Estudio del comportamiento de salmu

SPE-160029

Study on the Volumetric Behavior of Base Oils, Brines, and Drilling Fluids Under Extreme Temperatures and Pressures

Mario Zamora, Sanjit Roy, Kenneth Slater, and John Troncoso, M-I SWACO, a Schlumberger company Copyright 2012, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in San Antonio, Texas, USA, 8-10 October 2012. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract

Drilling fluid densities vary significantly over wide ranges of temperature and pressure, a concern that is particularly

critical in deepwater, Arctic, and high-temperature/high-pressure wells. The variations can impact well integrity, well design,

regulatory compliance, and drilling efficiency.

Drilling fluid densities depend on the compressibility and thermal expansion of the fluids (liquids) and solids used in their

formulation. Suitable pressure-volume-temperature correlations for these fluids previously have been fairly inaccessible, due

primarily to continually changing base fluids and blends, and the lack of readily available test equipment.

This study was conducted to measure the volumetric behavior under extreme temperatures and pressures of a broad range

of the oils, synthetics, and brines currently used in industry to prepare oil, synthetic, and water-based drilling fluids. It

follows a recent study that successfully qualified the commercially available test equipment.

For the most part, tests were run at temperatures from 36 to 600F and pressures from atmospheric to 30,000 psi, ranges

that generally exceed those used in published studies. Correlation coefficients are provided for reference and to demonstrate

their use in a compositional, material-balance model to accurately predict drilling fluid density as a function of temperature

and pressure. Tests run on field drilling fluids are included to demonstrate how these data can be used in procedures and

software to predict equivalent static densities and hydrostatic pressure during drilling operations.

Introduction It can be challenging to predict hydrostatic pressures in high-temperature/high-pressure (HTHP) and deepwater wells,

especially when using synthetic and oil-based drilling fluids. Concerns arise because these wells exhibit wide surface-to-TD

temperature and pressure spreads, and invert emulsion drilling fluid densities are highly sensitive to temperature and

pressure. As such, their downhole densities can depart significantly from those measured at the surface.1,2

Downhole density

is a depth-dependent profile since downhole temperatures and pressures also vary with depth. For true hydrostatic pressure, it

follows that the so-called equivalent static density (ESD) is the preferred density term for use in the fundamental hydrostatic-

pressure equation.

Unfortunately, the technique for determining ESD is somewhat involved, and typically uses a step-wise integration of

short well segments whose individual fluid densities have been corrected for compressibility and thermal-expansion effects.

Ideally, the pressure-volume-temperature (PVT) characteristics of the field drilling fluid could be measured periodically

during drilling operations. A proven alternative involves predicting these characteristics based on temperature/pressure

relationships of the individual drilling fluid constituents, a process quite suitable for well planning and regulatory compliance

activities.

Table 1 lists many of the industry publications that have included PVT data on various base fluid used to formulate water,

oil and synthetic-based drilling fluids, as well as on fully formulated versions. Some of the base fluid data were derived from

tables or calculated using equations of state; however, most were generated by tests using customized variable-volume or

calibrated-screw cells. Except for the most recent work, maximum test temperatures and pressures were 400F and 24,000

psi, respectively.

However, up-to-date PVT experimental data and regression analyses for many common base fluids have been relatively

inaccessible. Furthermore, base oils and synthetics can change periodically for engineering, manufacturing, and/or

commercial motives. The lack of readily available, fit-for-purpose test equipment has also contributed. The next-to-the-last

2 M. Zamora, S. Roy, K. Slater and J. Troncoso SPE-160029

row in Table 1 references a study undertaken to qualify a recently commercialized test device. Experimental work conducted

with that device for this paper is listed in the bottom row of the table.

The main purpose of this paper is to present measured PVT data and correlation coefficients to add to the industrys volumetric-behavior database used to predict drilling fluid densities under extreme temperatures and pressures. The test fluids

included base oils, synthetics, brines, and field drilling fluids. A secondary purpose is to demonstrate an established process

to determine ESD and hydrostatic pressure profiles using these coefficients with a compositional, material-balance model.

The process also is demonstrated with correlations calculated from PVT tests on representative field muds.

Experimental Test Equipment Test equipment for this study was a PVT pycnometer (PVTP) developed and commercialized by an oilfield instrument

supplier to test the compressibility and thermal expansion of liquid and solid samples.13

The PVTP cell is an add-on module

that replaces the rotor/bob assembly in that suppliers ultra-HPHT viscometer, both of which are rated from 20 to 600F and atmospheric to 30,000 psi. Other manufacturer-provided specifications are given in Table 2.

Fig. 1 is a picture of the combined equipment showing from left to right the chiller, viscometer pressure tower with PVTP

cell installed, control console, and computer. Fig. 2 is a close up of the PVTP cell placed inside of the pressure tower, just

before making up the two pressure connections and closing up the tower.

The PVTP was described and successfully validated in a previous paper.12

Standardized test fluids included deionized

water and undecane, a liquid paraffin that is a component of diesel fuel. CaCl2, diesel, a low-aromatic mineral oil, and C16C18

IO synthetic were among the base fluids tested and compared to PVT data published in API RP13D.8

Experimental Results

Tests were run on five low-aromatic mineral oils, five synthetics, three diesel oils, five brines, and four drilling fluids.

Table 3 identifies and describes the base oils, among the most commonly used to formulate non-aqueous drilling fluids. The

Sample IDs are used later for identification. Results previously reported in the qualification study are included for reference.

The base fluids also were tested on a GC-FID (gas chromatograph - flame ionization detector) to analyze their

components and on a pycnometer for density. Peak identifications were confirmed by GC/MS (gas chromatograph/mass

spectrometry). Figs. 3 8 are the fingerprint scans for MO1, S1, S4, D1, D2, and D3, respectively. The scans serve to classify and document the test fluids.

Table 1: Industry Publications Summarizing Drilling-Fluid Related PVT Studies

Year Reference Equipment Tmin (F)

Tmax (F)

Pmax (psi)

Test Fluids

1982 Hoberock, et al.3 Derived only 75 575 25,000 Water, sea water, saturated salt water, diesel

1982 McMordie, et al.1 Autoclave 70 400 14,000 WBM, OBM

1990 Peters, et al.4 Blind PVT cell 78 350 15,000 Diesel, 2 mineral oils

1996 Isambourg, et al.5 PVT cell 68 392 20,300 OBM, CaCl2, mineral oil

2000 Zamora, et al.6 Huxley-Bertram viscometer 70 400 14,500 LVT 200, C16C18 LAO, Saraline 200, EMO-4000

2005 Hemphill and Isambourg7 Referenced only 40 - 77 302 - 400 20 - 24,000 CaCl2, diesel, mineral oil, IO, paraffin

2006 API RP-13D8 Referenced only 40 - 77 302 - 400 20 - 24,000 CaCl2, diesel, mineral oil, IO, paraffin

2007 Demiral, et al.9 Mercury-free PVT cell 80 280 5,000 n-Paraffin-based oil, mud

2007 Demirdal and Cunha10 Mercury-free PVT cell 77 347 14,000 C16C18 IO, C12C14 LAO

2010 Hussein and Amin11 Vapor-Liquid Equilibrium 80.6 300 5,000 Vegetable oil, mineral oil, blend of the two

2012 Zamora, et al.12 PVT pycnometer13 40 500 30,000 CaCl2, diesel, C16C18 IO, undecane, water

2012 This work PVT pycnometer13 36 600 30,000 Synthetics, mineral oils, diesels, brines, drilling fluids

Table 2: PVTP Specifications13 Resolution: 0.5% of initial density

Density Range: 71 to 142%

Sample Size: Small piston: 185 - 193 mL; Large piston: 120 - 170 mL

Temperature Range: Ambient (20F w/chiller) to 600F

Pressure Range: Atmospheric to 30,000 psi

Maximum Compressibility: 71% @ 170 mL starting volume (50% opt.)

Maximum Expandability: 142% @ 120 mL starting volume (200% opt.)

Stirring magnet: 0 to 600 rpm

Computer Requirements: Windows PC

Fig. 1: Complete PVTP equipment set up

showing (from left to right) the chiller,

pressure tower with PVTP cell installed,

control console, and computer.

Fig. 2: Close-up of PVTP cell placed in

open HTHP viscometer pressure tower.

SPE-160029 Study on the Volumetric Behavior of Base Oils, Brines, and Drilling Fluids Under Extreme Temperatures and Pressures 3

( ) (

)

Table 3: GC-FID and GC/MS Data for Base Fluids

Fluid Type Sample

ID Density* (lbm/gal)

Kinematic Viscosity**

(cSt @104F) GC-FID Remarks (peak identifications confirmed by GC/MS***)

Mineral Oils

MO1 6.5708 @73F 1.84 Normal, branched and cyclic hydrocarbons from C10 to C15, strongest peaks at C12 and C13

MO2 6.6852 @73F 1.93 C9 to C21 normal, cyclic, and branched hydrocarbons with strongest peaks from C11 to C14

MO3 6.8304 @73F 2.58 Mostly branched and cyclic hydrocarbons from C11 to C17, strongest peaks between C13 and C14

MO4 6.8111 @69F 3.30 C9 to C23 normal, cyclic, aromatic, branched hydrocarbons with strongest peak from C11 to C20

MO5 6.5725 @69F 1.89 C10 to C17 normal, cyclic, and branched hydrocarbons with strongest peaks from C11 to C14

Synthetics

S1 6.5425 @75F 3.44 C14 to C22 Olefins with C16 and C18 being the strongest peaks

S2 6.6718 @69F 3.18 C10 to C20 normal, cyclic, and branched hydrocarbons with strongest peaks from C12 to C17

S3 6.5408 @73F 3.53 C16 and C18 olefins with smaller amounts of C14, C20, C22, C24 olefins

S4 6.4056 @73F 2.44 Mixture of normal paraffins from C10 to C16 and olefins from C14 to C19

S5 6.5299 @73F 3.34 C14 to C20 Olefins with C15, C16, C17 and C18 being the strongest peaks

Diesel Oils

D1 6.9147 @73F 2.85 Normal, branched, cyclic, and aromatic hydrocarbons from C7 to C27



* Density Modified ASTM D1217-93 (Reapproved 2007) Standard Test Method for Density and Relative Density (Specific Gravity) of Liquids by Bingham Pycnometer ** Kinematic Viscosity ASTM D445-12 Standard Test Method for Kinematic Viscosity of Transparent and Opaque Liquids *** GC Fingerprint Scans EPA Method 8015C Nonhalogenated Organics by Gas Chromatography, Hewlett Packard 6890 Gas Chromatograph, Agilent DB-5MS column

Three PVTP test schedules (Table 4) were used to address the expected use of the fluids. All were tested over the

minimum and maximum ranges in the row labeled Standard. In addition, fluids for cold environments were exposed to lower temperatures, and those for hot environments were tested to temperatures as high as 600F. Ranges for each specific

fluid are identified in later tables. As noted, several fluids were not tested over their scheduled temperatures and pressures.

Table 4: PVTP Testing Schedules

Schedule Temperature (F) Pressure (psi)

Min Max Min Max

Standard 75 500 200 30,000

Cold 35 500 200 30,000

Hot 75 600 200 30,000

Regression analyses on the PVTP data were conducted with a 2nd

order polynomial equation to determine fluid density

as a function of temperature and pressure. The goal was to determine the three pressure and three temperature correlation

coefficients for Eq. 1 below based on the volumetric behavior of each base oil (or synthetic), brine, and drilling fluid exposed

to the extreme temperatures and pressures listed in Table 4. This relationship6,7

has proven to fit a very high percentage of

drilling fluids and their liquid components, and is published in API RP13D.8

(1)

Eq. 1 units are (lbm/gal), temperature (F) and pressure (psi). Correlation-coefficient units are consistent with this units set. Figs. 9-11 are isotherm plots for the three base fluids whose fingerprint scans are shown in Figs. 3-5. The curves were

generated by Eq. 1 using correlation coefficients in Tables 5-8, grouped as mineral oils, synthetics, diesel oils, brines, and

drilling fluids. Other PVTP graphs can be found in another publication12

for deionized water, undecane, CaCl2 (19.3 wt%),

red-dyed diesel, C16C18 IO, a low-aromatic mineral oil, and a lab-prepared 12.23 lbm/gal synthetic-based drilling fluid.

Figs. 12-14 are isothermal plots of the oil, synthetic, and water-based field drilling fluids. Their regression coefficients are

shown in Table 9 and their pertinent physical properties are listed in Table 10. SBM1 is the 12.23 lbm/gal synthetic-based

drilling fluid that was prepared in the laboratory and used to validate the compositional, material-balance model3,4

discussed

later. For these drilling fluids, the compressibility of the water-based drilling fluid was only slightly lower than oil-based or

the synthetic-based drilling fluids. Additionally, the pressure effect on the water-based drilling fluid was somewhat linear,

while the non-aqueous fluids exhibited decreasing compressibility with pressure. As expected, the order of magnitude of

change in density was very close to that of their respective make-up base fluids.

Figs. 15-16 are comparisons of all the base fluids at 39 and 450F. Figs. 15a and 15b compare five different mineral oils

and synthetics, while Figs. 16a and 16b compare three diesels and two concentrations of two brines commonly used to

formulate non-aqueous drilling fluids, respectively. As noted, all the mineral-oil, synthetic and diesel isotherms are

comparable and clustered together, while the brine isotherms are parallel to each other and laterally shifted depending on

their respective salinities.


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Fig. 3: GC-FID fingerprint scan of MO1. Fig. 6: GC-FID fingerprint scan of D1 red-dyed diesel #2.

Fig. 4: GC-FID fingerprint scan of S1. Fig. 7: GC-FID fingerprint scan of D2 diesel from Mexico.

Fig. 5: GC-FID fingerprint scan of S4. Fig. 8: GC-FID fingerprint scan of D3 winterized diesel from Alaska.

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Fig. 12: PVTP-measured isotherms for OBM1.

Fig. 13: PVTP-measured isotherms for SBM2.

Fig. 14: PVTP-measured isotherms for WBM1.

Fig. 9: PVTP-measured isotherms for MO1.

Fig. 10: PVTP-measured isotherms for S1.

Fig. 11: PVTP-measured isotherms for S4.

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Table 9: Correlation Coefficients for Selected Drilling Fluids

Reference OBM1 SBM1 SBM2 WBM1

Source Field Laboratory Field Field

Pressure Coefficients

a1 (lbm/gal) 16.3144 12.5549 15.5659 17.2693

b1 (lbm/gal/psi) 4.18 E-05 3.48 E-05 4.15 E-05 3.78 E-05

c1 (lbm/gal/psi2) -3.04 E-10 -1.87 E-10 -1.88 E-10 -1.49 E-10

Temperature Coefficients

a2 (lbm/gal/F) -4.40 E-03 -4.10 E-03 -4.37 E-03 -3.13 E-03

b2 (lbm/gal/psi/F) 9.49 E-08 1.07 E-07 9.32 E-08 6.67 E-09

c2 (lbm/gal/psi2/F) -1.31 E-12 -1.62 E-12 -1.56 E-12 -8.93 E-14

Fitting Statistics for Modeled Data

Avg. Error % 0.11 0.11 0.35 0.37

r2 coefficient 0.999 0.999 0.997 0.996

Range of Validity

Max. Pressure (psi) 30,000 30,000 30,000 30,000

Min. Temperature (F) 37 75 37 36

Max. Temperature (F) 500 500 500 250

Table 5: Correlation Coefficients for Mineral Oils Table 6: Correlation Coefficients for Synthetics

MO1 MO2 MO3 MO4 MO5 S1 S2 S3 S4 S5

Reference/Source PVTP PVTP PVTP PVTP PVTP PVTP PVTP PVTP PVTP PVTP


a1 (lbm/gal) 6.7422 6.8701 7.0844 7.0043 6.7609 6.6962 6.8467 6.7252 6.6351 6.6805

b1 (lbm/gal/psi) 3.32 E-05 3.13 E-05 3.03 E-05 2.74 E-05 2.99 E-05 2.83 E-05 3.05 E-05 2.87 E-05 3.12 E-05 3.05 E-05

c1 (lbm/gal/psi2) -3.46 E-10 -2.22 E-10 -2.02 E-10 -1.93 E-10 -2.79 E-10 -1.90 E-10 -2.43 E-10 -1.59 E-10 -2.98 E-10 -3.69 E-10


a2 (lbm/gal/F) -2.85 E-03 -2.82 E-03 -2.80 E-03 -2.60 E-03 -2.71 E-03 -2.72 E-03 -2.72 E-03 -2.75 E-03 -2.93 E-03 -2.58 E-03

b2 (lbm/gal/psi/F) 6.3 1E-08 6.11 E-08 6.85 E-08 6.20 E-08 6.40 E-08 6.87 E-08 5.35 E-08 6.50 E-08 6.52 E-08 5.37 E-08

c2 (lbm/gal/psi2/F) -8.40 E-13 -9.47 E-13 -1.07 E-12 -9.43 E-13 -8.44 E-13 -1.00 E-12 -6.99 E-13 -1.03 E-12 -7.97 E-13 -4.70 E-13


Avg. Error % 0.40 0.19 0.17 0.25 0.27 0.41 0.21 0.24 0.20 0.28

r2 coefficient 0.996 0.998 0.998 0.998 0.997 0.996 0.998 0.998 0.998 0.997

Range of Validity

Max. Pressure (psi) 30,000 30,000 30,000 30,000 30,000 30,000 30,000 30,000 30,000 30,000

Min. Temperature (F) 39 77 78 77 77 75 36 76 38 77

Max. Temperature (F) 500 400 500 500 500 500 400 500 400 500

Table 7: Diesel Coefficients Table 8: Correlation Coefficients Brines D1

Red-dyed D2

Mexico D3

Alaska B0

Water B1 CaCl2 19.3 wt%

B2 CaCl2 25 wt%

B3 NaCl 10 wt%

B4 NaCl 20 wt%

Reference/Source PVTP PVTP PVTP PVTP PVTP PVTP PVTP PVTP


a1 (lbm/gal) 7.3459 7.0465 7.1570 8.7471 10.0290 10.5728 9.2944 9.8426

b1 (lbm/gal/psi) 3.00 E-05 3.25 E-05 3.04 E-05 1.65 E-05 1.68 E-05 2.42 E-05 1.87 E-05 1.95 E-05

c1 (lbm/gal/psi2) -2.38 E-10 -2.98 E-10 -3.49 E-10 7.22 E-11 1.11 E-10 -7.72 E-11 4.19 E-11 -1.01 E-10


a2 (lbm/gal/F) -2.99 E-03 -2.63 E-03 -2.65 E-03 -3.91 E-03 -3.09 E-03 -2.78 E-03 -3.49 E-03 -3.14 E-03

b2 (lbm/gal/psi/F) 8.62 E-08 5.12 E-08 4.86 E-08 6.06 E-08 3.43 E-08 5.00 E-09 3.88 E-08 2.31 E-08

c2 (lbm/gal/psi2/F) -1.69 E-12 -5.58 E-13 -3.56 E-13 -9.34 E-13 -6.36 E-13 5.70 E-14 -6.22 E-13 -8.74 E-14


Avg. Error % 0.81 0.37 0.33 1.22 0.41 0.30 0.64 0.33

r2 coefficient 0.992 0.996 0.996 0.987 0.996 0.997 0.994 0.997

Range of Validity

Max. Pressure (psi) 20,000 30,000 30,000 30,000 30,000 30,000 30,000 30,000

Min. Temperature (F) 37 77 37 84 76 76 76 78

Max. Temperature (F) 500 600 500 500 500 500 500 500


Table 10: Drilling Fluids Correlation Coefficients and Physical Properties

Reference No. OBM1 SBM1 SBM2 WBM1

Source Field Lab-Prepared Field Field

Physical Properties

Density (lbm/gal) 15.94 12.23 15.10 16.84

Base Fluid Diesel C16C18 IO C16C18 IO Water

S/W or O/W Ratio 77 / 23 75 / 25 77 / 23 n/a

Brine (wt%) CaCl2 (18%) CaCl2 (19%) CaCl2 (24%) n/a

Rheology Temp (F) 150 150 150 120

Plastic Viscosity (cP) 35 17 32 24

Yield Point (lbf/100 ft2) 10 15 14 7

LSYP (lbf/100 ft2) 4 7 10 2

10-sec Gel (lbf/100 ft2) 8 12 22 4

10-min Gel (lbf/100 ft2) 15 20 29 6

Figs. 15a-15b: Isotherm comparisons for the (a) mineral oils and (b) synthetics listed in Tables 5 and 6.

Figs. 16a-16b: Isotherm comparisons for (a) diesel oils and (b) brines shown in Tables 7 and 8.

5.0

5.5

6.0

6.5

7.0

7.5

8.0

0 5000 10000 15000 20000 25000 30000

Den

sit

y (

lb/g

al)

Pressure (psi)

S1

S2

S3

S4

S5

39 F

450 F

Fig. 15b

5.0

5.5

6.0

6.5

7.0

7.5

8.0

0 5000 10000 15000 20000 25000 30000

Den

sit

y (

lb/g

al)

Pressure (psi)

MO1

MO2

MO3

MO4

MO5

39 F

450 F

Fig. 15a

5.5

6.0

6.5

7.0

7.5

8.0

8.5

0 5000 10000 15000 20000 25000 30000

Den

sit

y (

lb/g

al)

Pressure (psi)

D1 (Red)

D2 (Mexico)

D3 (Alaska)

39 F

450 F

Fig. 16a

7.5

8.0

8.5

9.0

9.5

10.0

10.5

11.0

11.5

0 5000 10000 15000 20000 25000 30000

Den

sit

y (

lb/g

al)

Pressure (psi)

B1 (19.3% CaCl2)B2 (25% CaCl2)B3 (10% NaCl)B4 (20% NaCl)

39 F

450 F

Fig. 16b


( )

(

) (

)

Determining ESD Profile and Hydrostatic Pressure Determining the ESD profile is a key step in the process to accurately calculate downhole hydrostatic pressure. This

process involves a step-wise integration of short well segments whose individual fluid densities have been corrected for

compressibility and thermal-expansion effects. It is important to note that ESD cannot be determined from entering

bottomhole pressure and temperature into a chart like Fig. 12. This would instead yield a local density, or the average drilling fluid density in a short well segment referred to above.

If PVT behavior on a fully formulated drilling fluid is unknown, it can be estimated from considering the concentration,

compressibility and thermal expansion of the included fluids and solids. This compositional, mass-balance model3,4

is a good

choice for this calculation:

(2)

In this equation, (P2,T2) is the drilling fluid density at the pressure P2 and temperature T2 of interest. Also, o2 and w2 represent the oil and water densities at P2 and T2, respectively, and o1 and w1 are the same at a reference P1 and T1, all four of which need to be calculated using Eq. 1. The terms fo, fw, fs, and fc represent the respective volume fractions for the oil,

water, solids and chemicals not already considered in the equation. Typically, solids are assumed incompressible, chemical

volumes are ignored, and water is considered brine of a given salt concentration. Eq. 2 applies equally to oil-in-water (water-

based drilling fluids) and water-in-oil emulsions (oil and synthetic-based drilling fluids).

The process for determining ESD involves a step-wise integration of 50 to 100-ft well segments for which the contained

fluid densities have been corrected for compressibility and thermal-expansion effects using Eq. 2. The method is suitable for

implementation in a spreadsheet application. Starting requirements for this process are a directional profile, a temperature

profile, and correlation coefficients either for the drilling fluid itself or its constituents. The directional profile is critical

because all hydrostatic-pressure-related calculations consider only true vertical depths.

Simply stated, the pressure on the fluid in a given segment is the cumulative hydrostatic pressure acting on that segment.

Using temperature taken from the temperature profile, the local density can be calculated by Eq. 1 if correlation coefficients are available for the drilling fluid. Otherwise, Eq. 1 is first used for each of the fluid constituents and then

combined in Eq. 2. The product of the calculated local density gradient and the segment true vertical length yields the

segment hydrostatic pressure that can be incrementally added to provide the hydrostatic pressure value on the next segment

below (Eq. 3). The ESD of the segment is then calculated using Eq. 4:

(3)

(4)

In Eq. 3, Hi is the hydrostatic pressure (psi) at the bottom of segment i and Hi-1 is the hydrostatic pressure at the top; i is the local density (lbm/gal) and Li is the segment true vertical length (ft). In Eq. 4, ESDi is the equivalent static density (lbm/gal) at

true vertical depth TVD (ft).

Fig. 17 demonstrates use of this process to determine the ESD profile of SBM2 in an offshore well drilled in 5,000 ft of

water. Fig. 17a shows the static geothermal (formation) temperature profiles and a representative circulating profile. Fig. 17b

plots the local density of the fluid as a function of depth for the two temperature profiles. As expected, the local density increases in the riser section, and the pressure effect (increasing density) dominates the temperature effect for the circulating

case. The ESD profiles (Fig. 17c) respond similarly; however, the effects are not as pronounced because the entire column of

fluid above any point is considered in the ESD calculation. Calculated ESD using the static versus the circulating temperature

profile results in a difference of more than 0.1 lbm/gal (104 psi).

Fig. 18 illustrates the difference between downhole ESD and surface measured density for the three field drilling fluids

systems (Tables 9 and 10) in a 20,000-ft HTHP well and a deepwater well. The three lines on the left-hand side indicate the

HTHP well with assumed bottomhole temperature of 500F. The three lines on the right-hand side indicate the deepwater

well in 5,000 ft of water depth with a mudline temperature of 40F and bottomhole temperature of 200F. Surface

temperatures were assumed to be 70F in all cases. The deepwater well resulted in higher ESDs than the HTHP well for the

three fluids. The non-aqueous fluids also show higher compressibility than the water-based drilling fluid in the deepwater

well. Interestingly, the HTHP well showed that temperature had a bigger effect on the non-aqueous fluids than on the WBM,

even though the curves appear to converge at deeper depths. This was possibly due to the pressure effect dominating the

temperature effect at depth for the non-aqueous fluids. The overall range of the ESD variation downhole exceeds 0.7 lbm/gal,

which corresponds to more than 725 psi.


Conclusions 1. Data measured using a commercial PVT pycnometer and calculated correlation coefficients are provided for several

field drilling fluids and for a range of mineral oils, synthetics, diesel oils, and brines used to formulate water,

synthetic, and oil-based drilling fluids.

2. Most tests were run at temperatures from 40 to 600F and pressures from atmospheric to 30,000 psi, ranges that generally exceed those used in previously published studies.

3. Regression analyses of the data sets fit well to the 2nd order polynomial equation published in API RP13D. 4. The results extend the ability to predict drilling fluid densities and hydrostatic pressures under extreme temperatures

and pressures.

5. Procedures are presented to predict equivalent static densities and hydrostatic pressures during the well-planning phase and during drilling operations.

Acknowledgments

The authors thank the management of M-I SWACO for supporting this effort and Marc Churan and George McMennamy

for conducting the analytical tests. They also thank Grace Instruments Company for running duplicate and supporting tests.

Figs. 17a-17c: Comparison of (a) static and circulating temperature profiles, (b) downhole local densities, and (c) ESD

profiles for SBM2 for a deepwater well.

Fig. 18: Downhole equivalent static density profiles for three different drilling fluid systems for an HTHP and a

5,000-ft deepwater well.

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Dep

th (

ft)

Downhole ESD minus Surface Mud Weight (lbm/gal)

SBM2

OBM1

WBM1

HTHP Well

5,000-ft DW Well

0

5000

10000

15000

200000 50 100 150 200 250

De

pth

(ft

)

Fluid Temperature ( F)

Static

Circulating

Fig. 17a

15.2 15.3 15.4 15.5 15.6 15.7Local Density (lbm/gal)

Static

Circulating

Fig. 17b

15.2 15.3 15.4 15.5 15.6 15.7Equivalent Static Density (lbm/gal)

Static

Circulating

Fig. 17c


Nomenclature a1..c2 = Correlation coefficients (Eq. 1)

API = American Petroleum Institute

B = Brine

D = Diesel

ESD = Equivalent Static Density, lbm/gal

fo, fw,

fs, fc = Volume fractions for oil, water, solids, chemicals, dimensionless (Eq. 2)

H = Hydrostatic pressure, psi

HTHP = High-Temperature / High-Pressure

IO = Internal Olefin

L = True vertical length of well segment, ft

LSYP = Low-Shear Yield Point, lbf/100ft2

MO = Mineral Oil

OBM = Oil-Based Mud

P = Pressure, psi

PVT = Pressure-Volume-Temperature

PVTP = PVT Pycnometer

S = Synthetic

SBM = Synthetic-Based Mud

T = Temperature, F WBM = Water-Based Mud

= Density, lbm/gal o1, w1 = Oil and water densities at condition 1 (Eq. 2) o2, w2 = Oil and water densities at condition 2 (Eq. 2)

References 1. McMordie, W.O., Bland, R.G. and Hauser, J.M. Effect of Temperature and Pressure on the Density of Drilling

Muds. SPE 11114, 1982 SPE Annual Technical Conference, New Orleans, 26-29 September 1982. 2. Baranthol, C., Alfenore, J., Cotterill, M.D. and Poux-Guillaume, G. Determination of Hydrostatic Pressure and

Dynamic ECD by Computer Models and Field Measurements on the Directional HPHT Well 22130C-13. SPE/IADC 29430, 1995 SPE IADC Drilling Conference, Amsterdam, 28 February 2 March 1995.

3. Hoberock, L.L., Thomas, D.C. and Nickens, H.V. Heres How Compressibility and Temperature Affect Bottom-Hole Mud Pressure. Oil & Gas Journal (22 March 1982) 160.

4. Peters, E.J., Chenevert, M.E. and Zang, C. A Model for Predicting the Density of Oil-Based Muds at High Pressures and Temperatures. SPE 18036, 1988 SPE Annual Technical Conference, Houston, 2-5 October 1988 and SPE Drilling Engineering (June 1990) 141.

5. Isambourg, P., Anfinsen, B.T., and Marken, C. Volumetric Behavior of Drilling Muds at High Pressure and High Temperature. SPE 36830, 1996 SPE European Petroleum Conference, Milan, 22-24 October 1996.

6. Zamora, M., Broussard, P.N. and Stephens, M.P. The Top 10 Mud-Related Concerns in Deepwater Drilling Operations. SPE 59019, 2000 SPE International Petroleum Conference, Villahermosa, Tabasco, Mexico, 1-3 February 2000.

7. Hemphill, T. and Isambourg, P. New Model Predicts Oil, Synthetic Mud Densities. Oil & Gas Journal (25 April 2005) 56.

8. API Recommended Practice 13D Rheology and Hydraulics of Oil-Well Drilling Fluids, 6th ed. American Petroleum Institute, 2010.

9. Demirdal, B., Miska, S., Takach, N. and Cunha, J.C. Drilling Fluids Rheological and Volumetric Characterization Under Downhole Conditions. SPE 108111, 2007 SPE Latin American and Caribbean Petroleum Engineering Conference, Buenos Aires, 15-18 April 2007.

10. Demirdal, B. and Cunha, J.C. Olefin-Based Synthetic-Drilling-Fluids Volumetric Behavior Under Downhole Conditions. SPE 108159, Rocky Mountain Oil & Gas Symposium, Denver, 16-18 April 2007 and SPE Drilling & Completions (June 2009) 239.

11. Hussein, A.M.O. and Amin, R.A.M. Density Measurement of Vegetable and Mineral Based Oil Used in Drilling Fluids. SPE 136974, 2010 Annual SPE International Conference, Tinapa-Calabar, Nigeria, 31 July 7 August 2010.

12. Zamora, M., Enriquez, F., Roy, S. and Freeman, M.A. Measuring PVT Characteristics of Base Oils, Brines, and Drilling Fluids Under Extreme Temperatures and Pressures, AADE-12-FTCE-44, 2012 AADE Fluids Technology Conference and Exhibition, Houston, 10-11 April 2012.

13. Grace Instrument, Houston, M7500PVT Ultra HPHT Pycnometer. http://www.graceinstrument.com/M7500PVT_ Ultra_HPHT_Pycnometer.shtml.

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