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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
D2 6.9080 @74F 2.69 Normal, branched, cyclic, and aromatic hydrocarbons from C8 to C27
D3 6.9831 @73F 3.66 Normal, branched, cyclic, and aromatic hydrocarbons from C7 to C25
* 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.
4 M. Zamora, S. Roy, K. Slater and J. Troncoso SPE-160029
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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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SPE-160029 Study on the Volumetric Behavior of Base Oils, Brines, and Drilling Fluids Under Extreme Temperatures and Pressures 5
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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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6 M. Zamora, S. Roy, K. Slater and J. Troncoso SPE-160029
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
Pressure Coefficients
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
Temperature Coefficients
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
Fitting Statistics for Modeled Data
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
Pressure Coefficients
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
Temperature Coefficients
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
Fitting Statistics for Modeled Data
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
SPE-160029 Study on the Volumetric Behavior of Base Oils, Brines, and Drilling Fluids Under Extreme Temperatures and Pressures 7
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
8 M. Zamora, S. Roy, K. Slater and J. Troncoso SPE-160029
( )
(
) (
)
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.
SPE-160029 Study on the Volumetric Behavior of Base Oils, Brines, and Drilling Fluids Under Extreme Temperatures and Pressures 9
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
10 M. Zamora, S. Roy, K. Slater and J. Troncoso SPE-160029
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.
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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.