SPE 110194 A Consistent and Accurate Dead-Oil-Viscosity Method David F. Bergman, BP America, and Robert P. Sutton, Marathon Oil Company Copyright 2007, Society of Petroleum Engineers This paper was prepared for presentation at the 2007 SPE Annual Technical Conference and Exhibition held in Anaheim, California, U.S.A., 11–14 November 2007. 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, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes 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 where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, Texas 75083-3836 U.S.A., fax 01-972-952-9435.
Abstract The calculation of pressure drop resulting from the flow of oil through porous media or pipes requires the evaluation of viscosity. This is the single most important transport property necessary to accurately calculate pressure drop. The basis for oil viscosity calculations using a traditional black oil approach is the determination of dead or gas free oil viscosity. A total of 23 dead oil viscosity calculation methods have been identified from the literature and evaluated in this paper. A large database consisting of data from conventional PVT reports, crude oil assays and the literature was compiled from over 3000 samples from around the world. The number of actual viscosity measurements exceeded 9800. An evaluation of the correlations yielded unacceptable results largely due to the failure of the methods to properly account for the physics of the problem. In general this results from the methods’ failure to properly account for the change in viscosity with temperature and to address the chemical nature of the oil. A significant improvement in results can be realized through the use of the Watson characterization factor in addition to oil API gravity and temperature in the correlation of viscosity. This work has identified the character of the crude to have a significant effect on oil viscosity especially for oils with gravities less than 25 API. Methods have been proposed in the literature that utilize the Watson characterization factor; however, these have been largely ignored in the upstream oil industry. Therefore, a new method has been developed which shows significant improvement over existing methods. At reservoir conditions, a 2-13 fold reduction in average absolute error was noted when compared with the error observed from traditional methods. At surface process conditions, this improvement ranged 3-60 fold. In addition, an updated correlation for Watson characterization has been developed. The ASTM density correction for changing temperature has been
examined. Revised coefficients were developed which enhance the method’s accuracy for both oils and pure components and provide a suitable means to convert kinematic viscosity to absolute viscosity. Introduction Numerous relationships have been proposed over the years that relate dead oil viscosity and temperature to commonly measured oil properties. Table 1 summarizes many of these relationships and supplements the information presented by Lake47. A review of these methods shows that the correlations can be placed into one of the following functional categories. Category
Equation Type
Method Beal, Beggs & Robinson, Glasø, Labedi, Ng & Egbogah, Kaye, AlKhafaji, Petrosky, Kartoatmodjo & Schmidt, De Ghetto, Bennison, Elsharkawy, Bergman, Dindoruk & Christman, Hossain, and Naseri
1
μ od = f (γ API , T )
2
μ od = f (μ ref , Tb , T )
3
μ od = f (γ API , K w , T )
Standing
4
ν = f (γ API , Tb , T )
Twu, Fitzgerald
Orbey & Sandler
The table shows category 1 is most popular equation choice for correlating viscosity, and traditionally this has been the approach used in the upstream section of the oil and gas industry. It is also the least accurate approach for calculating viscosity and the change in viscosity with temperature. A further note on this table - some methods substitute specific gravity for API gravity. These properties are directly related from the following well known equation.
γ =
141.5 ................................................................ (1) 131.5 + γ API
Additionally other methods require the boiling point to provide an additional characterization parameter for the oil. This quantity can be derived from the definition of the Watson51,52 characterization factor as follows:
2
SPE 110194
Tb = (γ K w )3 .......................................................................(2)
In this paper, the Watson characterization factor (or Watson K factor) is used to further describe the character of the oil. Methods utilizing the functional form offered by Category 4 require knowledge of density at temperature to convert from kinematic viscosity to absolute viscosity.
μ = ν ρ ...............................................................................(3) Therefore, an examination of auxiliary relationships between density and temperature is appropriate and is presented in a later section of this paper. Furthermore, the basic relationship of dead oil viscosity and temperature is investigated to provide a sound physical basis to explore the accuracy of existing methods and to provide a foundation for the development of a more robust viscosity calculation method. Database In order to ascertain the accuracy of the published dead oil viscosity methods and the supporting auxiliary relationships, a database was developed. Data from conventional oil PVT reports, crude oil assays and pure component data was included in the database which encompassed the following ranges of properties2,3,6,10,11,13,18,33,34,38,41,42,43,45,46,48,50. Property Oil gravity, °API Watson characterization factor Density (at temperature), g/cc Dead oil viscosity, cp Temperature, °F
Minimum 0.45 10.8 0.389 0.0596 -40
Maximum 135.9 14.25 1.061 1.357 × 1012 500
A total of 9837 viscosity measurements from 3047 fluid samples are present in the database which represent samples from many of the major producing basins around the world. The distribution of the data is shown in Figs. 1-4. For many of the fluid samples, viscosity was measured at several temperatures which help to validate the measurement and ensure this behavior is properly correlated. Auxiliary Relationships The development of a relationship to calculate dead oil viscosity requires methods to reliably determine fluid properties such as density that change with temperature. Correlations that relate kinematic viscosity to temperature must include the evaluation of density at temperature to convert results to absolute viscosity. The Watson K factor is defined from the average boiling point temperature and specific gravity. Boiling point temperature is rarely reported for crude oils and therefore must be derived from other more commonly measured liquid properties. Furthermore, the basic relationship of viscosity and temperature must be explored to provide a realistic metric to evaluate both data and correlations.
Viscosity-Temperature Relationships Dead oil viscosity and temperature have a relationship where viscosity decreases with increasing temperature for any given hydrocarbon liquid. Using the proper technique, a linear relationship can be established. The relationship is valid over a wide range of temperatures from the wax appearance temperature (WAT) to the boiling point temperature (BPT) of the sample. At temperatures below the WAT, the viscositytemperature slope trend increases as wax crystals appear in the liquid. This phonomenon does not occur at the WAT but usually 20-30 °F below the WAT (as defined by rigorous methods such as cross polar microscopy) when sufficient wax crystals are formed which perturb the normal viscositytemperature relationship. At temperatures between the WAT and BPT, deviation from the straight line is an indication of inconsistencies in the measurement. Over the years, several techniques have been proposed within the industry for linearizing viscosity with temperature. ASTM55 provides such a relationship between kinematic viscosity and temperature. The resulting equation is a modification of an earlier work dating to 1921 which related kinematic viscosity and temperature by using a double log form equation. ln (ln(Z )) = A − B ln (Tabs ) ................................................... (4)
where27
(
)
Z = ν + 0.7 + exp − 1.47 − 1.84ν − 0.51ν 2 .......................... (5)
The exponential term in Eqn. 5 is only significant for viscosity less than 2 cSt. For viscosity greater than 2 cSt, the exponential term goes to zero and is therefore insignificant to this method. The ASTM method is used routinely throughout the oil industry to relate changes in kinematic viscosity with temperature. Andrade4 proposed a method to relate dead oil viscosity to absolute temperature. ln (μ od ) = A +
B .............................................................. (6) Tabs
which is also expressed ⎛B ⎜ T
μ od = A e⎝
abs
⎞ ⎟ ⎠
................................................................. (7)
The method37 reportedly results in a linear relationship above the freezing point temperatures to reduced temperatures of approximately 0.7. Bergman54 demonstrated that dead oil absolute viscosity could be expressed in a linear form using the following relationship. The Bergman relationship was developed from an examination of pure component behavior with temperature.
SPE 110194
3
ln[ln(μ od + 1)] = A + B ln (T + 310 ) .......................................(8)
The use of the ASTM and Bergman’s method is further discussed in Table 2. A review of the database developed for this project was conducted for samples with viscosity measurements at three or more temperatures. A total of 1301 samples were identified containing 6614 measurements. As a supplement to Bergman’s method, the coefficients (310 and 1.0) in Eqn. 8 were allowed to vary in a nonlinear regression to determine an optimized function that reduced equation error. Results (labeled Bergman and Sutton) showed a slight variation (302.7 and 0.974) in Bergman’s original values confirming the robustness of the method. The overall results are summarized in the following table. Method ASTM Andrade Bergman Bergman & Sutton
% AE -0.01 0.19 -0.01 0.00
Std Dev 1.13 6.10 1.31 1.20
% AAE 0.77 3.85 0.93 0.84
Std Dev 0.83 4.74 0.93 0.85
Despite it’s acceptance by the industry, the Andrade method performed poorly. The ASTM and updated Bergman and Sutton relationships performed comparably but only slightly better than the original Bergman method. Further correlation work with these three methods resulted in essentially the same statistical results. From a practical standpoint, the ASTM method using kinematic viscosity requires a density at each temperature to convert to absolute viscosity. At extreme temperature conditions, the adjustment of density for temperature effects can be a potential source of error. Therefore, the original Bergman method which directly uses absolute viscosity is recommended based on it accuracy and simplicity. Fig. 5 shows the linear relationship of viscosity with temperature. Pure component data from the n-paraffin, aromatic, cyclohexane, olefin, and naphthalene hydrocarbon families are depicted in the plot. In addition, actual crude oil data is included to illustrate the behavior over a wide range of hydrocarbon liquids. In general, the data forms a linear relationship with well behaved slopes. This presentation is useful in the determination of consistent viscosity measurements. Density-Temperature Relationships Dead oil viscosity correlations are developed to determine kinematic or absolute viscosity. Kinematic viscosity is related to absolute viscosity through the following relationship.
ν=
μ ..............................................................................(9) ρ
The use of Eqn. 9 requires the knowledge of density at the temperature of interest. Since dead oil viscosity correlations require oil API gravity as a correlating parameter, the density at 60 °F is known.
ρ o60 = 0.999012
141.5 ......................................... (10) 131.5 + γ API
where the value 0.999012 g/cc is the density of water at 60 °F and the remainder of the equation is the standard relationship between specific gravity and API gravity. ASTM32 has developed a procedure for adjusting oil density to different temperature conditions. The thermal expansion coefficient with a base temperature of 60 °F is calculated from the equation below.
α 60 =
(K 0 + K1ρo ) ....................................................... (11a) 60
ρ o260
The coefficients K0 and K1 are determined experimentally for the liquid of interest. ASTM provides the following values for generalized crude oils through lubricating oils. Category Generalized crude oils Gasoline and naphthenes Jet fuels and kerosene Diesels, heating oils and fuel oils Lubricating oils Generalized crude oils (BS update) Pure component (BS)
K1 K0 3.410957 x 10-4 0.0 1.924571 x 10-4 2.438 x 10-4 3.303010 x 10-4 0.0 1.038720 x 10-4 2.701 x 10-4 1.440427 x 10-4 1.896 x 10-4 2.5042 x 10-4 8.302 x 10-5 3.4175 x 10-4 -4.542 x 10-5
The density is calculated from the following equation
ρ oT = ρ o60 e[−α 60 ΔT (1 + 0.8 α 60 ΔT )] ....................................... (11b) where ΔT = T − 60 ..................................................................... (11c)
ASTM publishes tables of volume correction factors (VCF) for various type of fluids and ranges of temperatures. The VCF is determined as follows VCF =
1 = e[−α 60 ΔT (1 + 0.8 α 60 ΔT )] ................................... (11d) Bo
Therefore, the resulting density as affected by a temperature change can be determined from the density at 60 °F and the VCF.
ρ oT = ρ o60 VCF ............................................................... (12) In 1992, Gomez21 published a method to determine VCF accounting for both liquid density and Watson K factor. The resulting equation is as follows:
4
SPE 110194
Y = a0 + a1 K wa2 γ oa3 Tabs 1.8 + a4 K wa5 γ oa6 a7 K wa8 γ oa9
(
a13 K wa14 γ oa15 X =
) +a ( )
Tabs
3
Tabs
)+ )+ 2
1.8
4 a11 a12 Tabs 10 K w γ o 1.8
1.8
Tabs
( (
5
where a0 = a1 = a2 = a3 = a4 = a5 = a6 = a7 = a8 = a9 = a10 =
-0.21
0.59
0.35
0.52
0.39 -0.01
0.66 0.54
0.52 0.28
0.55 0.46
1.8
a16 + a17 K wa2 γ oa3 + a18 K wa5 γ oa6 + a19 K wa8 γ oa9 + a20 K wa11 γ oa12 + a21 K wa14 γ oa15
VCF =
...............(13a)
ASTM – API Weighted Combination Gomez BS Update to ASTM
Pure component data (2121 measurements) reported by API was also evaluated. ....................(13b) Method
Y ........................................................................(13c) X
0.3569622 -0.1399101 -1.765440 -2.125040 0.03861655 -3.530880 -4.250080 -5.385089 × 10-3 -5.296320 -6.375120 3.627542 × 10-4
a11 = a12 = a13 = a14 = a15 = a16 = a17 = a18 = a19 = a20 = a21 =
-7.061760 -8.500160 -9.508922 × 10-6 -8.827200 -10.62520 0.3566053 -40.35242 3,215.505 -129,456.5 2,517,668. -19,053,400.
The equation is unnecessarily complex but offers a comparison to the ASTM procedure as well as adding Watson K as a correlating parameter. The VCF methods offered by ASTM and Gomez were further tested against crude oil data (1516 measurements) derived from differential liberation studies and data published by ASME (224). A total of 1740 measurements were evaluated with the results summarized below and in Fig. 6. Despite the addition of another correlating parameter, the results show the ASTM method to be more accurate than the method proposed by Gomez. It is interesting to note that the ASTM options for kerosenes and lubricating oils yielded more accurate results than the general crude oil option for this data set. To ensure that the errors were minimized for the viscosity calculations in this paper, the coefficients were updated. The accuracy of the updated ASTM method is depicted graphically in Fig. 7. These results show that in general, errors should be on the order of ±1.0% over the temperature range of interest. Errors do increase with temperature above the base temperature of 60 °F. For most cases below 300 °F, measured data yielding errors greater than 1% should be considered suspect. Method ASTM – General Crude Oil ASTM – Gasolines & Naphthenes ASTM – Kerosenes ASTM – Diesels ASTM – Lube Oils
% AE
Std Dev
% AAE
Std Dev
-0.24
0.60
0.36
0.53
-1.01
1.07
1.08
1.00
0.11 -0.19 0.17
0.56 0.58 0.55
0.31 0.34 0.32
0.48 0.51 0.48
ASTM – General Crude Oil ASTM – Gasolines & Naphthenes ASTM – Kerosenes ASTM – Diesels ASTM – Lubricating Oils ASTM – API Weighted Combination Gomez BS fit to Pure Component Data
% AE
Std Dev
% AAE
Std Dev
-0.63
0.86
0.75
0.76
-1.42
1.57
1.51
1.49
-0.44 -0.20 0.21
0.71 0.62 0.73
0.59 0.47 0.49
0.59 0.45 0.58
-0.84
1.35
0.97
1.26
0.03
0.67
0.48
0.47
0.00
0.59
0.39
0.43
The accuracy of the Gomez method improved slightly for the pure components while the accuracy of the ASTM method declined. However, the equation coefficients offered by ASTM are calibrated for crude oils and refinery products. A nonlinear regression was used to develop coefficients suitable for the pure component data. Results are shown in Fig. 8. As with the crude oil data, the accuracy of the ASTM method is generally within ± 1.0% over the temperature range of interest with errors increasing at extreme temperatures. Therefore, it is desirable to limit the required temperature range to minimize the introduction of error. As a matter of practicality, dead oil viscosity measurements are considered to have an accuracy of 5-15%28,49 so the procedure for determining VCF is more than adequate. Crude Oil Characterization Watson characterization factors are useful since they remain reasonably constant for chemically similar hydrocarbons. The Watson characterization factor provides a means of determining the paraffinicity or character of a crude oil or hydrocarbon component. A characterization factor of 12.5 or greater indicates a hydrocarbon compound predominately paraffinic in nature. Lower values of this factor indicate hydrocarbons with higher amounts of naphthenic or aromatic components. Highly aromatic hydrocarbons exhibit values of 10.0 or less. For crude oils, the following ranges were observed by Nelson30. Crude Oil Base Paraffinic Intermediate Naphthenic
Watson K factor 12.2-12.9 11.5-12.2 10.5-11.5
As defined, the Watson characterization factor is a function of boiling point temperature and specific gravity.
SPE 110194
Kw =
Tb1 / 3
γo
5
........................................................................(14)
Using equations developed by Riazi-Daubert39 relating molecular weight to boiling point temperature and specific gravity, Whitson54 reexpressed Eqn. 14 as a function of molecular weight and specific gravity. K w = 4.5579 M o0.15178 γ o−0.84573 ........................................(15)
The equation used by Whitson was developed from data taken from pure component hydrocarbons from C5 to C20 which has a limited range of applicability to compounds with molecular weights from 70 to 300. Riazi40 later updated the equation relating boiling point temperature to molecular weight and specific gravity increasing the upper limit to molecular weights ranging 300700; however, it was also stated that this method could also be used for molecular weights as low as 70. This equation modified to calculate Watson K is
[
K w = a1 exp(a2 M o + a3 γ o + a4 M o γ o ) M oa5 γ oa 6
]
a7
γ oa8 .(16)
where a1 = a2 = a3 = a4 =
16.80642 1.6514 × 10-4 1.4103 -7.5152 × 10-4
a5 = a6 = a7 = a8 =
0.5369 -0.7276 0.3333 -1.0
Some of the oil and fraction data from the crude oil assays reported specific gravity, molecular weight and the Watson characterization factor. A total of 561 data points were identified as shown in Fig. 9. The data ranged as follows: Property API gravity Specific gravity Molecular weight Watson K factor
Minimum 0.8 0.661 92 10.16
Maximum 82.7 1.070 1320 12.94
For comparison, the pure component data is also presented on the plot. It should be noted that the pure component data covers a wider range of Watson characterization factor values than the oil and fraction data with the latter typically constrained to 10.8 < Kw < 13.5. This range agrees with the ranges for crude oils reported by Nelson. Figs. 10-11 show the accuracy of the method proposed by Whitson. As expected, the accuracy degrades at molecular weights above 300 with values of Watson characterization factor overpredicted. The updated equation from Riazi (Figs. 12-13) shows increased accuracy up to molecular weights of approximately 700. It will be later demonstrated that the Watson characterization can be an important parameter in the correlation of oil viscosity. Therefore, Eqn. 16 was updated using nonlinear regression techniques to minimize the error in predicted Watson K resulting in the following equation.
[
K w = b1 exp(b2 M o + b3 γ o + b4 M o γ o ) M ob5 γ ob6
]
b7
γ ob8 ... (17)
where b1 = b2 = b3 = b4 =
2012.84 -1.8519 × 10-3 -3.70833 1.31441 × 10-3
b5 = b6 = b7 = b8 =
0.589485 3.36211 0.3333 -1.0
The accuracy of Eqn. 17 is shown in Figs. 14-15. It should be noted that Eqns. 15-16 were developed from lower molecular weight, pure component data. Eqn. 17 was developed using higher molecular weight oil and fraction data and is accurate over a wide range of properties as evidenced in Figs. 14-15. However, Eqn. 17 is not suitable for lighter pure components with API gravity greater than 60, a specific gravity less than 0.74 and a molecular weight less than 150. The table below summarizes the results of the three methods. Method Whitson Riazi Bergman & Sutton
% AE 1.27 -0.11 -0.15
Std Dev 2.20 1.15 0.85
% AAE 1.52 0.70 0.50
Std Dev 2.04 0.92 0.71
For the purposes of this paper, the Watson K factor can be estimated from a TBP analysis using techniques discussed by UOP12. Alternatively, it can be calculated from the molecular weight and specific gravity using Eqn. 17. These values can be obtained for the oil itself or derived from the plus fraction values reported in PVT report. Fig. 16 shows the values derived for the entire database used in this study. This plot should provide guidance for typical values of Watson K factor with oil API gravity. Dead Oil Viscosity Correlations A review of viscosity measurements shows common evaluation temperatures of 100 and 210 °F. The measured data used in the viscosity-temperature section of this paper was utilized to determine the viscosity at a constant temperature of 100 °F. The results are shown as a function of API gravity and Watson characterization factor in Fig. 17. The authors note that the lines in this plot are not meant to be correlations but are placed simply as a reference to aid in visualizing the trends. The plot clearly shows the effect of Watson characterization factor on viscosity. As the characterization factor increases (i.e. the oil becomes more paraffinic containing long chain paraffin molecules), viscosity increases for a given oil gravity. Furthermore, as the API gravity decreases, the effect of the characterization factor becomes more important. Fig. 18 illustrates the change in viscosity for a hypothetical set of oils with a base Watson K of 11.5. The change in viscosity with Watson K factor is greater as API gravity decreases. It is also noted that the change is less significant at higher temperatures. Correlations proposed by Twu, Fitzgerald, Orbey and Standing evaluate viscosity using the Watson K factor (or derived boiling point temperature) as a correlating parameter
6
SPE 110194
while other methods ignore this parameter. Fig. 19 illustrates this result. The Beggs and Robinson method is plotted to illustrate the problem of not accounting for the effect of crude character on viscosity. By eliminating this key property, one cannot hope to accurately correlate viscosity. The Orbey-Sandler and Fitzgerald methods display anomalous behavior at low gravity and high values of Watson K factor. Referring to Fig. 19, this behavior could impact the method’s accuracy as the anomaly occurs within a range of expected properties. Standing’s method tends to overpredict viscosity at the higher values of Watson K while the Twu method is more reasonably behaved. Based on observations of the performance of the Twu model, it was decided to use it as a basis for an updated dead oil viscosity correlation. Various forms from Twu were tested against the database using a nonlinear regression technique to minimize the error in calculated oil viscosity. The final resulting equations follow: ⎞ ⎛ 0.533272 +1.91017 ×10 −4 Tb + ⎟ ⎜ Tco = Tb ⎜ 7.79681×10 −8 Tb2 − 2.84376 ×10 −11Tb3 + ⎟ ⎟ ⎜ ⎟ ⎜ 9.59468×10 27 Tb−13 ⎠ ⎝
α = 1 − Tb
Tco
−1
.......(18a)
...................................................................(18b)
ln (ν 2 − 0.152995) = 2.40219 − 9.59688α + 3.45656α 2 −143.632α 4
..................(18c)
ln (ν 1) = 0.701254 + 1.38359 ln (v 2) + 0.103604 [ln (ν 2)]2 ..(18d)
γ oo = 0.843593 − 0.128624 α − 3.36159 α 3 −13749.5α 12 .(18e) Δγ o = γ o − γ oo ..................................................................(18f) x = 2.68316 − 62.0863 Tb0.5 ..........................................(18g) f 2 = x Δγ o − 47.6033 Δγ o2 Tb0.5 .....................................(18h) ⎛ 1+ 2 f 2 ln (ν 210 + 232.442 Tb ) = ln (ν 2 + 232.442 Tb ) ⎜⎜ ⎝ 1− 2 f 2
2
⎞ ⎟⎟ .(18i) ⎠
f1 = 0.980633 x Δγ o − 47.6033 Δγ o2 Tb0.5 .......................(18j) 2
⎛ 1 + 2 f1 ⎞ ⎟⎟ ...(18k) ln (ν 100 + 232.442 Tb ) = ln (ν 1 + 232.442 Tb ) ⎜⎜ ⎝ 1 − 2 f1 ⎠
ρ o100 = 0.999012 γ o60 VCF100 ............................................(18l)
μ od100 = ν 100 ρ o100 ............................................................. (18m) ρ o210 = 0.999012 γ o60 VCF210 ........................................... (18n) μ od 210 = ν 210 ρ o210 ............................................................ (18o) As a point of further discussion, Eqns. 18a-k follow the outline proposed by Twu. Eqns. 18 (c,d, and g-k) have been modified from the original Twu equations using a nonlinear regression routine designed to minimize the error in the calculated viscosity. The 9837 data points included in the regression came from measurements from oils, petroleum fractions identified in crude assays and pure component data from API 42 and API 44. As the goal of this work is the accurate simulation of crude oil viscosity, the pure component data was limited to data with Watson characterization factors of 10.8 to 13.0 – a range consistent for crude oils. Furthermore the data included API gravity ranges from 0.45 to 135.9 to maintain the integrity of the correlation over the target area of interest (5-80 API). The method determines oil viscosity at temperatures of 100 and 210 °F which are standard temperatures historically used in viscosity correlations and product specifications. The viscosity at the temperature of interest is then determined using the linear relationship determined from earlier work by Bergman described in Table 2. The practical limits of this technique approximately constrain temperatures to the WAT and boiling point of the oil. The determination of the WAT or boiling point limit is beyond the scope of this paper. The data included in the regression included measured data over the temperature range -40 to 500 °F which should easily cover the range of expected temperature conditions. The resulting correlation was tested to ensure it met physical behavior criteria from real fluids. Fig. 20 shows the behavior of viscosity with the Watson characterization factor. Over the range of available data, the method is well behaved. Turning to the change in viscosity with temperature, Figs. 21-22 compare the behavior of pure components and crude oil with published correlations assuming an oil gravity of 30 °API and a Watson K factor of 11.5. Noticeable anomalies are detected in the behavior of the many of the methods. These anomalies are typically an abnormal change in the slope of the line primarily at extreme temperatures below 100 °F or above 200 °F. Some methods will even predict a decrease in viscosity with decreasing temperature which is physically impossible. Using measured pure component data as a standard, the table below subjects the methods to a rigorous consistency test to check for proper change in viscosity with temperature over the temperature range 35-350 °F for the API gravities indicated. The methods either pass or fail. Methods not listed in the table did not pass any of the criteria.
SPE 110194
Method Twu Orbey & Sandler Fitzgerald Bennison Bergman Dindoruk & Christman Hossain Bergman & Sutton
7
20 °API X X X X X X X X
30 °API X X X
40 °API X X X
X
X
X
X
The statistical accuracy of the correlations is summarized in Tables 3-6 and Figs. 23-46. It is important to note both the accuracy and consistency of the methods which can be seen in the average absolute error and standard deviation columns in the tables and can also be visualized in the plots. As the range of data is rather large, histograms were constructed to examine correlation accuracy over selected ranges of temperature, API gravity and Watson K factor. These results are depicted in Figs. 47-53. Fig. 48 examines correlation accuracy over selected temperature ranges. Measured data was available to a minimum value of -40 °F. Several correlations are not designed to evaluate viscosity at a temperature less than 0 °F. This range was included to solely to illustrate the consistency of the new method. A more conventional (35-100 °F) temperature range was included for a comparison of all of the methods. Conclusions 1. A large database of crude oil, petroleum fractions and pure component properties was created with the purpose of evaluating existing dead oil viscosity correlations and developing a new consistent and accurate method. 2. The existing dead oil viscosity correlations were categorized into four groups. Most of the methods fall into category 1 which utilizes oil gravity and temperature to estimate absolute viscosity. This is the traditional approach and is also the least accurate approach. Improvments are seen in the category 2 and 3 approaches; however, the category 2 method lacks flexibility while category 3 is physically inconsistent at lower temperatures. Category 4 methods add an additional parameter which further characterizes the oil and offers increased accuracy in the calculated viscosity. 3. The determination of the Watson characterization parameter was evaluated using standard industry accepted techniques. These were found to be in error when used to characterize the heavier crude oils with API gravities less than 20-30 API. A new method was developed which offers accurate results to 10 API. 4. Methods to depict linear trends in viscosity with temperature were evaluated. The Andrade method which has been widely used in the industry was found to be inaccurate. The accuracy of the ASTM and Bergman methods were found to be comparable.
5.
6.
7.
8.
The Bergman method is recommended over the ASTM method as it is easier to apply. Methods to correct density for temperature changes were evaluated. A modified ASTM approach was found to be suitably accurate for both crude oils and pure components. A chart illustrating the effect on Watson characterization factor on oil viscosity was prepared to emphasize the importance of proper oil characterization to the accurate correlation of viscosity. Existing correlations were compared for the consistency of the calculated viscosity with changing temperature using measured data trends as a metric. Several of the correlations failed this consistency test. A new method was developed from data collected for the database. The new method provides for accurate and consistent results over a wide range of conditions. All of the viscosity methods were tested against the database and the results were reported. These results can aid in the section of suitable methods for engineering calculations that require viscosity over the wide range of conditions encountered in production and processing applications.
Acknowledgment The authors would like to thank the management of Marathon Oil Company and BP America for permission to publish this paper. Finally, the primary author would like to thank his wife, Nancy. Without her patience and understanding, this would have never been written. Statistical Quantities AE = average error, % N X icalc − X imeas 100 AE = N i =1 X i meas
∑
AAE
=
average absolute error, % 100 N
AAE =
S
=
N
X icalc − X i meas
i =1
X imeas
∑
standard deviation
∑ (X N
S=
X N
= =
i
−X
)2
i =1
N −1 generic dependent variable number of observations
Nomenclature = oil formation volume factor, Bbl/STB Bo Kw = Watson characterization factor Rs = solution gas-oil ratio, SCF/STB T = temperature, °F Tb = average boiling point temperature, °R Tc = critical temperature, °R Tabs = temperature, °R VCF = volume correction factor
8
α α60
= reduced boiling point temperature = coefficient of thermal expansion at a base temperature of 60 °F ν = kinematic viscosity, cSt μ = absolute viscosity, cp μod = dead oil viscosity, cp ρ = density, g/cm3 = oil density, g/cm3 ρo ρo60 = oil density at 60 °F, g/cm3 ρoT = oil density at temperature “T”, g/cm3 γo = oil specific gravity γAPI = oil API gravity x,f1,f2,ν1,ν2 are correlating parameters Subscripts 100 = property at 100 °F 210 = property at 210 °F Superscripts ° = n-alkanes property
References 1. Al-Khafaji, A.H., Abdul-Majeed, G.H. and Hassoon, S.F.: “Viscosity Correlation For Dead, Live And Undersaturated Crude Oils,” J. Pet. Res. (Dec., 1987) 116. 2. Amin, M.B. and Beg, S.A.: “Generalized Kinematic Viscosity-Temperature Correlation for Undefined Petroleum Fractions of IBP -95 °C to 455 °C+ Boiling Ranges,” Fuel Science and Tech. Int. vol. 12 (1994) 97129. 3. Amin, M.B. and Maddox, R.N.: “Estimate Viscosity vs. Temperature,” Hyd. Proc. (Dec., 1990) 131-135. 4. Andrade, E.N. da C.: “The Viscosity of Liquids,” Nature, (1930) 125, 309. 5. API Technical Data Book – Petroleum Refining: API, Washington DC 6th ed, (April, 1997) Chap 11. 6. API Project 42 – Properties of Hydrocarbons of High Molecular Weight, Synthesized by Research Project 42 of American Petroleum Institute, published by API Division of Science and Technology, 1966. 7. Beal, C.: “The Viscosity of Air, Water, Natural Gas, Crude Oil and Its Associated Gases at Oil Field Temperatures and Pressures,” SPE Reprint Series No. 3 Oil and Gas Property Evaluation and Reserve Estimates, SPE, Richardson, TX (1970) 114-127. 8. Beggs, H.D. and Robinson, J.R.: “Estimating the Viscosity of Crude Oil Systems,” J. Pet. Tech. (Sept., 1975) 1140-1141. 9. Bennison, T.: “Prediction of Heavy Oil Viscosity,” presented at the IBC Heavy Oil Field Development Conference, London (Dec. 2-4, 1998). 10. BHP Crude Oil Assays, available from World Wide Web: http://globaloil.bhpbilliton.com/ 11. BP Crude Oil Assays, available from World Wide Web: http://www.bp.com/ 12. Calculation of UOP Characterization Factor and Estimation of Molecular Weight of Petroleum Oils UOP Method 375-88, UOP Inc. (1986).
SPE 110194
13. Chevron Crude Oil Assays, available from World Wide Web: http://crudemarketing.chevron.com/ 14. De Ghetto, G., Paone, F. and Villa, M.: “Reliability Analysis on PVT Correlations,” paper SPE 28904 presented at the European Petroleum Conference in London U.K. (Oct. 25-27, 1994). 15. Dindoruk, B. and Christman, P.G.: “PVT Properties and Viscosity Correlations for Gulf of Mexico Oils,” paper SPE 71633 presented at the 2001 SPE ATCE in New Orleans, LA (Sept 30-Oct 3, 2001). 16. Egbogah, E.O. and Ng, J.T.: “An Improved Temperature-Viscosity Correlation For Crude Oil Systems,” J. Pet. Sci. Eng. (July, 1990) 197-200. 17. Elsharkawy, A.M. and Alikhan, A.A.: “Models For Predicting The Viscosity of Middle East Crude Oils,” Fuel (June, 1999) 891-903. 18. Exxon Crude Oil Assays, available on World Wide Web: http://www.exxonmobil.com/apps/crude_oil/index.html 19. Fitzgerald, D.J.: “A Predictive Method for Estimating the Viscosity of Undefined Hydrocarbon Liquid Mixtures,” M.S. Thesis, The Pennsylvania State University (1994). 20. Glasø, Ø.: “Generalized Pressure-Volume-Temperature Correlations,” J. Pet. Tech. (May, 1980) 785-795. 21. Gomez, J.V.: “New Correlation Predicts Density of Petroleum Fractions,” Oil and Gas J. (July 13, 1992) 4952. 22. Hossain, M.S., Sarica, C., Zhang, H.Q., Rhyne, L., and Greenhill, K.L.: “Assessment and Development of Heavy-Oil Viscosity Correlations,” SPE/PSCIM/CHOA 97907 PS2005-407 presented at the 2005 SPE International Thermal Operations and Heavy Oil Symposium, Calgary, Canada (Nov. 103, 2005). 23. Kartoatmodjo, R.S.T. and Schmidt Z.: “Large Data Bank Improves Crude Physical Property Correlations,” Oil and Gas J. (Jul. 4, 1994) 51-55. 24. Kaye, S. E.: “Offshore California Viscosity Correlations,” COFRC, TS85000940, (Aug. 1985). 25. Labedi, R.M.: “PVT Correlations of the African Crudes,” PhD Thesis, Colorado School of Mines (May, 1982). 26. Labedi, R.M.: “Improved Correlations For Predicting The Viscosity of Light Crudes,” J. Pet. Sci. Eng. (Oct, 1992) 221-234. 27. Manning, R.E.: “Computational Aids for Kinematic Viscosity Conversions from 100 and 210 °F to 40 and 100 °C.” J of Testing and Evaluation, JTEVA, Vol. 2, No. 6 (Nov. 1974) 522-528. 28. Mehrotra, A.K., Monnery, W.D. and Svrcek, W.Y.: “A Review of Practical Calculation Methods for Viscosity of Liquid Hydrocarbons and Their Mixtures,” Fluid Phase Equilibria (1996) 344-355. 29. Naseri, A.., Nikazar, M. and Mousavi Dehghani, S.A.: “A Correlation Approach for Prediction of Crude Oil Viscosities,” J. Pet. Sci. Eng. (2005) 163-174. 30. Nelson, W.L.: Petroleum Refinery Engineering, 4th Ed., McGraw-Hill book company Inc, New York (1958). 31. Orbey, H. and Sandler, S.I.: “The Prediction of the Viscosity of Liquid Hydrocarbons and Their Mixtures as
SPE 110194
32.
33. 34. 35.
36. 37. 38. 39. 40. 41.
42.
43. 44. 45. 46. 47.
48. 49.
50. 51.
a Function of Temperature and Pressure,” The Cdn. J. of Chem. Eng. (June, 1993) 437-446. Petroleum Measurement Tables – Volume Correction Factors, Volume X-Background, Development, and Program Documentation, ASTM D 1250-80, ASTM, Philadelphia, PA. (73-80). Petronas Crude Oil Assays, available on World Wide Web: http://www.petronas.com.my/ Petrosky, G.E., Jr.: “PVT Correlations for Gulf of Mexico Crude Oils,” M.S. Thesis, University of Southwestern Louisiana (1990). Petrosky, G.E., Jr. and Farshad, F.F.: “Viscosity Correlations for Gulf of Mexico Crude Oils,” paper SPE 29468 presented at the SPE Production Operations Symposium, Oklahoma City, OK (April 2-4, 1995). Pipeflow 2, Main Reference Manual, Volume No. 1, CEPS (Chevron Geosciences), (1984). Reid, R.C., Prausnitz, J.M., and Sherwood, T.K.: The Properties of Gases and Liquids, Third Edition, McGraw-Hill Book Co. (1977) 437-439. Reservoir Fluid Database (http://www.RFDbase.com), GeoMark Research, Inc., Houston, TX (2006). Riazi, M.R. and Daubert, T.E.: “Simplify Property Predictions,” Hyd. Proc. (Mar., 1980) 115-16. Riazi, M.R.: Characterization and Properties of Petroleum Fractions, 1st Edition, ASTM, West Conshohocken, PA (2005) Chapt. 2. Rønningsen, H.P.: “Correlations for Predicting Viscosity of W/O-Emulsions based on North Sea Crude Oils,” paper SPE 28968 presented at the SPE International Symposium on Oilfield Chemistry, San Antonio, TX (Feb., 1995). Rossini, F.D., Pitzer, K.S., Arnett, R.L., Braun, R.M. and Pimentel, G.C.: Selected Values of Physical and Thermodynamic Properties of Hydrocarbon and Related Compounds, Carnegie Press, Pittsburg, PA (1953). Santos Crude Oil Assays, available on the World Wide Web: http://www.santos.com/ Standing, M.B.: Volumetric and Phase Behavior of Oil Hydrocarbon Systems, 9th Printing, Society of Petroleum Engineers of AIME, Dallas, TX (1981). Statoil Crude Oil Assays, available on World Wide Web: http://www.statoil.com/crudeinfo Strategic Petroleum Reserve Crude Oil Assays, available on World Wide Web: http://www.spr.doe.gov/ Sutton, R.P..: Petroleum Engineering Handbook, General Engineering, Vol. 1, J. Fanchi and L.W. Lake (eds.) Society of Petroleum Engineers, Richardson, TX (2006) 257-331. Total Crude Oil Assays, available on World Wide Web: http://www.totsa.com/ Twu, C.H.: “Internally Consistent Correlation for Predicting Liquid Viscosities of Petroleum Fractions,” Ind. Eng. Chem. Process Des. Dev. Vol. 24 No. 4 (1985) 1287-1293. Watkins, R.N.: Petroleum Refinery Distillation, 2nd Ed., Gulf Publishing Company, Houston, (June, 1979). Watson, K.M. and Nelson, E.F.: “Improved Methods for Approximating Critical and Thermal Properties of Petroleum,” Ind. Chem. Eng. (1933) 880.
9
52. Watson, K.M. Nelson, E.F. and Murphy, G.B.: “Characterization of Petroleum Fractions,” Ind. and Eng. Chem. (1935) 1460-64. 53. Whitson, C.H.: “Characterizing Hydrocarbon Plus Fractions,” SPEJ (Aug., 1983) 683-693. 54. Whitson, C.H. and Brulé, M.R.: Phase Behavior, 1st ed, Society of Petroleum Engineers, Richardson, TX (2000) Chapt. 3. 55. Wright, W.A.: “An Improved Viscosity-Temperature chart for Hydrocarbons,” J of Materials, JMLSA, Vol. 4, No. 1 (Mar. 1969) 19-27.
SI Metric Conversion Factors 141.4/(131.5+°API) = bbl × 0.1589873 = = ft3 × 0.02831685 cp × 1.0E−03* = (°F–32)/1.8* = psi × 6.894757E+00 = °R × 5/9* = *Conversion factor is exact
g/cm3 m3 m3 Pa•s °C kPa °K
10
SPE 110194
Author
Beal 1
7,44
(1946)
Correlation
Origin
No. of Data Points
μod Range (cp)
T Range (°F)
API Range
AE (%)
SD (%)
AAE (%)
U.S.A
753
0.865 to 1,550
98 to 250
10.1 to 52.5
24.2
na
na
U.S.A
753
0.865 to 1,550
98 to 250
10.1 to 52.5
24.2
na
na
na
460
na
70 to 295
16.0 to 58.0
−0.64
13.53
na
North Sea
29
0.616 to 39.10
50 to 300
20.1 to 48.1
na
na
na
Libya
91
0.66 to 4.79
100 to 306
32.2 to 48.0
−2.61
23.06
na
Nigeria and Angola
29
0.72 to 21.15
104 to 221
25.5 to 45.5
−5.87
33.03
na
na
394
na
59 to 176
5.0 to 58.0
−5.13
55.51
na
⎡ ⎛ 8.33 ⎞ ⎤ ⎟⎥ ⎢ 2 .302585 ⎜⎜ 0.43 + γ API ⎟⎠ ⎥⎦ ⎝
X = e ⎣⎢
μ od
⎛ 1 .8 × 10 7 = ⎜⎜ 0 .32 + 4 .53 γ API ⎝
⎞ ⎛ 360 ⎞ ⎟⎜ ⎟ ⎟ ⎜ T + 200 ⎟ ⎠ ⎠⎝
X
2 3 A = C1 + C 2 γ API + C3 γ API + C 4 γ API + C5 T + 2 C 6 T 2 + C7 T 3 + C8 γ API T + C9 γ API T + C10 γ API T 2
Beal 2
7,36
(1946)
Beggs & 8 Robinson (1975) 20
Glasø
(1980) Labedi
25,26
(1982) Labedi
25
(1982) Egbogah & 16 Ng (1983)
μ od = 10 A
where C1 = C2 = C3 = C4 = C5 =
0.1054399 × 102 -0.4452142 0.6647024 × 10-2 -0.3359724 × 10-4 -0.4705169 × 10-1
C6 = C7 = C8 = C9 = C10 =
0.8315574 × 10-4 -0.7890499 × 10-7 0.1351673 × 10-2 -0.114495 × 10-4 -0.9550553 × 10-6
X = 10 (3.0324 − 0.02023γ API )T −1.163
μod = 10 X − 1.0 ⎛ 3.141 ×1010 ⎞ ⎟ log (γ API )[10.313 log (T ) − 36.447 ] 3.444 ⎟ T ⎝ ⎠
μod = ⎜⎜
−4.7013 −0.6739 μ od = 10 9.224 γ API T
−2.92 −2.0356 μ od = 10 9.37 γ API T
X = 10 [1.8653 − 2.5086 ×10
−2
]
γ API − 0.56441 log (T )
μ od = 10 − 1.0 X
Table 1 – Summary of published dead oil viscosity methods
SPE 110194
11
Author
Correlation Tco =
Origin
No. of Data Points
μod Range (cp)
T Range (°F)
API Range
AE (%)
SD (%)
AAE (%)
100 & 210
-4.0 to 93.1
na
na
7.85
Tb 0.533272 + 1.91017 ×10 − 4 Tb + 7.79681×10 −8 Tb2 − 2.84376 ×10 −11 Tb3 + 9.59468 ×10
α = 1−
Tb
27
Tb13
Tco
( ) ln (ν ) = 0.801621 + 1.37179 ln (v )
o + 1.5 = 4.73227 − 27.0975 α + 49.4491α 2 − 50.4706 α 4 ln ν 210 o 100
Twu
γ oo = 0.843593 − 0.128624 α − 3.36159 α 3 − 13749.5 α 12
49
x = 1.99873 − 56.7394 Tb0.5
(1985)
0.25 to 290 cSt
o 210
Δγ o = γ o − γ oo
f 2 = x Δγ o − 21.1141 Δγ o2 Tb0.5
(
)
⎛ 1+ 2 f 2 o + 450 Tb ⎜⎜ ln (ν 210 + 450 Tb ) = ln ν 210 ⎝ 1− 2 f 2
⎞ ⎟⎟ ⎠
2
Pure Components (C6-C44)
at 100 °F 563 0.33 to 1,750 cSt at 210 °F
Petroleum Fractions
f1 = 1.33932 x Δγ o − 21.1141 Δγ o2 Tb0.5
(
)
⎛ 1 + 2 f1 ⎞ o ⎟ ln (ν 100 + 450 Tb ) = ln ν 100 + 450 Tb ⎜⎜ ⎟ ⎝ 1 − 2 f1 ⎠
2
see ASTM method in Table 2 to find ν and μod at temperature
γ API ≤ 12 Kaye
μod = 10[T γ API > 12
24
(1986)
Al-Khafaji
μod = 10[T
1
(1987)
μ od =
34,35
Petrosky
(1990)
Kartoatmodjo 23 & Schmidt (1991)
μ od =
μ od =
−0.65
−0.65
10 ( 2.203 − 0.0254 γ API )
] −1
10 ( 2.305 − 0.03354 γ API )
] −1
10 (4.9563 − 0.00488 T )
(γ API
+ T 30 − 14.29 )2.709
2.3511×10 7 T 2.10255
1.6 ×10 9 T 2.8177
log (γ API )[4.59388 log (T ) − 22.82792 ]
[5.7526 log (T ) − 26.9718 ]
log(γ API )
Table 1 – Summary of published dead oil viscosity methods (continued)
California Offshore
na
na
143 to 282
6.6 to 41.1
na
na
na
na
350
na
60 to 300
15.0 to 51.0
−2.4
4.8
3.2
Gulf of Mexico
118
0.725 to 10.25
114 to 288
25.4 to 46.1
−3.48
16.4
12.38
Indonesia, North America, Middle East, and Latin America
661
0.506 to 682.0
80 to 320
14.4 to 59.0
−13.16
na
39.61
12
SPE 110194
Author
Correlation
⎡ ⎞ ⎛ ⎟ = k ⎢− 1.6866 + 1.4010 ⎜ Tb ⎜T ⎟ ⎢ ⎝ abs ⎠ ⎣ where for the alkanes C 3 to C 20
⎛μ ln ⎜ od ⎜ μ ref ⎝ Orbey & 31 Sandler (1993)
⎞ ⎛ T ⎟ + 0.2406 ⎜ b ⎟ ⎜T ⎠ ⎝ abs
Origin
⎞ ⎟ ⎟ ⎠
2⎤
⎥ ⎥ ⎦
μ ref = 0.225 cp k = 0.143 + 2.5722 ×10 −3 Tb −1.25 ×10 −6 Tb2
No. of Data Points
μod Range (cp)
T Range (°F)
API Range
AE (%)
SD (%)
AAE (%)
na
0.2 to 7830
-310 to 644
6.3 to 147.6
na
na
6.4
API<10
API<10
Pure component data nC1-nC20, Olefins and Cyclic Hydrocarbons from API Project 44
for this database
μ ref = 0.229 cp k = 1.2148 + 5.227 ×10 − 4 Tb −1.402 ×10 −7 Tb2
Selected samples from API Project 42
Extra heavy oil (°API ≤ 10)
X = 10 [1.90296 − 1.2619×10 γ API − 0.61748 log (T )] Heavy oil (10 < °API ≤ 22.3) −2
X = 10 [2.06492 − 1.79×10
−2
]
γ API − 0.70226 log (T )
Light oil (°API > 31.1) 14
De Ghetto (1994)
X
= 10 [1.67083 − 1.7628×10
−2
]
γ API − 0.61304 log (T )
for each evaluation of X
μ od = 10 − 1.0 X
Medium oil ( 22.3 < °API ≤ 31.1)
μ od =
220.15 ×10
T 3.5560 Agip Model X
9
log(γ API )[12.5428 log (T ) − 45.7874 ]
= 10 [1.8513 − 2.5548 ×10
−2
]
γ API − 0.56238 log (T )
μ od = 10 X − 1.0
Table 1 – Summary of published dead oil viscosity methods (continued)
Mediterranean Basin, Africa, Persian Gulf, and North Sea
195
0.46 to 1,386.9
81 to 342
6.0 to 56.8
17.4
8.9
10
10
37.8
21.9
22.3
22.3
35.1
22.8
API>31.1
API>31.1
21.6
15.6
Agip
Agip
30.7
20.0
na
SPE 110194
13
Author
Correlation
No. of Data Points
μod Range (cp)
T Range (°F)
API Range
Saudi Arabia, Iran, Iraq, Kuwait, Libya, North Sea, U.S.A., Indonesia, Soviet Union, Romania, and South America
7,267
0.3 to 30,000 cSt
−30 to 500
North Sea
16
6.4 to 8,396
Middle East
254
Worldwide
na
Origin
AE (%)
SD (%)
AAE
-2 to 71.5
−3.77
na
14.08
39 to 300
11.1 to 19.7
na
na
16.0
0.6 to 33.7
100 to 300
19.9 to 48
−2.5
25.8
19.3
454
0.5 to 500,000
40 to 400
12 to 60
-4.65
38.52
27.23
na
na
na
na
na
na
na
(%)
A1 = 34.931 − 8.84387 ×10 −2 Tb + 6.73513 ×10 −5 Tb2 − 1.01394 ×10 − 8 Tb3 −3
A2 = − 2.92649 + 6.98405 ×10 Tb − 5.09947 ×10 Fitzgerald
7.49378 ×10
5,19
−10
−6
Tb2
+
Tb3
log X 1 = A1 + A2 K w
(1997)
log X 2 = − 1.35579 + 8.16059 ×10 − 4 Tb + 8.38505 ×10 − 7 Tb2
ν 100 = X 1 + X 2
logν 210 = − 1.92353 + 2.41071×10 − 4 Tb + 0.51130 log(Tb ν 100 )
see ASTM method in Table 2 to find ν and μod at temperature Bennison
9
(1998) 17
Elsharkawy (1999)
μ od = 10 (−0.8021γ API + 23.8765 )T (0.31458γ API − 9.21592 ) X = 10 [2.16924 − 0.02525 γ API − 0.68875 log (T )]
μ od = 10 X − 1.0
Bergman
53
X = e [22.33 − 0.194 γ API
]
2 + 0.00033 γ API + (−3.2 + 0.0185 γ API )ln (T + 310 )
μ od = e − 1.0 X
(2000)
log (μ od ρ o ) =
1 − 2.17 X 3 [K w − (8.24 γ o )] + 1.639 X 2 − 1.059
where X 1 = 1 + 8.69 log[(T + 459.67 ) 559.67 ] Standing (2000)
53
X 2 = 1 + 0.544 log[(T + 459.67 ) 559.67 ] X3
(2.87 X 1 − 1)γ o = − 0.1285
ρo =
2.87 X 1 − γ o
γo
1 + 0.000321(T − 60 )10 (0.00462 γ API )
Table 1 – Summary of published dead oil viscosity methods (continued)
14
SPE 110194
Author
Correlation
μ od = Dindoruk & 15 Christman (2001)
No. of Data Points
μod Range (cp)
T Range (°F)
API Range
Gulf of Mexico
95
0.896 to 62.63
121 to 276
na
184
12 to 451
Iran
250
0.75 to 54
Origin
AE (%)
SD (%)
AAE
17.4 to 40.0
−2.86
16.74
12.62
32 to 215
7.1 to 22.3
na
na
27.4
105 to295
17 to 44
6.61
na
7.77
(%)
a3T a 4 log (γ API )[a1 log (T ) + a 2 ] a5 pba 6 + a7 Rsa8
where a1 = 14.505357625
a5 = − 3.1461171 ×10 − 9
a2 = − 44.868655416
a6 = 1.517652716
a3 = 9.36579 ×109
a7 = 0.010433654
a4 = − 4.194017808
a8 = − 0.000776880
22
Hossain (2005) Naseri
μ od = 10 (−0.71523γ API + 22.13766) T (0.269024γ API −8.268047 )
29
(2005)
μ od = 10[11.2699 − 4.2699 log(γ API )− 2.052 log(T )]
Table 1 – Summary of published dead oil viscosity methods (continued)
SPE 110194
15
Method
Calculation Procedure The ASTM method is defined ln ln (Z ) = A + B ln (T + 459.67 )
(
Z = ν + 0.7 + exp − 1.47 −1.84ν − 0.51ν 2
[
)
ν = Z − 0.7 − exp − 0.7487 − 3.295 (Z − 0.7 ) + 0.6119 (Z − 0.7 )2 − 0.3193 (Z − 0.7 )3
]
the slope, B, is determined from known viscosity at two temperatures, 100 and 210 °F Z100 = ν 100 + 0.7 + e (−1.47 −1.84ν 100 − 0.51ν 100 ) 2
Z 210 = ν 210 + 0.7 + e (−1.47 −1.84ν 210 − 0.51ν 210 ) 2
ASTM
B=
[ln ln(Z 210 ) − ln ln(Z100 )] [ln(669.67 ) − ln(559.67 )]
and the viscosity at any temperature, T, can then be determined ln ln (Z T ) = ln ln (Z100 ) + B [ln (Tabs ) − ln (559.67 )]
[
ν T = Z T − 0.7 − exp − 0.7487 − 3.295 (ZT − 0.7 ) + 0.6119 (Z T − 0.7 )2 − 0.3193 (ZT − 0.7 )3
]
convert kinematic viscosity to absolute viscosity
ρ oT = 0.999012 γ o60 VCFT μ od = ρ oT ν T Note: for clarification ln ln (Z ) = ln[ln(Z )] Bergman’s method is defined ln[ln(μ od + 1)] = A + B ln (T + 310)
the slope, B, is determined from known viscosity at two temperatures, 100 and 210 °F Bergman
B=
[(
)] [ (
)]
ln ln μ od 210 + 1 − ln ln μ od100 + 1 ln (520 ) − ln (410 )
and the viscosity at any temperature, T, can then be determined
[ ( ( (
))
)]
μ od = exp exp ln ln μ od100 + 1 + B(ln(T + 310) − ln(410)) − 1 Table 2 – Summary of methods relating viscosity and temperature and procedure to calculate viscosity at any temperature
16
SPE 110194
>10% Error Count Beal 1 8950 18.6 102.8 59.6 85.8 7684 Beal 2 9024 34.5 120.9 68.1 105.7 7862 Beggs & Robinson 9024 222.9 2693.0 248.7 2690.7 8203 Glaso 9024 13.2 144.8 52.2 135.7 7647 Labedi-Libya 9024 87.5 523.4 121.6 516.5 8087 Labedi-Nigeria/Angola 9024 47.4 153.0 85.8 135.3 7890 Ng & Egbogah 9024 29.1 95.5 61.8 78.4 7893 Twu 9024 -9.6 28.7 20.4 22.4 5228 Kaye 9024 32.3 216.0 72.6 205.9 7758 Al-Khafaji 8973 17.4 342.4 66.5 336.3 7883 Petrosky 9024 19.4 141.5 57.1 130.9 7830 Kartoatmodjo & Schmidt 9024 18.8 245.7 60.3 238.9 7600 Orbey & Sandler 9024 -32.9 30.7 34.6 28.9 6793 De Ghetto 9024 26.2 93.7 60.0 76.6 7852 De Ghetto-Agip 9024 15.7 85.1 55.2 66.6 7886 Fitzgerald 9024 -9.1 25.9 19.4 19.5 4939 Bennison 9024 1.8 502.7 125.6 486.8 8668 Elsharkawy 9024 49.9 129.4 73.7 117.4 8015 Bergman 9024 33.8 130.3 61.6 119.7 7730 Standing 9024 174.3 1.5E+04 202.4 1.5E+04 5839 Dindoruk & Christman 9024 -1.7 85.3 45.3 72.3 7792 Hossain 9024 -50.4 105.2 81.8 83.1 8681 Naseri 9024 -15.2 91.8 55.7 74.6 8153 Bergman & Sutton 9024 -5.1 21.4 16.6 14.5 4992 Table 3 – Statistical accuracy of viscosity methods (API gravity range: 5-80; temperature range: 35-500 °F) >10% Error Method # Pts % AE Std Dev % AAE Std Dev Count Beal 1 1440 63.1 158.2 91.2 143.8 1258 Beal 2 1442 68.0 201.4 90.5 192.3 1251 Beggs & Robinson 1442 1150.0 6660.0 1150.0 6660.0 1413 Glasø 1442 19.1 130.5 61.2 116.8 1242 Labedi-Libya 1442 -17.4 82.9 52.1 66.8 1285 Labedi-Nigeria/Angola 1442 184.1 287.5 209.2 269.7 1346 Ng & Egbogah 1442 12.3 120.4 58.4 106.0 1247 Twu 1442 -11.7 40.3 25.8 33.2 975 Kaye 1442 39.2 390.0 91.8 381.0 1262 Al-Khafaji 1433 55.2 144.6 84.3 129.8 1256 Petrosky 1442 9.6 101.5 60.5 82.0 1293 Kartoatmodjo & Schmidt 1442 43.2 152.8 76.4 139.3 1268 Orbey & Sandler 1442 -38.8 33.2 40.9 30.6 1174 De Ghetto 1442 32.1 150.4 74.4 134.5 1272 De Ghetto-Agip 1442 -2.2 102.2 54.4 86.5 1282 Fitzgerald 1442 -15.5 25.7 22.4 19.9 924 Bennison 1442 -80.0 130.7 97.7 118.1 1425 Elsharkawy 1442 72.5 233.2 95.5 224.8 1286 Bergman 1442 52.8 235.6 80.9 227.4 1229 Standing 1442 11.5 545.0 70.8 540.5 1109 Dindoruk & Christman 1442 2.8 117.4 55.7 103.3 1276 Hossain 1442 -76.5 149.6 98.5 136.1 1428 Naseri 1442 36.1 150.6 77.6 134.0 1279 Bergman & Sutton 1442 -9.3 21.9 18.1 15.3 847 Table 4 - Statistical accuracy of viscosity methods (API gravity range: 5-80; temperature range: 35-100 °F) Method
# Pts
% AE
Std Dev
% AAE
Std Dev
SPE 110194
17
>10% Error Count Beal 1 4442 30.8 97.8 61.6 82.0 3761 Beal 2 4462 45.5 107.4 70.0 93.3 3880 Beggs & Robinson 4462 73.9 126.8 96.9 110.2 4060 Glasø 4462 7.5 123.8 49.8 113.6 3762 Labedi-Libya 4462 23.4 129.6 60.9 116.8 3867 Labedi-Nigeria/Angola 4462 42.0 101.5 77.4 77.9 3962 Ng & Egbogah 4462 14.2 77.5 52.0 59.1 3829 Twu 4462 -9.4 27.3 20.6 20.3 2654 Kaye 4462 13.1 154.9 58.7 144.0 3735 Al-Khafaji 4433 38.8 468.0 69.7 464.4 3833 Petrosky 4462 6.3 99.6 49.3 86.7 3792 Kartoatmodjo & Schmidt 4462 10.2 189.3 52.8 182.0 3766 Orbey & Sandler 4462 -34.5 30.3 35.9 28.6 3423 De Ghetto 4462 14.1 73.7 52.9 53.2 3848 De Ghetto-Agip 4462 1.9 69.0 47.1 50.4 3827 Fitzgerald 4462 -9.5 25.9 19.8 19.2 2503 Bennison 4462 -69.7 65.0 82.3 48.1 4341 Elsharkawy 4462 36.3 95.4 64.1 79.4 3903 Bergman 4462 37.0 112.8 63.3 100.4 3819 Standing 4462 338.1 2.1E+04 367.1 2.1E+04 2959 Dindoruk & Christman 4462 -4.6 76.9 45.5 62.1 3853 Hossain 4462 -68.5 77.2 84.9 58.7 4376 Naseri 4462 -20.3 60.0 47.6 41.7 3964 Bergman & Sutton 4462 -5.0 22.3 17.6 14.6 2657 Table 5 - Statistical accuracy of viscosity methods (API gravity range: 5-80; temperature range: 100-200 °F) >10% Error Method # Pts % AE Std Dev % AAE Std Dev Count Beal 1 2404 -13.6 53.7 40.5 37.9 2044 Beal 2 2434 15.7 73.7 54.6 51.9 2103 Beggs & Robinson 2434 10.0 67.0 50.1 45.6 2100 Glasø 2434 16.0 188.6 50.7 182.4 2037 Labedi-Libya 2434 161.8 348.2 174.6 342.0 2296 Labedi-Nigeria/Angola 2434 -5.4 56.1 41.6 37.9 2063 Ng & Egbogah 2434 51.0 95.8 73.3 80.1 2224 Twu 2434 -8.9 24.0 18.1 18.1 1318 Kaye 2434 49.8 158.0 77.1 146.6 2121 Al-Khafaji 2421 -21.2 125.4 49.9 117.0 2121 Petrosky 2434 32.8 176.2 59.0 169.2 2105 Kartoatmodjo & Schmidt 2434 14.1 347.9 56.9 343.5 2000 Orbey & Sandler 2434 -29.5 29.2 31.2 27.4 1778 De Ghetto 2434 34.3 82.7 60.5 65.9 2109 De Ghetto-Agip 2434 37.0 86.9 63.5 69.8 2175 Fitzgerald 2434 -5.5 26.1 18.2 19.6 1239 Bennison 2434 -6.4 86.4 63.5 58.8 2218 Elsharkawy 2434 54.4 98.2 75.6 83.1 2236 Bergman 2434 22.3 73.8 52.1 56.9 2072 Standing 2434 15.9 102.8 28.3 100.1 1462 Dindoruk & Christman 2434 -1.0 85.7 42.2 74.6 2075 Hossain 2434 -30.3 76.4 64.4 51.2 2260 Naseri 2434 -33.2 64.7 52.9 49.9 2273 Bergman & Sutton 2434 -3.6 20.2 15.2 13.8 1253 Table 6 - Statistical accuracy of viscosity methods (API gravity range: 5-80; temperature range: 200-300 °F) Method
# Pts
% AE
Std Dev
% AAE
Std Dev
18
SPE 110194
Data Distribution by Oil Gravity
Data Distribution by Watson K Factor
2500
3000 2500
2000
2000
1500
1500 1000
1000
500
500
0 1 00 50 75 00 25 50 75 00 25 -1 1. 1. 2. 2. 2. 2. 3. 3. 1. .8 -1 -1 -1 -1 -1 -1 -1 -1 >1 5 0 5 0 5 0 5 1 10 1 .2 .5 .7 .0 .2 .5 .7 11 11 11 12 12 12 12
>8 0
-8 0
-7 0
70
-6 0
60
-5 5
55
50
-5 0
-4 5
45
-3 5
-4 0
40
35
30
20
-3 0
-2 0 10
010
0
Watson K Factor Range
Oil Gravity Range, °API
Fig. 2 - Distribution of data by Watson characterization factor
Fig. 1 – Distribution of data by API gravity Data Distribution by Temperature
Data Distribution by Viscosity
3000
1400
2500
1200 1000
2000
800
1500
600
1000
400
500
200 0 0. 00 0. .25 25 0. -0. 5- 5 0 0. .75 75 -1 1. . 0 01 1. . 5 52 2. . 0 02 2. . 5 53 3. . 0 05. 5. 0 01 10 0 -2 25 5 50 50 10 10 0- 0 25 250 0 50 -50 10 0-1 0 00 00 -5 0 00 >5 0 00 0
0 35 50 75 00 25 50 75 00 25 50 00 50 00 00 0- 35- 50- 5-1 0-1 5-1 0-1 5-2 0-2 5-2 0-3 0-3 0-4 >4 -4 7 10 12 15 17 20 22 25 30 35
Temperature Range, °F
Viscosity Range, cp
Fig. 4 - Distribution of data by viscosity
Fig. 3 – Distribution of data by temperature
Viscosity of Pure Hydrocarbons by Family 3
n-Paraffins Aromatics Cyclohexanes Naphthalenes
10,000 cp
2
1000 cp
Olefins
Wax
Crude Oils
Ln Ln (Viscosity,cp + 1)
100 cp
1
Inconsistent Measurement
10 cp 3 cp
0 1 cp 0.5 cp
-1
0.3 cp
-2 0.1 cp 0 °F
-3 5.6
50 °F
5.8
100 °F
6
150 °F
6.2
200 °F
250 °F
6.4
300 °F
400 °F
6.6
Ln (T + 310)
Fig. 5 – Relationship between viscosity and temperature for pure components compared with crude oil
SPE 110194
19
Volume Correction Factor Error
Volume Correction Factor Error
(Bergman & Sutton)
5
5
4
4
3
3
2
2 VCF Error, %
VCF Error, %
(ASTM D 1250 General Crudes)
1 0 -1
1 0 -1
-2
-2
-3
-3
-4
-4
-5
-5 0
100
200
300
400
500
0
100
200
Temperature, °F
500
Watson Characterization Factor
Volume Correction Factor Error
(Pure Components, Oils & Fractions)
(Bergman & Sutton - Pure Component)
5
14.0
4
13.5
3
13.0
2
12.5
Watson K Factor
VCF Error, %
400
Fig. 7 - Accuracy of ASTM VCF calculation for crude oil using updated coefficients
Fig. 6 – Accuracy of ASTM VCF calculation for crude oil using general crude values
1 0 -1 -2 -3
Oils & Fractions API Project 44
12.0 11.5 11.0 10.5 10.0
-4
9.5
-5 -100
0
100
200
300
400
500
9.0
600
0
20
40
Temperature, ° F
60
80
100
API Gravity
Fig. 9 – Reported Watson characterization factors for pure components, crude oils and petroleum fractions
Fig. 8 – Accuracy of ASTM VCF calculation for pure components using Bergman & Sutton coefficients
Whitson Method
Whitson Method 15
15
10
10
5
5
% Error
% Error
300
Temperature, °F
0
0
-5
-5
-10
-10 0
20
40
60
API Gravity
Fig. 10 – Error in Whitson method for Watson characterization factor
80
100
0
200
400
600
800
1000
Mole Weight
Fig. 11 - Error in Whitson method for Watson characterization factor
1200
1400
20
SPE 110194
Riazi Method
15
15
10
10
5
5
% Error
% Error
Riazi Method
0
0
-5
-5
-10
-10
0
20
40
60
80
0
100
200
400
800
1000
1200
1400
1200
1400
Fig. 13 - Error in Riazi method for Watson characterization factor
Fig. 12 – Error in Riazi method for Watson characterization factor Bergman & Sutton Method
Bergman & Sutton Method
15
15
10
10
5
5
% Error
% Error
600
Mole Weight
API Gravity
0
0
-5
-5
-10
-10 0
20
40
60
80
0
100
200
Fig. 14 – Error in Bergman & Sutton method for Watson characterization factor
400
600
800
1000
Mole Weight
API Gravity
Fig. 15 - Error in Bergman & Sutton method for Watson characterization factor Trends in Viscosity with Watson K at 100 °F 1.0E+06
15 API 20 API
1.0E+05
30 API 40 API 50 API
Viscosity, cp
1.0E+04
1.0E+03
1.0E+02
1.0E+01
1.0E+00
1.0E-01 10.5
Fig. 16 – Relationship between the Watson characterization factor and oil API gravity
11
11.5 12 12.5 Watson K Factor
13
13.5
Fig. 17 – Relationship between API gravity, Watson K factor and viscosity
SPE 110194
21
Change in Viscosity with Watson K at 100 °F
1000
15 API 15 API & 210 °F
% Change in Viscosity
20 API 30 API 40 API
100
50 API 50 API & 210 °F 1
10
1 11.4
11.5
11.6
11.7
11.8
11.9
12
12.1
Watson K Factor
Fig. 18 – Change in viscosity with Watson characterization factor for constant API gravity
Trends in Viscosity with Watson K at 100 °F 1E+06
Trends in Viscosity with Watson K at 100 °F (Bergman & Sutton) 1.0E+06
15 API 20 API
20 API
30 API
1E+05
15 API
1.0E+05
40 API 50 API
30 API 40 API 50 API
Beggs & Robinson
1E+04
Twu
1.0E+04
Orbey & Sandler
1E+03
Standing
Viscosity, cp
Viscosity, cp
Fitzgerald
1E+02
1.0E+03
1.0E+02
1E+01
1.0E+01
1E+00
1.0E+00
1E-01 10.5
11
11.5 12 12.5 Watson K Factor
13
Fig. 19 – Characteristics of correlations for modeling viscosity behavior - 20 °API oil and variable Watson K
13.5
1.0E-01 10.5
11
11.5 12 12.5 Watson K Factor
13
Fig. 20 – Bergman & Sutton method for modeling viscosity behavior - variable Watson K and API 15-50
13.5
22
SPE 110194
Viscosity of Pure Hydrocarbons by Family 3
n-Paraffins Aromatics Cyclohexanes
10,000 cp
2
Naphthalenes
1000 cp
Olefins Beal 1
Ln Ln (Viscosity,cp + 1)
100 cp
Beal 2 Beggs & Robinson
1
Glaso
10 cp
Labedi-Libya Labedi-Nigeria/Angola
3 cp
Ng & Egbogah
0
Kaye Al-Khafaji
1 cp
Petrosky Kartoatmodjo & Schmidt
0.5 cp
-1
De Ghetto De Ghetto-Agip
0.3 cp
Bennison Elsharkawy Bergman
-2
Dindoruk & Christman Hossain
0.1 cp
Naseri
0 °F
-3 5.6
5.7
50 °F
5.8
5.9
100 °F
6
150 °F
6.1
6.2
200 °F
250 °F
6.3
300 °F
6.4
400 °F
6.5
6.6
6.7
Ln (T + 310)
Fig. 21 – Accuracy of Category 1 correlations to model viscosity change with temperature for 30 °API oil
Viscosity of Pure Hydrocarbons by Family 3
n-Paraffins Aromatics Cyclohexanes
10,000 cp
2
Naphthalenes
1000 cp
Olefins
Ln Ln (Viscosity,cp + 1)
100 cp
Twu Orbey & Sandler
1
Fitzgerald
10 cp
Standing Bergman & Sutton
3 cp
0 1 cp 0.5 cp
-1
0.3 cp
-2 0.1 cp 0 °F
-3 5.6
5.7
50 °F
5.8
5.9
100 °F
6
150 °F
6.1
6.2
200 °F
6.3
250 °F
300 °F
6.4
400 °F
6.5
6.6
Ln (T + 310)
Fig. 22 - Accuracy of Category 2-4 correlations to model viscosity change with temperature for 30 °API 11.5 Kw oil
6.7
SPE 110194
23
Fig. 23 – Accuracy of Beal 1 method
Fig. 24 – Accuracy of Beal 2 method
Fig. 25 – Accuracy of Beggs & Robinson method
Fig. 26 - Accuracy of Glasø method
Fig. 27 - Accuracy of Twu method
Fig. 28 - Accuracy of Labedi (Libya) method
24
SPE 110194
Fig. 29 – Accuracy of Labedi (Nigeria/Angola) method
Fig. 30 - Accuracy of Ng & Egbogah method
Fig. 31 – Accuracy of Kaye method
Fig. 32 - Accuracy of Al-Khafaji method
Fig. 33 - Accuracy of Petrosky method
Fig. 34 - Accuracy of Kartoatmodjo & Schmidt method
SPE 110194
25
Fig. 35 – Accuracy of Orbey & Sandler method
Fig. 36 - Accuracy of De Ghetto method
Fig. 37 – Accuracy of De Ghetto – Agip method
Fig. 38 - Accuracy of Fitzgerald method
Fig. 39 - Accuracy of Bennison method
Fig. 40 - Accuracy of Elsharkawy method
26
SPE 110194
Fig. 41 – Accuracy of Bergman method
Fig. 42 - Accuracy of Standing method
Fig. 43 – Accuracy of Dindoruk & Christman method
Fig. 44 - Accuracy of Hossain method
Fig. 45 - Accuracy of Naseri method
Fig. 46 - Accuracy of Bergman & Sutton method
&
R
1
2 ob in so n
Be al
Be al
Ka ye Al -K Ka h rto af aj at i Pe m od tro jo sk & y Sc O rb hm ey id & t Sa nd le D r e D G e he G tto he t to -A gi p Fi tz ge ra ld Be nn is on El sh ar ka w y Be rg m D an in do St ru an k di & ng C hr is tm an H os sa in Be rg N m as an er i & Su tto n
Tw u
G La La la so be be di d i-L -N ib ig ya er ia /A N ng g ol & a Eg bo ga h
Be gg s
Average Absolute Error, %
& R
1
2 ob in so n
Be al
Be al
Ka ye Al -K Ka h af rto aj at i Pe m od t ro jo sk & y Sc O rb hm ey id & t Sa nd le D r e D G e he G t to he tto -A gi p Fi tz ge ra ld Be nn is on El sh ar ka w y Be rg m D in an do St ru an k di & ng C hr is tm an H os sa in Be rg N m as an er i & Su tto n
Tw u
G La La la so be be di d -N i-L ig ib er ya ia /A N ng g o & Eg l a bo ga h
Be gg s
Average Absolute Error, %
SPE 110194 27
Effect of Oil API Gravity
100 All Temperatures
90
80
70
60
50 5
40
30 3050
20
10
0
Fig. 47 – Summary of dead oil viscosity methods by API gravity for temperatures ranging 35-500 °F
Effect of Temperature
(All API)
100
90
80
70
60
50 35-500 °F -40-100 °F 35-100 °F
40
100-200 °F 200-300 °F >300 °F
30
20
10
0
Fig. 48 – Summary of dead oil viscosity methods by temperature for all ranges of API gravity
&
R
1
2 ob in so n
Be al
Be al
Ka ye Al -K Ka h rto af aj at i Pe m od tro jo sk & y Sc O rb hm ey id & t Sa nd le D r e D G e he G tto he tto -A gi p Fi tz ge ra ld Be nn is on El sh ar ka w y Be rg m D in an do St ru an k di & ng C hr is tm an H os sa in Be rg N m as an er i & Su tto n
Tw u
G La La la so be be di d -N i-L ig ib er ya ia /A N ng g o & Eg l a bo ga h
Be gg s
Average Absolute Error, %
& R
1
2 ob in so n
Be al
Be al
Ka ye Al -K Ka ha rto fa at ji Pe m od tro jo sk & y Sc O rb h m ey id & t Sa nd le D r e D G e he G tto he tto -A gi p Fi tz ge ra ld Be nn is on El sh ar ka w y Be rg m D in an do St ru an k di & ng C hr is tm an H os sa in Be rg N m as an er i & Su tto n
Tw u
G La La la so be be di d -N i-L ig ib er ya ia / An N g go & Eg l a bo ga h
Be gg s
Average Absolute Error, %
28 SPE 110194
Effect of Oil API Gravity
100 Temperature 35-100 °F
90
80
70
60 5
50
40 API<20 2050
30
20
10
0
Fig. 49 – Summary of dead oil viscosity methods by API gravity for temperatures ranging 35-100 °F
Effect of Oil API Gravity
100 Temperature 100-200 °F
90
80
70
60
50 5
40
30
3050
20
10
0
Fig. 50 – Summary of dead oil viscosity methods by API gravity for temperatures ranging 100-200 °F
&
R
1
2 ob in so n
Be al
Ka ye Al -K Ka ha rto fa at ji Pe m od tro jo sk & y Sc O rb h m ey id & Sa t nd le D r e D G e he G t to he tto -A gi p Fi tz ge ra ld Be nn is on El sh ar ka w y Be rg D m in an do St ru an k di & ng C hr is tm an H os sa in Be rg N m as an er i & Su tto n
Tw u
La La Gla be so be di di -N -L ig ib er ya ia /A N n g go & Eg l a bo ga h
Be gg s
Be al
Average Absolute Error, %
& R
1
2 ob in so n
Be al
Be al
Ka ye Al -K Ka h af rto aj at i Pe m od tro jo sk & y Sc O rb hm ey id & t Sa nd le D r e D G e he G tto he t to -A gi p Fi tz ge ra ld Be nn is on El sh ar ka w y Be rg m D an in do St ru an k di & ng C hr is tm an H os sa in Be rg N m as an er i & Su tto n
Tw u
G La la La so be be di d -N i-L ig ib er ya ia /A N ng g o & Eg l a bo ga h
Be gg s
Average Absolute Error, %
SPE 110194 29
Effect of Oil API Gravity Temperature 200-300 °F
100
90
80
70
60
50
40
30 550
20
10
0
Fig. 51 – Summary of dead oil viscosity methods by API gravity for temperatures ranging 200-300 °F
Effect of Oil API Gravity
100 Temperature >300 °F
90
80
70
60
50 5
40
30
3050
20
10
0
Fig. 52 – Summary of dead oil viscosity methods by API gravity for temperatures ranging >300 °F
& R
1
2 ob in so n
Be al
Be al
Tw u Ka ye Al -K Ka h rto af aj at i Pe m od t ro jo sk & Sc y O rb hm ey id & Sa t nd le D r e D G e he G t to he tto -A gi p Fi tz ge ra ld Be nn is on El sh ar ka w y Be rg D m in an do St ru an k di & ng C hr is tm an H os sa in Be rg N m as an er i & Su tto n
La La Gla be so be di di -N -L ig ib er ya ia / A N n g go & Eg l a bo ga h
Be gg s
Average Absolute Error, %
30 SPE 110194
Effect of Watson K Factor (35 < T <500 °F)
100
90
80
70
60
50
40 All Kw Kw<11.5 11.5
30 Kw>12.5
20
10
0
Fig. 53 – Summary of dead oil viscosity methods by Watson K factor for temperatures ranging 35-500 °F 
