Khalid Elyas Mohamed Elamin AlKhidir^{*}
1.
Abstract
1.
Introduction
Its
bubble pressure fractal dimension and pressure head fractal dimension which was
derived from pore size distribution index and the fitting parameter m*n
respectively also indicates similar values (Table 1).
(Figure 3) delineates straight line plot of log
(Pb/p) versus log effective saturation, and log (α*h)
versus log effective saturation of sample SJ2 which is defined as medium 
grained, porous, permeable, well sorted, yellow sandstone (Figure 1). It acquired a pore size distribution index
of about 0.2252 whose value equal to m*n (Figure 3).
It
is also characterized by similarity in bubble pressure fractal dimension and
pressure head fractal dimension as displayed in (Table 1).
As we proceed from sample SJ2 to SJ3 a pronounced reduction in permeability due
to compaction was reported from 1955 md to 56 md which reflects an increase in
pore size distribution index from0.2252 to 0.5621 and reduction in fractal dimension from 2.7748 to 2.4379 as
stated in (Table 1). Again, an increase in grain
size and permeability was recorded from sample SJ4 which is characterized by 0.3157 pore size distribution index and 2.6843 bubble pressure fractal dimension which
agree with the pressure head fractal dimension (Table 1). In contrast,
the Middle Shajara reservoir which is separated from the Lower Shajara
reservoir by an unconformity surface (Figure 1) was designated by three samples out of four, namely SJ7,
SJ8, and SJ9 as illustrated in (Figure 1). Their pore size distribution index and fitting parameters
m*n were reported in (Figures 6, 7, 8, and Table
1).
Their bubble pressure fractal dimensions and
pressure head fractal dimensions are higher than those of samples SJ3 and SJ4
from the Lower Shajara Reservoir due to an increase in their permeability (Table 1).
On the other hand, the Upper Shajara reservoir is
separated from the Middle Shajara reservoir by yellow green mudstone as
demonstrated in (Figure 1). It is defined by three samples so called SJ11, SJ12, SJ13
as explained in (Figure 1). Furthermore, their pore size distribution index and the
fitting parameters m*n were demonstrated in (Figure
9,10,11, and Table 1).
The lower fractal dimension value2.43 allocates
to sample SJ3 from the Lower Shajara reservoir as shown in (Figure 12).
The three Shajara fractal dimension zones were also
confirmed by plotting pressure head fractal dimension versus bubble pressure
fractal dimension as illustrated in (Figure 13).
4. Conclusion
1.
The
obtained Shajara bubble pressure fractal dimension reservoir units were also
confirmed by pressure head fractal dimension.
2.
It
was found that, the higher the bubble pressure fractal dimension and pressure
head fractal dimension, the higher the permeability leading to better Shajara
reservoir characteristics.
3.
It was also reported that, the bubble pressure
fractal dimension and pressure head fractal dimension increases with decreasing
pore size distribution index and fitting parameters m*n owing to possibility of
having interconnected channels.
4.
Digenetic
features such as compaction plays an important role in reducing bubble pressure
fractal dimension and pressure head fractal dimension due to reduction in pore
connectivity.
Figure 1: Stratigraphic column of the type section of the PermoCarboniferous
Shajara Formation of the Unayzah Group, Wadi Shajara, Qusayba area, al Qassim district,
Saudi Arabia, N 2652 17.4, E 4336 18.
Figure 2: Log (Pb/pc) versus log Se in red color and Log (α*h)
versus log Se in blue Color.
Figure 3: Log (Pb/pc)
versus log Se in red color and log (α*h) versus
log Se in blue color.
Figure
4: Log (Pb/pc) versus log Se in red color and log (α*h) versus log Se in blue.
Figure 5: Log (Pb/pc) versus log Se in red color and log (α*h)
versus log Se in blue Color.
Figure 6: Log (Pb/pc) versus log Se in red color and log (α*h)
versus log Se in blue.
Figure 7: Log (Pb/pc) versus log Se in red color and log (α*h)
versus log Se in blue color.
Figure 8: Log (Pb/pc) versus log Se in red color and log (α*h)
versus log Se in blue Color.
Figure 9: Log (Pb/pc) versus log Se in red color and log (α*h)
versus log Se in blue Color.
Figure 10: Log (Pb/pc) versus log Se in red color
and log (α*h) versus log Se in
blue Color.
Figure 11: Log (Pb/pc) versus log Se in red color and log (α*h) versus log Se in
blue Color.
Figure 12: Pore size distribution index (λ) in red color and
fitting parameter (n) in blue color versus fractal Dimension (D).
Figure 13: Pressure head fractal dimension (Dαh) versus bubble
pressure fractal dimension (DP/pc).
Reservoirs 
Sample 
Φ (%) 
k (md) 
λ 
m*n 
m 
n 
Dp/pc 
Dαh 
Lower Shajara Reservoir 
SJ1 
29 
1680 
0.2141 
0.2141 
0.176345 
1.2141 
2.7859 
2.7859 
SJ2 
35 
1955 
0.2252 
0.2252 
0.183807 
1.2252 
2.7748 
2.7748 

SJ3 
34 
56 
0.5621 
0.5621 
0.359836 
1.5621 
2.4379 
2.4379 

SJ4 
30 
176 
0.3157 
0.3157 
0.239948 
1.3157 
2.6843 
2.6843 

Middle Shajara Reservoir 
SJ7 
35 
1472 
0.2317 
0.2317 
0.188114 
1.2317 
2.7683 
2.7683 
SJ8 
32 
1344 
0.2248 
0.2248 
0.18354 
1.2248 
2.7752 
2.7752 

SJ9 
31 
1394 
0.2214 
0.2214 
0.181267 
1.2214 
2.7786 
2.7786 

Upper Shajara Reservoir 
SJ11 
36 
1197 
0.2414 
0.2414 
0.194458 
1.2414 
2.7586 
2.7586 
SJ12 
28 
1440 
0.2141 
0.2141 
0.176345 
1.2141 
2.7859 
2.7859 

SJ13 
25 
973 
0.2128 
0.2128 
0.175462 
1.2128 
2.7872 
2.7872 
Table 1: Petrophysical properties characterizing Shajara reservoirs of the Shajara Formation of the PermoCarboniferous Unayzah Group.
5.
Oostrom M, Lenhard
RJ (1998) “Comparison of Relative Permeability SaturationPressure Parametric
Models for Infiltration and Redistribution of a Light NonAqueous Phase Liquid
in Sandy Porous Media”. Advances in
Water Resources 212: 145157.
10. Li K (2010b) “Analytical Derivation of BrooksCorey
Type Capillary Pressure Models Using Fractal Geometry and Evaluation of Rock
Heterogeneity”. Journal of Petroleum
Science and Engineering 73: 2026.
Citation: AlKhidir KEME (2017) Pressure Head Fractal Dimension for Characterizing Shajara Reservoirs of the Shajara Formation of the PermoCarboniferous Unayzagh Group, Saudi Arabia. Arch Pet Environ Biotechnol: APEB 113. DOI: 10.29011/25747614. 100113