Picket Plott Development
Picket Plott Development
Picket Plott Development
a
Geology Department, Faculty of Sciences, Zagazig University, Egypt
b
Department of Exploration, Egyptian Petroleum Research Institute, Egypt
KEYWORDS Abstract The present work was devoted to evaluate the reservoir characteristics of the Abu Roash
North Western Desert; Formation in the vicinity of El-Razzak Oil Field, North Western Desert, Egypt. The area of study is
Well logging; bounded by latitudes 30 250 and 30 550 N and longitudes 27 500 and 28 400 E. Nine distributed
Pickett plot; wells were utilized for this study.
Cross plot; A new technique has been applied through Picketts plot, to develop some of reservoir petrophys-
Porosity; ical parameters. These parameters include capillary pressure, pore throat aperture radii, height
Permeability above the free water table and bulk volume of water. This technique depends on the use of log
log plots of effective porosity versus resistivity combined with empirical relationships for calculating
the capillary pressure expressed as a function of permeability, porosity and water saturation. Also,
this technique gave the values of petrophysical exponents (m, n and a) which were used to calculate
the accurate value of water saturation in both clean and shaly rocks and then adjust estimation of
hydrocarbon saturation. The integration of these petrophysical parameters on a loglog graph of
porosity versus resistivity gives the importance for Pickett plot to be used in reservoir interpretation.
2014 Production and hosting by Elsevier B.V. on behalf of Egyptian Petroleum Research Institute.
Open access under CC BY-NC-ND license.
1. Introduction
1110-0621 2014 Production and hosting by Elsevier B.V. on behalf of Egyptian Petroleum Research Institute.
Open access under CC BY-NC-ND license. http://dx.doi.org/10.1016/j.ejpe.2014.02.007
46 A.A. El-Khadragy et al.
shown in Figs. 1 and 2. Sanyal and Ellithorpe [3] and Green- from Picketts plot for the G member of Abu Roash Forma-
gold [4] have shown that, Picketts plot should result in a tion are tabulated in Table 1.
straight line with a slope equal to m. Many lines are drawn at different values of porosity (90%,
This plot shows a useful model for putting together the 60%, and 20%) equivalent to the rst drawn line.
petrophysical parameters including water saturation, perme- Aguilera [5] used the following steps to show how to con-
ability, capillary pressure, pore throat aperture radii and struct Picketts plot incorporating capillary pressure, pore
height above free water table [5]. This technique highers throat aperture radii and height above the free water table,
Picketts plot as one of the most important plots for reservoir where the technique is applied on the nine wells for the G
evaluation, where the use of this plot enables the log analyst to Member of Abu Roash Formation in the El-Razzak Oil Field.
see within one single plot several keys of geological and IE36-1 well is taken as an example in this paper.
reservoir engineering parameters.
2.1. Permeability
2. The theory of Picketts plot
Reservoir rock must have the ability to allow petroleum uids
The theory of this plot started with Archies formulae [6]. By to ow through its interconnected pores. The rocks ability to
rearranging the Archie equation we get: conduct uids is termed as permeability which depends on its
effective porosity.
SW I1=n 1 Many empirical equations are derived to estimate the rela-
tive permeability. The following equation estimates the perme-
I Rt =R0 Rt =FRw 2
ability [9] in terms of irreducible water saturation, as follows:
F aUm
t 3 K1=2 250U3t =Swi 6
Eqs. (1) and (3) can be combined to yield. The water saturation in Eq. (6) is irreducible, that corre-
Rt aUm aUm 4 sponds to the beginning of a Krw, which equals zero.
t Rw I t Rw Sw
The irreducible water saturation, in turn, can be solved by
By using the logarithm with base 10, the Eq. (4) [7] leads using the following equation:
log Rt m log Ut logaRW log I 5 Swi Ut Sw =Ueff 7
This is the equation of a straight line on loglog paper. The After incorporating into Eq. (4), the following formula is
line has a slope of (m) which is determined manually by mea- obtained [10]
suring a distance on the Rt axis (in cm) and dividing it by the n
corresponding distance on the porosity axis. The intercept Rt aUm 3
t Rw 250Ut =K
1=2
8
when PHI = 1 is the value of aRw as shown in Fig. 3, and n
by knowing the value of Rw, the value of tortuosity factor or Rt aU3nm
t Rw 250=K1=2 9
(a) can be determined. By having the logarithm of both sides, the proceeding equa-
According to [8], the saturation exponent n which is a tion becomes [11]:
function of water saturation equals the value of porosity expo- n
nent m. The results of the petrophysical exponents obtained log Rt 3n m log Ut logaRw 250=K1=2 10
Figure 1 Generalized sketch map of Egypt showing the location of the studied area.
Picketts plot in determining the reservoir characteristics 47
1
Porosity
aRw=0.025
0.1
m=x/y=1.7
0.01
Figure 3 Picketts plot for G Member of Abu Roash Formation in IE 36-1 well.
Table 1 The results of petrophysical exponents and slopes obtained from Picketts plot for the G Member of Abu Roash Formation
in the nine wells.
No. Well name aRw a m Slope of Sw Slope of K Slope of Pc Slope of r Slope of BVW
1 IG 30-1 0.019 0.63 1.79 0.56 7.16 3.24 3.24 0.0
2 IJ 30-1 0.016 1.00 1.97 0.51 7.88 3.60 3.60 0.0
3 IG 33-1 0.025 1.00 1.82 0.55 6.88 3.10 3.10 0.0
4 IH 35-2 0.021 1.00 2.00 0.50 8.0 3.60 3.60 0.0
5 IG 34-1 0.014 1.00 2.26 0.45 9.04 4.10 4.10 0.0
6 IF 32-1 0.032 1.00 1.79 0.56 7.16 3.20 3.20 0.0
7 IF 34-2 0.025 0.70 1.66 0.60 6.64 3.00 3.00 0.0
8 IE 34-6 0.040 1.00 1.83 0.55 7.30 3.30 3.30 0.0
9 IE 36-1 0.025 1.00 1.70 0.59 6.80 3.10 3.10 0.0
48 A.A. El-Khadragy et al.
From Eq. (10), by plotting Rt vs. A on loglog coordinates, where: porosity and water saturation are expressed as fractions
the relation should result in a straight line with a slope equal to and
(3n m) with a constant (aRw) and permeability. Since 0:8
m = n, the slope equals (4m). The intercept of the straight Pc Swi Ut2:25 =0:929 14
line with 100% porosity gives aRw (250/K1/2)n. By solving Eq. (14) for Swi and inserting it into Eq. (4), this
Aguilera [10] used Eq. (10) to construct parallel lines of leads to the following equation:
constant permeability. From Eq. (10), the slope of
(3n m) was determined. 1=0:8 n
Rt Um 2:25
t aRw 0:0929Pc=Ut 15
The line of constant permeability equal to (1 md) can be
drawn by calculating Rt from Eq. (9), using a Rw and porosity or Rt Utm2:8125n aRw 1:0961Pc1:25
n
16
for each well as shown in Fig. 4 for the G Member. The per-
meability ranges from 0.01 to 100 md, then by determining a Taking the logarithm of both sides of the proceeding
certain value of porosity, the corresponding value of Rt can equation, this leads to the following form:
be calculated for each value of permeability. n
log Rt m 2:8125 n log Ut logaRw 1:0961 Pc1:25
2.2. Capillary pressure 17
Eq. (17) indicates that, a crossplot of Rt vs. Ut on a loglog
Capillary pressure is the difference in pressure between two paper results in a straight line with a slope equal to
immiscible uids across a curved interface at equilibrium. (m + 2.8125 n) with a constant (aRw) and constant capillary
The following section presents the involvement of capillary pressure. The straight line cuts the 100% porosity axis at a
pressure (Pc) into Picketts plots by using an empirical rela- point equal to [aRw (1.0961 Pc 1.25)n] on the resistivity
tionship. Kwon and Pickett [12] published an empirical rela- scale. Since m = n, the slope will be equal to the values as
tionship incorporating the capillary pressure, as follows: shown in Table 1.
Pc AK=1000Ut B 11 Fig. 5 for the G Member exhibits a Picketts plot including
parallel lines of constant capillary pressures that range from 10
where: to 800 psi. First, a line of constant capillary pressure equal to
100 psi is drawn by assuming a value for t and calculating the
Pc is the mercuryair capillary pressure in pounds per corresponding value of Rt from Eq. (16). The point with the
square inch, values of Rt and t is plotted and from it, a straight line is
B is approximately equal to 0.45, drawn through this point with a positive slope. This straight
A is a constant ranging between 151.35 and 22.91. line corresponds to a constant capillary pressure of 100 psi.
The same procedure is followed for the other capillary
They based their correlation on the loglog cross plots of A pressures of interest.
vs. water saturation and found the following equation:
A 19:5Sw1:7 12 2.3. Pore throat aperture radii
1
90% 50% 20%
Porosity
100%
100
0.1
10
1md
0.1
0.01md
aRw=0.025 m=n=1.7
0.01
Figure 4 Picketts plot incorporating formation permeability for G Member of Abu Roash Formation in IE 36-1 well.
Picketts plot in determining the reservoir characteristics 49
Pc(psi)
1 10 25 50
90% 50% 20%
Porosity
100% 100
200
400
100
800
0.1
10
1md
0.1
0.01md
aRw=0.025 m=n=1.7
0.01
Figure 5 Picketts plot incorporating formation permeability and capillary pressure for G Member of Abu Roash Formation in IE 36-1
well.
MACRO
1 8 Aperture(Mm) 4
2
90% 50% 20%
Porosity
100%
MESO
0.5
MICRO
0.25
100
NANO
0.1
10
1md
0.1
0.01md
aRw=0.025 m=n=1.7
0.01
Figure 6 Picketts plot incorporating formation permeability and pore throat aperture for G Member of Abu Roash Formation in IE
36-1 well.
50 A.A. El-Khadragy et al.
lm. The calculated slopes from Eq. (21) are recorded in The lines of constant height above the free water table are
Table 1. drawn through the calculation of Rt from Eq. (24) as follows:
First, the line of constant pore throat aperture equal to m2:8125n
(1 lm) is drawn, where Rt is calculated by assuming a value Rt Ut faRw 1:09610:433qw qh
for t and with a constant value of aRw for each member. By hr cos h=rh cos hh 1:25 gn 26
the values of Rt and Ut, a point is plotted and from it a line
Using aRw, qw qh, rh, hh, r, h and any porosity for these
is drawn with the calculated slope. The same process is applied
data, Eq. (26) reduces to the form:
for the other pore radii of interest. The gure includes pore size
m2:8125n n
which is ranging between macropores and nanopores. Rt Ut aRw 1:09611:4182 h1:25 27
Fig. 7 for the G Member shows Picketts plot presented pre- 3. Summary and conclusion
viously, showing parallel lines of constant height above the
free water table that ranges from 50 to 500 ft. Different slopes A new technique has been applied through Picketts plot, to
are calculated and recorded in Table 1. develop some of reservoir petrophysical parameters. These
25 height(ft)
1
90% 50% 20% 50
Porosity
100%
100
200
400
100
0.1
10
1md
0.1
0.01md
aRw=0.025 m=n=1.7
0.01
Figure 7 Picketts plot incorporating formation permeability and high above free water table for G Member of Abu Roash Formation in
IE 36-1 well.
Picketts plot in determining the reservoir characteristics 51
Porosity
100%
100
0.1
10
1md
0.1
0.01md
aRw=0.025 m=n=1.7
0.01
Figure 8 Picketts plot incorporating formation permeability and bulk volume of water for G Member of Abu Roash Formation in IE
36-1 well.
parameters include capillary pressure, pore throat aperture [7] G.R. Pickett, A review of current techniques for determination
radii, height above the free water table and bulk volume of of water saturation from log, J. Petrol. Technol. 18 (1966) 1425
water. This technique depends on the use of loglog plots of 1433.
effective porosity versus resistivity combined with empirical [8] G.R. Pickett, Pattern recognition as a means of formation
evaluation, in: Society of Professional Well Log Analysts 14th
relationships for calculating the capillary pressure expressed
Annual Logging Symposium Transactions Paper A, 1973, pp.
as a function of permeability, porosity and water saturation.
A1A21.
The result plot is a straight line, where the slope of this line will [9] R.L. Morris, W.P. Biggs, Using log-derived values of water
be controlled by the value of m. The intersection of the line pass- saturation and porosity, in: Society of Professional Well Log
ing through the data point and the 100% porosity will be a Rw. Analysts Annual Logging Symposium, 1967, 26pp.
The integration of these petrophysical parameters on a log [10] R. Aguilera, A new approach for analysis of the nuclear
log graph of porosity versus resistivity gives the importance for magnetic log, resistivity log combination, J. Can. Pet. Technol.
Pickett plot to be used in reservoir interpretation. 29 (1) (1990) 6771.
[11] R. Aguilera, Naturally Fractured Reservoirs, PennWell Books,
Tulsa, Oklahoma, 1995.
References [12] B.S. Kwon, G.R. Pickett, A new pore structure model and pore
structure interrelationship, in: Society of Professional Well Log
[1] A.J. Martin, S.T. Solomon, D.J. Hartmann, Characterization of Analysts, 16th Annual Logging Symposium, 1975, 14pp.
petrophysical ow units in carbonate reservoirs, AAPG Bull. 81 [13] E.W. Washburn, Note on a method of determining the
(5) (1997) 734759. distribution of pore sizes in a porous material, Proc. Natl.
[2] R. Aguilera, M.S. Aguilera, The integration of capillary pressures Acad. Sci. 7 (4) (1921) 115116.
and Pickett plots for determination of ow units and reservoir [14] A.J. Martin, S.T. Solomon, D.J. Hartmann, Characterization of
containers, SPE Reservoir Eval. Eng. 5 (6) (2002) 465471. petrophysical ow units in carbonate reservoirs, AAPG Bull. 83
[3] S.K. Sanyal, J.E. Ellithorpe, A generalized resistivityporosity (7) (1999) 11641173.
crossplot concept, Society of petroleum engineers California. [15] J.H. Doveton, W.J. Guy, W.L. Watney, G.C. Bohling, S. Ullah,
Regional meeting, SPE paper 7145, 1978, 8pp. D. Adkins-Heljeson, Log analysis of petrofacies and ow units
[4] G.E. Greengold, The graphical representation of bulk volume of with microcomputer spreadsheet software; Kansas Geological
water on the Pickett crossplot, The Log Analyst 27 (3) (1986) 125. Survey, University of Kansas, Lawrence, Kansas, 1996.
[5] R. Aguilera, Incorporating capillary pressure, pore throat [16] R.S. Buckles, Correlating and averaging connate water
aperture radii, height above free-water table and Winland r35 saturation data, J. Can. Petrol. Technol. 5 (1965) 4252.
values on Pickett plots, AAPG Bull. 86 (4) (2001) 605620. [17] R. Aguilera, Extension of Pickett plots for the analysis of
[6] G.E. Archie, The electrical resistivity logs as an aid in shaly formation by well logs, The Log Analyst 31 (6)
determining some reservoir characteristics, Trans. AIME 146 (1990) 304313.
(1942) 5467.