a function of mud density.
Viscometer Dial Reading
PV
Shear stress=YP+PV (rev/min)/300
Actual shear rate/shear stress curve
0 100 200 300 400 500 600 700
Viscometer, rev/min
YP
Apparent Viscosity. In evaluating drilling fl uids, it is common practice to report the effective viscosity at 600 rev/min using Eq. 3.15. This quantity is called the apparent viscosity, and is given by
600 1 2 600 300 , 600 AV T T
. . . (3.16)
where AV is apparent viscosity.
Effective Viscosity. Effective viscosity is defined as the viscosity of a Newtonian fluid that exhibits the same shear stress at the same rate of shear as the actual fluid being tested. Although it is a very useful pa- rameter in hydraulic equations when the shear rate is known, the value of the effective viscosity is meaning- less unless the rate of shear at which it is measured is specified. Furthermore, it is not a reliable parameter for comparing the viscous properties of two fluids; at least two parameters are necessary for that purpose.
Yield P
oint at 120°F
Mud Weight, lbm/gal
40 30 20 10 0 9 10 11 12 13 14 15 16 17 18 19 High range Low range
Fig. 3.18—Recommended range of yield point (Annis 1974). Reprinted courtesy of ExxonMobil.
Plastic V
iscosity at 120°F
Mud Weight, lbm/gal
High ra nge Minimu m rang e 70 60 50 40 30 20 10 0 9 10 11 12 13 14 15 16 17 18 19
Drilling Fluids 115
Gel Strength. Gel strength is the third rheological parameter commonly used to describe non-Newtonian fl u- ids. The gel strength is the shear stress measured at low shear rate after a mud has set quiescently for a period of time. In other words, it is the measure of ability of a colloidal solid at rest to form a gel. A colloid is a fi nely di- vided solid that does not deposit by gravity when dispersed in a liquid medium. Gel strength has the unit of pres- sure usually reported in lbf/100 ft2. It is a measure of the same interparticle forces of a fl uid as determined by the yield point, except that gel strength is measured under static conditions.
This rheological parameter is useful in drilling operations for determining the swabbing effect on pulling the drillpipe, the pressure required to break circulation, the ease of release of gas, and the settling of particles in the mud pits. The common gel strength measurements are initial and 10-min gels, which can be measured with a V-G meter as follows:
The fl uid is stirred at 600 rev/min until a stable dial reading is achieved. Then the instrument is turned off. After 10 seconds of rest, the cylinder is rotated at 3 rev/min and the highest dial reading is recorded. This is called the “initial gel strength.” The same procedure is applied to measure the 10-min gel strength using a resting time of 10 minutes after stirring the mud.
Example 3.7 A mud sample in a rotational viscometer equipped with a standard torsion spring gives a dial reading of 46 when operated at 600 rev/min and a dial reading of 28 when operated at 300 rev/min. Compute the apparent viscosity of the mud at each rotor speed. Also compute the plastic viscosity and yield point.
Solution. Use of Eq. 3.15 for the 300-rev/min dial reading gives
300(28)
28 cp. 300
a
P
Similarly, use of Eq. 3.15 for the 600-rev/min dial reading gives
300(46) 23 cp. 600
a
P
Note that the apparent viscosity does not remain constant but decreases as the rotor speed is increased. This type of non-Newtonian behavior is shown by essentially all drilling muds.
The plastic viscosity of the mud can be computed using Eq. 3.13:
300(46) 23 cp. 600
a
P
The yield point can be computed using Eq. 3.14:
2
Y 300 p 28 18 10 lbf/100 ft .
W T P
3.7.4 Lubricity Testing. Increasing the lubricity of a drilling fl uid is a technique used to help prevent stuck pipe. In this application, lubricity is the coeffi cient of friction between the drillpipe and the mud fi lter cake. The API recommended practices for mud testing do not include a specifi cation for lubricity. Lubricity testing has under- gone developmental changes to obtain a more accurate correlation between test results and actual wellbore con- ditions .
In 1999, a specially designed fully automated device to accurately measure the coeffi cient of friction between metal and mud fi lter cake was tested on several drilling-fl uid types (Isambourg 1999). To simulate downhole conditions, drilling fl uid is circulated inside a pressurized cell with a temperature capability of 100°C. The cell is also equipped with an internal porous cylinder to simulate fi ltrate invasion and fi lter cake buildup across a permeable formation. Lubricity measurements are obtained through sensors on the rotating captor, which repre- sents the drillstring.
Once the fi lter cake has been deposited on the metal screen, the rotating captor moves laterally to make contact with the cake. At this point, cake thickness can be determined and recorded, and the captor can be further embedded in the cake at a preselected speed. The outer cell can be rotated at one-quarter intervals to obtain measurements at four points on the fi lter cake. The apparatus and procedure produced accurate and
reproducible coeffi cients of friction existing between the fi lter cake and “drill pipe” under simulated down- hole conditions. A schematic of the lubricity tester is illustrated in Fig. 3.20. The test measures the applied force F and the applied torque Mt. The coeffi cient of friction is μf calculated on the basis of the three follow- ing formulas: t f cp M F r
,
. . . (3.17a) Ff FN F F F 2 2 2 + = G<G=,
. . . (3.17b) P f f N F F , . . . (3.17c)where rcpis the radius of the captor, FN is the normal force andFf is the friction force. Moment equilibrium gives the value of Ff in Eq. 3.17a. The sum of the friction force and the normal force equals the applied force FG, so their magnitudes are equal, as given in Eq. 3.17b. Having determined FN, we can now calculate the friction coeffi cient mf with Eq. 3.17c.
Similar apparatuses were use to analyze differential sticking forces, pull forces, and associated mud-cake pore pressures. This leads to the conclusion that fi lter-cake compaction and permeability have a greater impact on the likelihood of differential sticking than cake thickness alone. The type and amount of solids affect fi lter-cake char- acteristics, the degree of pipe sticking, and the pull-out force to get it free. Potassium chloride concentration in the mud may play an important role in the pull-out force because it changes the mud-cake strength through the potassium-inhibitive effect on clays.
3.7.5 Filtration Properties. The fi ltration and wall-building properties of drilling fl uids are acknowledged as being the most signifi cant in the good drilling of wells. This ability of the mud to seal permeable zones with a thin, low-permeabil- ity fi lter cake represents the key for successful completion of the hole. The mud would continuously invade the permeable formations allowing the fi ltrate to enter if a fi lter cake were not formed.
F
y CakeF
f Captor x Rotation rcp MtF
NDrilling Fluids 117
The API Filter Press—Static Filtration. The fi lter press (Fig. 3.21) is used to determine the fi ltration rate through a standard fi lter paper and the rate at which the mudcake thickness increases on the standard fi lter pa- per under standard test conditions. This test is indicative of the rate at which permeable formations are sealed by the deposition of a mudcake after being penetrated by the bit.