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SPE-178271-MS
Gas-Oil Gravity Drainage and Reinfiltration in Naturally Fractured
Reservoirs
Francis D. Udoh, Chemical & Petroleum Engineering Department, University of Uyo, Uyo-AKS, Nigeria, Chemical
& Petroleum Engineering Department, Afe Babalola University, Ado Ekiti, Ekiti State, Nigeria; Anselem I. Igbafe,
Chemical & Petroleum Engineering Department, Afe Babalola University, Ado Ekiti, Ekiti State, Nigeria;
Anietie N. Okon, Chemical & Petroleum Engineering Department, University of Uyo, Uyo-AKS, Nigeria
Copyright 2015, Society of Petroleum Engineers
This paper was prepared for presentation at the Nigeria Annual International Conference and Exhibition held in Lagos, Nigeria, 4 – 6 August 2015.
This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents
of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect
any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written
consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may
not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.
Abstract
The prediction of production performance in naturally fractured reservoirs is dependent on reinfiltration
and capillary continuity phenomena. In fractured reservoirs, reinfiltration and capillary continuity phe-
nomena have been the major setback during gas-oil gravity drainage. The oil contained within the matrix
of the gas invaded zone begins to drain down into the fracture system and into the lower matrix blocks,
due to the force of gravity. Some of the oil that is drained out of the upper matrix blocks can reinfiltrate
into the lower matrix blocks from the top or side surfaces and can flow down through the areas of contact
between blocks. To evaluate the effect of reinfiltration in gravity drainage mechanism and fractured
reservoir parameters: fracture width (b
f
) and storativity capacity (
) on reinfiltration process, a fractured
porous media was modeled with ECLIPSE-100 Simulator. The base-case simulation runs (SIM-1 and
SIM-2) showed that 55.14% and 53.40% of the oil in-place in the modeled fractured porous media were
recovered by gas-oil gravity drainage mechanism without reinfiltration and with reinfiltration, respec-
tively. Furthermore, the sensitivity study of the aforementioned fractured reservoir properties on gas-oil
gravity drainage and reinfiltration with simulation runs (SIM-3 through SIM-10) indicate that fracture
porosity as well as storativity capacity influence the ultimate oil recovery in naturally fractured reservoirs.
Additionally, the fracture width has no influence on gas-oil gravity drainage and reinfiltration in the
modeled fractured reservoir. Therefore, gravity drainage recovery mechanism proliferation is affected by
oil reinfiltration within the matrix blocks that resulted in 3.173% production reduction. Hence, fracture
porosity and storativity capacity are considerable factors in reinfiltration mechanism in naturally fractured
reservoirs.
Keywords Gravity drainage, Reinfiltration, Oil recovery, Fracture width, Fracture porosity, Storativity capacity,
Naturally fractured reservoirs
Introduction
Oil recovery in naturally fractured reservoirs is dominated by two recovery mechanisms: imbibition and
gravity drainage. The former is controlled by capillary and viscous forces either by countercurrent or
concurrent imbibition, depending on the directions of the displacing and displaced phases. Gravity
drainage which mostly occurs in gas-oil system during gas injection as oil recovery technique in naturally
fractured reservoirs has long been established (Okon and Udoh, 2013). This recovery mechanism is
predominated by gravity forces and densities difference between the oil and gas phase in the fractured
porous media. On the other hand, the two important phenomena associated with gravity drainage in gas-oil
system are reinfiltration and capillary continuity (Fung, 1991). Reinfiltration which in some literature is
referred to as reimbibition simply depicts the phenomenon where the drained (displaced) oil from one
matrix block to the fracture is spontaneously imbibed into another matrix block underneath in the
fractured porous media. Saidi (1987) has emphasized that this phenomenon exists and should be
considered during reservoir behaviour prediction. Uleberg and Kleppe (1996) opined that several publi-
cations (Firoozabadi and Markeset, 1992;Barkve and Firoozabadi, 1992, and others) have shown that the
reinfiltration is a function of both capillary forces and gravity. Therefore, the term reinfiltration should be
used instead of the much used word “reimbibition,” since the latter could imply the capillary effect only.
Kazemi et al. (1976) described the fluids flow in naturally fractured reservoir (NFR), considering the
gravity drainage and reinfiltration phenomena. Their modeled equations have been used to evaluate oil
reinfiltration effect in naturally fractured reservoirs (NFRs) in most literature. In addition, Movazi and
Jaberi (2009) work looked at the rate of gravity drainage and oil reinfiltration in NFR’s matrix blocks.
Their study establishes that, block-to-block interaction is the dominant process in fracture reservoir that
should be considered in predicting oil production rate by gravity drainage. Furthermore, several works in
the literature like Ladron de Guevara-Torres et al. (2009) evaluated the efficiency of their in-house
simulator SIMPUMA-FRAC compared to other commercial simulators to model gravity drainage and
reinfiltration processes in NFR. However, this phenomenal evaluation looked at the effect of oil
reinfiltration in NFR from the stand point of its oil recovery. Regrettably, limited or no work has been
done to establish the contributing effect of NFR parameters such as fracture width (b
f
), matrix block size,
storativity capacity (
), among others on the gas-oil gravity drainage and reinfiltration effect in NFRs.
This paper, therefore, takes a look at the effect of fracture width and storativity capacity on gas-oil gravity
drainage and reinfiltration mechanisms in naturally fractured reservoirs using ECLIPSE-100 (Black oil)
Simulator.
Fluid Flow Equations in Naturally Fractured Reservoirs
In the literature, fluid flow in naturally fractured reservoirs is analyzed using three broad approaches:
continuum, discrete fracture and integrated approach. Discrete fracture and integrated approaches mainly
focus on the actual performance of fractures but these techniques have time consuming, expensive and
dimensional limitations (Zahoor and Haris, 2012). Therefore, continuum approach becomes the most
adopted fluid flow model in fractured reservoirs. This approach can consider NFR as single and dual
continuum. In single continuum, the fracture and matrix are considered as single continuum whilst dual
continuum takes fractures and matrix as two continuums. Interestingly, most simulators are modeled to
handle continuum approach of fluid flow in NFRs. Generally, the fluid flow equations in naturally
fractured reservoirs as handled by the ECLIPSE-100 simulator in discretized form are expanded in
equations 1 and 2. These equations describe the fluid flow in the fracture and matrix block of the fractured
reservoir. Additionally, Kazemi et al. (1976) presented the fluid flow equations (as expressed in equations
3through 6) in NFR that considered and accounted for gravity drainage and oil reinfiltration processes in
fractured reservoir. These equations have been modeled into the ECLIPSE simulation to handle these
recovery mechanisms by turning on the keywords: GRAVDR and GRAVDRM for gravity drainage and
reinfiltration, respectively.
2 SPE-178271-MS
Matrix:
(1)
Fracture:
(2)
Where:
Gravity drainage and Reinfiltration Fluid Flow in NFRs
●Fracture Flow Equation:
Oil:
(3)
Gas:
(4)
●Matrix/Fracture Flow Equation:
Oil:
(5)
Gas:
(6)
Reservoir Description and Model:
The reservoir description (as presented in Table 1) and model in this study are based on the previous work
of Okon and Udoh (2013) although modifications are made on the number of grid blocks. The grid model
comprised of five matrix blocks with forty (40) grid blocks surrounded by fractures as presented in Figure
1. The gas that initiates the gas-oil gravity displacement in the modeled reservoir is injected at the top of
the matrix block (1, 1, 1). The produced oil is observed from the block (1, 1, 106) at the bottom of the
matrix block. The multiphase flow parameters: relative permeability (K
r
) and capillary pressure (P
c
)inthe
matrix are presented in Table 2. In the fracture, the multiphase flow relative permeability for oil and gas
are modeled based on the expanded equations 7 and 8, respectively.
SPE-178271-MS 3
Table 1—Reservoir Description
Description Value
Matrix Compressibility (C
m
) 5.29⫻10
-5
Pa
-1
Fracture Compressibility (C
f
) 7.61⫻10
-5
Pa
-1
Matrix Porosity (
m
) 0.22
Matrix Permeability (k
m
) 1.0mD
Matrix Block 0.05m
Fracture Width (b
f
) 0.01m
Fractured Porosity (
f
) 1.0
Fractured Permeability (k
f
) 30mD
Oil Viscosity (
o
) 0.190cP
Gas Viscosity (
g
) 0.023cP
Oil Density (
o
) 850kg/m
3
Gas Density (
g
) 0.83kg/m
3
Oil Formation Volume Factor (B
o
) 1.0250
Gas Formation Volume Factor (B
g
) 0.0042
Reference Pressure (P
ref
) 350Bar
Injection Pressure 370Bar
Figure 1—Reservoir model
4 SPE-178271-MS
In this study, the saturation exponent is unity (i.e., n ⫽1). Thus, equations 7 and 8imply that the
relative permeability (K
r
) in the fracture is a direct function of phase saturation. Meaning that, there is no
residual phase saturation in the fractures network of the modeled fractured reservoir. On the other hand,
the capillary pressure (P
c
) in the fracture is assumed to be zero as there is no holding back of any phase
saturation.
(7)
(8)
Where:
K
ro
⫽Oil relative permeability
K
rg
⫽Gas relative permeability
S
g
⫽Gas saturation
n⫽Saturation exponent
Simulation Studies:
The gas-oil gravity drainage and oil reinfiltration in this study were performed using ECLIPSE-100
Simulator. The modeled fractured reservoir was simulated as the base-case runs (SIM-1) and (SIM-2) for
gas-oil gravity drainage and reinfiltration with the keywords GRAVDR and GRAVDRM, respectively,
and were included in the RUNSPEC section of the ECLIPSE data file. The dual porosity and permeability
option of the modeled reservoir were activated using DUALPORO and DUALPERM keywords in the
data file. The results of both base-cases were evaluated based on their ultimate oil recovery, oil and gas
saturations (i.e., BOSAT and BGSAT) in the upper and lower matrix block stack. The obtained results
from the base-case simulation runs are presented in Figures 2 through 4. To evaluate the sensitivity of
some NFR parameters on gas-oil gravity drainage and reinfiltration processes, two (2) simulation
scenarios were simulated using eight (8) runs for each process. Scenario one (1) analyzed the effect of
fracture width (b
f
) on these recovery mechanisms, while scenario two (2) examined the sensitivity of
fracture porosity (storativity capacity) on gravity drainage and reinfiltration process. The equation that
depicts the storativity capacity in the fracture is expanded in equation 9. The results of this sensitivity
studies are presented in Figures 5 through 9.
Table 2—Multiphase Parameters
S
g
K
rg
P
cog
S
o
K
rog
0.00 0.0000 0.00690 0.30 0.00000
0.05 0.0000 0.00827 0.40 0.00020
0.10 0.0183 0.01034 0.50 0.00096
0.15 0.0477 0.01241 0.60 0.00844
0.20 0.0835 0.01517 0.70 0.03939
0.30 0.1692 0.02206 0.80 0.13010
0.40 0.2695 0.03448 0.85 0.21670
0.50 0.3815 0.05309 0.90 0.34540
0.60 0.5036 0.07929 0.95 0.53020
0.70 0.6345 0.13238 1.00 1.00000
SPE-178271-MS 5
Figure 2—Comparison of oil recovery from gravity drainage and reinfiltration
Figure 3—Comparison of oil saturation from gravity drainage and reinfiltration
6 SPE-178271-MS
Figure 4 —Comparison of gas saturation from gravity drainage and reinfiltration
Figure 5—Comparison of oil recovery from gravity drainage and reinfiltration
SPE-178271-MS 7
Figure 6 —Comparison of oil saturation from gravity drainage and reinfiltration
Figure 7—Comparison of oil recovery from gravity drainage and reinfiltration
8 SPE-178271-MS
Figure 8 —Comparison of gas saturation from gravity drainage and reinfiltration
Figure 9 —Comparison of oil saturation from gravity drainage and reinfiltration
SPE-178271-MS 9
(1)
Where:
f
⫽Fracture porosity
m
⫽Matrix porosity
C
f
⫽Fracture compressibility
C
m
⫽Matrix compressibility
Results and Discussion
Gravity Drainage and Reinfiltration (Base-case)
As earlier mentioned, the gas-oil gravity drainage and reinfiltration in fractured porous media was studied
with ECLIPSE-100 Simulator. The results of the simulation scenarios are presented in Figures 2 through
9.Figures 2 through 4present the Base-case simulation study of gas-oil gravity drainage and reinfiltration
of the modeled fractured reservoir. The depicted results of the Base-case simulation study are oil recovery,
oil and gas saturations at the upper and lower matrix block stack of the modeled reservoir. The Base-case
simulation study of oil reinfiltration indicates decrease in oil recovery when compared with gravity
drainage. From Figure 2, the oil recovery of 0.5515 and 0.5340 were obtained from gravity drainage and
reinfiltration, respectively. This result indicates decreased oil production of about 3.173% with reinfil-
tration process. Meaning that, 3.173% of the oil was reinfiltrated in to the matrix block of fractured media
at the lower stack. Additionally, the increased oil recovery from gravity drainage indicates that most of
the displaced or drained oil from the matrix block are produced from the fractures without any
reinfiltration in to the matrix block(s) beneath.
Subsequently, Figures 3 and 4present the oil and gas saturations in the lower and upper matrix block
of the modeled fracture media. From Figure 3, it is observed that the lower matrix block in the
reinfiltration process has more oil saturated than in gravity drainage process, as a result of the imbibed oil
in the lower matrix block. Therefore, this result accounted for the high oil recovery and recovery factor
(RF) in gravity drainage when compared to reinfiltration, as presented in Figure 2. In the same vein, the
oil saturation in the upper matrix block from both gravity drainage and reinfiltration resulted in less
saturation than the lower matrix block in both recovery processes. Thus, a comparison of the oil saturation
in upper and lower matrix blocks for both recovery processes in Figure 2 further indicates that the upper
matrix block in reinfiltration has high oil saturation than gravity drainage. This observation indicates that
some of the recovered oil is reinfiltrated in to the matrix block which resulted in high oil saturation in the
upper matrix blocks in reinfiltration than gravity drainage recovery mechanism.
Figure 4 depicts the gas saturation in the upper and lower matrix blocks in both gravity and
reinfiltration oil recovery from the modeled reservoir. The result indicates that the lower matrix blocks in
both processes have more gas saturated than the upper matrix blocks. This result is attributed to the
displacement of oil from the matrix block by the gas in the fractured network of the media; thus, replacing
Table 3—Sensitivity simulation runs
Scenario 1 Scenario 2
Simulation Run Fracture width (m) Simulation Run Fracture porosity Storativity capacity (
)
Base-case 0.0015 Base-case 1.00 0.87
SIM-3 0.0030 SIM-7 0.80 0.84
SIM-4 0.0045 SIM-8 0.65 0.81
SIM-5 0.0090 SIM-9 0.55 0.78
SIM-6 0.0105 SIM-10 0.45 0.75
10 SPE-178271-MS
the oil in the matrix block. Consequently, the lower matrix blocks have more gas saturated as the occupied
oil in the matrix is displaced by the gas in both processes: gravity drainage and reinfiltration. Interestingly,
the gas saturation in the lower matrix block from gravity drainage is higher than its counterpart in
reinfiltration process. This result indicates that, in gravity drainage more pore volumes are occupied by
the displacing gas as more oil are displaced than in reinfiltration where the displaced oil are reinfiltrated
or imbibed in to the matrix block beneath.
Sensitivity of Fracture Width (b
f
) on Gravity Drainage and Reinfiltration
Figures 5 and 6present the sensitivity result of the fracture width (b
f
) in gas-oil gravity drainage and
reinfiltration on the modeled fractured reservoir. Figure 5 depicts the oil recovery from gravity drainage
and reinfiltration in the fractured media. From the simulation result, it is observed that varying the fracture
width (b
f
) has no significant effect on the oil recovery obtained from gravity drainage and reinfiltration
mechanisms. The reason for this observation is that, fractures in NFRs are seen as flow channels or path
where displaced fluid (oil) flows through to the production channel. Thus, increasing the fracture width
(b
f
) may only expedite the rate of recovery not the ultimate (overall) oil recovery in gas-oil gravity
drainage and reinfiltration as depicted in Figure 5.
On the other hand, Figure 6 presents the oil saturation at the lower matrix block from gravity drainage
and reinfiltration under varying fracture widths (b
f
) in the modeled fractured porous media. This result
further shows that fracture width (b
f
) has little or no significant effect on gravity drainage and reinfiltration
recovery mechanism in NFRs. This assertion is based on the grounds that there was no disparity on the
obtained oil saturation at the lower matrix block under different fracture widths (b
f
) in the modeled
fractured reservoir. Zahoor and Haris (2012) mentioned that, when fracture width is increased, capillary
forces present in fractures are decreased for almost each fluid’s saturation. Thus, the assumption of zero
capillary pressure at the fracture in simulation study becomes imperative. Therefore, this explains the
reason for not including the fracture width (b
f
) in the gravity drainage and reinfiltration fluid flow
equations; as expanded in equations 3 through 6. Additionally, the same result was obtained for gas
saturation at the lower matrix block under gas-oil gravity drainage and reinfiltration.
Sensitivity of Storativity Capacity (
) on Gravity Drainage and Reinfiltration
The sensitivity of storativity capacity (
) on gas-oil gravity drainage and reinfiltration in the modeled
fractured porous media was performed by varying the fracture porosity (
f
). The obtained storativity
capacity (
) from the varied fracture porosity (
f
) as presented in Table 2 was based on the expressed
equation 9.Figures 7 through 9present the oil recovery, gas saturation and oil saturation at the lower
matrix block, respectively of the modeled reservoir under gas-oil gravity drainage and reinfiltration
mechanisms.
In gravity drainage, the obtained result which is presented in Figure 7 indicates that the storativity
capacity has no significant effect on the oil recovery in the gas-oil gravity drainage. Apparently, the reason
for this observation can be attributed to the non-storativity of the fractures in NFRs. In other words, the
fracture porosity variation has no significant effect on the ultimate oil recovery in gas-oil gravity drainage
mechanism; as the porous nature of the fractures only allow the transmissibility of fluids: oil and gas
without any fluid accumulation. Conversely, in oil reinfiltration process, storativity capacity has some
effect on the oil recovery from the modeled media. This is as a result of the reinfiltrated oil being held
back in the pores of the fractures to be infiltrated in to the matrix block beneath. Therefore, the more the
fracture storativity capacity the less oil recovered under reinfiltration mechanism.
Figures 8 and 9depict the gas and oil saturations at the lower matrix block of the modeled fractured
reservoir. The figures show that in gravity drainage, the fluid saturation at the lower matrix block was
unchanged at different storativity capacities. Whilst in reinfiltration, there was slight variation in the gas
and oil saturation at the lower matrix block for different storativity capacities. This indicates that fracture
storativity capacity slightly influences the reinfiltration process in fractured reservoirs. Thus, the observed
SPE-178271-MS 11
saturations (i.e., gas and oil) result further establishes the explanation made on the oil recovery result
(Figure 7) on gravity drainage and reinfiltration.
Conclusion
Gravity drainage, which predominates naturally fractured reservoir recovery mechanism, especially in
gas-oil system, is influenced by reinfiltration phenomenon. The effect of the fracture reservoir parameters
on the aforementioned phenomenon predicated upon this research endeavour. Based on the results
obtained, the following conclusions are drawn:
1. Fracture porosity as well as storativity capacity has no effect on the recovery in gas-oil gravity
drainage. However, in gas-oil gravity drainage with reinfiltration it influences the ultimate oil
recovery from naturally fractured reservoirs.
2. In gas-oil gravity drainage and reinfiltration in fractured reservoirs, fracture width has no influence
on the ultimate oil recovered from the porous media.
Nomenclature
q
␣
Well term
␣
Water/oil term
P
␣
Phase pressure
Porosity
V
b
Bulk volume
S
␣
Phase saturation
T
␣
Exchange term
n Time step
f Fracture
m Matrix
R
S
Solubility ratio of gas in oil
S
o
Oil Saturation
Oil reinfiltration rate for matrix block to fracture
Oil drainage rate for matrix block to fracture
Oil matrix-fracture exchange rate
Gas matrix-fracture exchange rate
Net free gas exchange rate
o
Oil mobility
g
Gas mobility
ⵜVector differential operator
␥
o
Oil specific weight
␥
g
Gas specific weight
Z Vertical depth
P
o
Oil pressure
P
g
Gas pressure
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12 SPE-178271-MS
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SPE-178271-MS 13
