European Journal of Scientific Research
ISSN 1450-216X Vol.71 No.1 (2012), pp. 5-13
© EuroJournals Publishing, Inc. 2012
http://www.europeanjournalofscientificresearch.com
New Referencing Technique for Reservoir Oil
Viscosity Estimation
Isehunwa, S. O.
Department of Petroleum Engineering, University of lbadan, Nigeria
E-mail: sunday.isehunwa@gmail.com
Tel: +2348023446164
Olamigoke, O.
Department of Petroleum Engineering, University of /badan, Nigeria
Abstract
Reservoir oil viscosity is important in understanding reservoir flow behaviour, l
facilities design and sizing and in the computation of recovery performance, well'
productivity and lift requirements. Direct viscosity measurements are expensive or
sometimes unavailable hence empirical correlations are often used for predictions.
However, several published correlations are either too simplistic or complex for routine
operational use and improved methods continue to receive attention. This study used a
semi-theoretical approach to relate reservoir oil viscosity to well-head oil viscosity which
can easily be obtained. Results were analyzed statistically and tested with field data
obtained from the Niger Delta. The viscosity relation factors developed gave an absolute
average relative error (AARE) of 14.1% for undersaturated reservoirs and an AARE of
2.4% for saturated oil reservoirs. It is concluded that measured well-head oil viscosity can
be used with good accuracy, as reference liquid instead of dead oil viscosity that has been
commonly used for estimating reservoir viscosity.
Keywords: Crude oil viscosity, referencing technique, viscosity correlations, iger Delta
Introduction and Literature Review
Viscosity is an important property of reservoir fluids. It is used during reservoir flow calculations,
design of pipelines, production equipment and pump sizing, in oil well testing calculations and
reservoir simulation. Several methods have been employed to model reservoir oil viscosity. However,
the self-referencing methods, seem to have been most successful, with the use of dead oil viscosity as
the reference point.
There are several viscosity correlations that are commonly used in the oil industry today. They
include those by Glaso (1980), Dindoruk, B., and Christman (200 I) and several others. The work by
Arnoo and Isehunwa (1990) specifically on Niger Delta crudes, used only oil specific gravity as the
main correlating parameter for estimating viscosity. This limited its accuracy to estimates above bubble
point. Kulchanyavivat (2005) has noted the significance of choosing the right parameters for
correlating viscosity of reservoir oil and developed a self-referencing model for estimating the
.viscosity of petroleum liquids and dead oils under operating conditions. The model utilized only the
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New Referencing Technique for Reservoir Oil Viscosity Estimation 6
measured viscosity at atmospheric pressure and room temperature. However, the correlation uses nine
coefficients, making it rather complex for routine applications.
In this work, following the method of Umeh et. at. (2003), surface oil viscosity obtained from
the well head was adopted as referencing point for estimating reservoir oil viscosity. Eze and Ajienka
(2006) have noted that subsurface conditions in oil wells may be monitored real time through the use
of surface data.
Theoretical Framework
For an undersaturated oil reservo[i1r, the pseudo-steady state solution for flow can be expressed as:- (/~7.J08kh kro(S,P)d (PIi-Ph) j (I)QO-[, --+3 5 ,] I',,' j1"B" P+(j1"B,,)_n - l)u.I'",
rIP 4
When a single phase is following in the reservoir, equation (I) reduces to:
7 .08kh (PII - p",)
(2)
«, ~ [In[::]-! + "](I',B,,)
Equation (2) can be expressed as:
s, = C r I (p II - P"t ) (3)
Ji"B" .
Where,
C,~ [In(~r+ s'l! (4)
At the well head, using Ros (1960) equation for choke performance, we have:
17 .4R~5 q
P'h = d 2 (5)
Thus,
d2s, = 17 .4R05 r; (6)
s
By equating equations (3) and (6), and simplifying we have:
17 .4 C r R~s (p Ii - P"t )
u ; = J (7)
d - B" P'h
Equation (7) shows that reservoir oil viscosity can be expressed in terms of oil PVT properties,
formation properties, choke dimensions, flowing well and tubing head pressures.
At surface, oil volumetric flow rate can be calculated from the equation for multiphase sub-
critical flow through the wellhead choke given as:
Q I. = 0.25C "d 2 (P,,, - Pd, (8)
PI
The liquid flow rate can also be calculated by treating the wellhead choke as a smooth pipe.
Recall the equation for flow through a horizontal pipe:
Q I. = 3574 .42 E I. [ D 19 3 ( /). P, ) 4] ~ (9)
u I. P I. L
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7 Isehunwa, S. O. and Olamigoke, O.
Replacing pipeline diameter, D and length L are replaced with choke diameter, d and length 1
gives the equation for flow through a wellhead choke. It becomes
1
Q I. = 3574 .42 E t. [ d 19 3 [ ~;f)417 (10)
f.11. PI.
Converting pipeline diameter inches to 1/64 inches in Eq. (10) gives
1
Q t. = 0.044742 E L [ d 19 3 [~ PI ) 4]7 (II)
f.11. p/.I
Surface oil viscosity can be calculated by equating Eqs. (8) and (II) to give:
5
/I =5.881 x10-6 C,;d (p/.(P,h _p(/,))05
1'""1. £7/4 ( 12)
I.
When critical flow occurs, the choke upstream pressure is about twice the downstream pressure
i.e. PdslP,h;;::: 0.5. Thus, Eq. (12) becomes
C 7 d 5 ( P )0.5
f.1 = 4.16 x 10-6 d P L Ih
L £7/4 ( 13)
L
From Eqns. (7) and (13) we have:
,u" = 4184432 E 7Z4 C R as (p p)I. ,. S II - wI ( 14)
/I C 7 d 7 as Bp1.5
r I. d PI. " th
Using Umeh et al (2003), we define a viscosity relation factor, VRF as:
VRF = _,u-----'" ._sc_ ( 15)
j.1 o.rc P ()SC
Therefore, substituting equation (14) into (15) and simplifying we have:
VRF = 2.39xlO-7CD'MCPR R Eo0.5 0.5 ( 16)
s PL
Where,
__C
C chIJIM C ( 17)r
C 7 d 7
C ch = £d ( 18)7/4
t.
p1.5
C
1'/1 = ( Ih ) ( 19)P/I-Pwf
Similarly for saturated reservoirs, viscosity relation factor is expressed as:
VRF = 9.56 x 10 -9 C !JIM C 1'/1 R B,,TII (20)0.5 0.5
s PI.
Where,
- P 1.5
C = (pP R IhPR R 2 _ P \If 2 )
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New Referencing Technique for Reservoir Oil Viscosity Estimation 8
Model Validation and Discussion of Results
Equations (16) and (20) are the equations that relate well head viscosity to reservoir viscosity in
undersaturated and saturated reservoirs respectivpely. It is clear however that some empirical data are
required before they can be used. The input parameters for the models are summarized in Table I.
However, field data should be used where available.
Table I: Input Parameters
Field Property Specification
Drawdown, (Pll-P"'I) ::::5%
Well radius, r, 0.3ft or 0.5n
Absolute Permeability, k 1000md
Relative Permeability, k.; ::::0.8
Skin, S 0
Choke diameter, d 2: 16/64ths in
Choke length, I < 6 in
The equpations were validated with data obtained from Shell Field A in the Niger Delta as
published by Umeh et al (2003). A summary of the range of the field data is shown Table 2.
Table 2: The range of the data used in model validation (from Umeh, et ai, 2003)
PVT Property Saturated Reservoirs Undersaturated Reservoirs
Reservoir Oil Viscosity, cp 0.8 - 12.69 6.67 - 36.17
Surface Oil Viscosity, cSt 6.44 - 114.2 22.66 - 121.90
Bubble Point Pressure, psia 642 - 3995 391 - 1995
Initial Solution Gas Oil Ratio, scf/stb 198 - 600 45 - 232
Oil Density @ reservoir conditions 0.76 - 0.875 0.76 - 0.875
Relative Oil Density 0.89 - 0.95 0.92 - 0.95
Reservoir Temperature, OF 120 - 165 120-180
Initial oil formation volume factor, rb/stb 1.09 - 1.32 1.06-1.16
Well head Temperature, OF 100 100
The results for seven undersaturated oil reservoirs are presented in Tables 3 - 6. Statistical
analysis in Table 4 established the accuracy of the viscosity relation factors.
Table 3: Predicted and Actual viscosity relation factors in some undersaturated reservoirs
Reservoir Estimated VRF Field VRF Average Error (%)
All 3.33 3.37 -1.19
A21 3.17 3.61 -12.19
A31 7.61 5.44 39.89
A41 5.78 4.50 28.44
A51 3.30 3.40 -2.94
A61 3.71 3.40 9.12
A71 3.14 3.31 -5.14
Table 4: Statistical accuracy of VRF in selected undersaturated reservoirs
This Study (Estimated VRF)
Average Relative Error, ARE 8.00
Average Absolute Relative Error, AARE 14.13
Coefficient of Correlation, R2 0.97
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.' ,
9 lsehunwa, S. O. and Olamigoke, 0'.
Table 5: Predicted and Actual reservoir oil viscosity (cP) in some undersaturated reservoirs
Reservoir Estimated 110 rc Field 110 rc Average Error (%)
All 36.12 36.17 -0.14
A21 33.94 34.2 -0.76
A31 5.10 4.88 4.51
A41 6.54 5.14 27.24
A51 6.27 6.67 -6.00
A61 7.01 6.90 1.59
A71 6.97 7.03 -0.85
Table 6: Predicted and Actual surface oil viscosity (cSt) in some undersaturated reservoirs
Reservoir Predicted 110 sc Measured 110sc Average Error (%)
All 113.04 114.59 -1.35
A21 102.3 117.14 -12.67
A31 36.67 24.67 48.64
A41 34.76 21.27 63.42
A51 19.00 20.85 -8.87
A61 23.96 21.59 10.98
A71 20.19 21.39 -5.61
The models gave better predictions of reservoir viscosity than surface oil viscosity as can be
seen from Tables 5 and 6.
The results for five saturated oil reservoirs of Field A are presented Tables 7 - 10. Statistical
analysis confirms low average errors and high coefficient of correlation.
Table 7: Predicted and Actual viscosity relation factors for selected saturated reservoirs
Reservoir Predicted VRF Measured VRF Average Error (%)
AI2 8.96 9.00 -0.44
A22 8.90 9.00 -I. I I
A32 8.61 8.69 -0.92
A42 10.25 10.68 -4.03
A52 8.51 8.05 5.71
Table 8: Statistical accuracy of predicted VRF in selected saturated reservoirs
This Study (Estimated VRF)
Average Relative Error (%), ARE 0.16
Average Absolute Relative Error (%). AARE 2.44
Coefficient of Correlation, R2 0.96
Table 9: Predicted and Actual reservoir oil viscosity (cP) in selected saturated reservoirs
Reservoir Estimated 110 rc Field 110 rc Average Error (%)
AI2 12.14 12.69 -4.33
A22 0.77 0.84 -8.33
A32 0.90 1.08 -16.67
A42 9.34 10.71 -12.79
A52 0.86 0.80 7.50
Table 10: Predicted and Actual surface oi I viscosity (Cst) in selected saturated reservoirs
Reservoir Estimated e Error (%)
AI2 102.22
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New Referencing Technique for Reservoir Oil Viscosity Estimation 10
Table 10: Predicted and Actual surface oil viscosity (Cst) in selected saturated reservoirs - continued
A22 6.10 6.73 -9.34
A32 6.97 8.45 -17.53
A42 91.03 108.68 -16.24
A52 6.52 5.73 13.76
Cashe Study: Oilfield B
B is another Niger Delta oilfield whose data were used in the model validation. The PVT data ranges
are given in Tapble 11:
Figure 2: Oil PVT properties vs. VRF in Undersaturated Reservoirs for B Oilfield
0.08
0.08
0.07
II>
0
'0' 0.07
VI
-~ 0.06'0
III 0.06 R2 = 0.96
0.05
0.05
0.04
3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6
Field VRF (cStlcp)
Table II: Summarty of the data for Odidi Oilfield
Saturated Reservoirs
PVT Property Ranee
Reservoir Oil Viscosity 0.23 - 4.06 cp
Surface Oil Viscosity 2.68 - 42 cSt
Bubble Point Pressure 2770 - 5038 psia
Initial Solution Gas Oil Ratio 333 - 1840 scf/stb
air Density @ reservoir conditions 0'.58"1' - (flffl'
Relative Oil Density 0.823 - 0.93
Temperature 142 - 246 OF
Initial oil formation volume factor 1.129 - 1.874 rb/stb
Undersaturated Reservoirs
Reservoir Oil Viscosity 1.01 - 9.149 cp
Surface Oil Viscosity 0.27 - 37.5 cSt
Bubble Point Pressure 2142 - 5505 psia
Initial Solution Gas Oil Ratio 266 - 1809 scf/stb
Oil Density @ reservoir conditions 0.537 - 0.851
Relative Oil Density 0.839 - 0.925
Temperature 144 - 270 OF
Initial oil formation volume factor I . I 12 - 1.84 rb/stb
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II Isehunwa, S. O. and Olamigoke, O.
Figure 3: Oil PYT properties vs. YRF in Saturated Reservoirs for B Oilfield
12
10- 110 • •oaVl. 10
c-:V::l 9 •~
I-- 8 • R2 = 0.65
0
III 7
6
6 8 10 12 14
Field VRF (cStfcp)
The results for four undersaturated and four saturated oil reservoirs of the B oilfield are
presented in Tables 12 and 13. The viscosity relation factor model for undersaturated oil reservoirs
performed better than the model for saturated oil reservoirs.
Table 12: Comparison of estimated viscosity relation factors with field viscosity relation factors for
undersaturated reservoirs for B Field
Reservoir Estimated VRF Field VRF Average Error (%)
BII 3.66 3.90 -6.15
B21 3.18 3.22 -1.24
B31 4.55 4.45 2.25
B41 3.97 4.43 -10.38
Table 13: Comparison of estimated viscosity relation factors with field viscosity relation factors for saturated
reservoirs for B Field
Reservoir Estimated VRF Field VRF Average Error (%)
B12 8.13 13.63 -40.35
B22 8.78 9.81 -10.50
B32 8.83 11.65 -24.21
B42 8.41 9.40 -10.53
Conclusion
A theoretical framework has been established for relating surface oil viscosity to reservoir oil viscosity
using PYT data, reservoir rock properties and production string dimensions. Empirical models
developed developed and validated with data from two oil fields in the Niger Delta show that wellhead
viscosity can be a good reference point for estimating reservoir oil viscosity.
Nomenclature
A - Area. fr'
°API - Oil gravity, °API
Bo - Oi I formation volume factor. RB/STB
Cd - Discharge coefficient
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New Referencing Technique for Reservoir Oil Viscosity Estimation 12
d - Choke diameter. 1/64th in.
EL - Liquid holdup
I' - Moody friction factor
g - Acceleration due to gravity (32.2 ftls2)
k - Absolute permeability, md
ko - Effective permeability to oil, md
k., - Relative permeability for oil
OVF - Oil formation viscosity factor. cp/cp
P - Pressure, psia
Pd, - Choke downstream pressure. psia
Pe - Reservoir boundary pressure. psia
PR - Average reservoir pressure, psia
Pth - Tubing head pressure, psia
Pwf - Flowing well pressure, psia
Pwh - Well head pressure. psia
bPI' - Pressure loss due to friction effects (psi)
Q.q - Production rate (Volumetric Flow rate). STB/D
r, - Drainage radius. ft
rw - Well radius. It
Re - Reynolds number
Rs - Solution gas-oil ratio. SCF/STB
s - Oil Saturation
s' - Skin factor
TR - Average reservoir temperature, of
v - Average velocity, Ills
Vsg - Superficial gas velocity. ftls
Vsl - Superficial liquid velocity. It'is
VRF - Viscosity relation factor. cSt/cp
Greek Letters
fJ - Diameter ratio (dID)
p - Density (g/crrr')
Yo - Oil relative density at 14.7 psia and 60°F
flo - Oil viscosity, cp
floh - Bubble point oil viscosity. cp
Subscripts
1 - Inlet
2 - Outlet
b - Bubble point
g - Gas
i - Initial conditions
L - Liquid
0 - Oil
r - Reduced conditions
sc - Surface conditions
rc - Reservoir conditions
Abbreviation
ARE - Average relati ve error
AARE - Average absolute relative error
GaR - Gas-oil ratio
PVT - Pressure- Volume- Temperature
SPDC - Shell Petroleum Development Company
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13 Isehunwa, S. O. and Olamigoke, O.
Statistical Criteria
100I.\' X -XARE = -- 1'0" 1"'.·0••.•
N i=! X
'1III:an\
AARE = -1-00IN X -X1"0/" I",ean.•
N i=! X
Iml'OI/.\
References
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