Research of Nonlinear Flow Numerical Simulation of

Physical and Numerical Simulation of Geotechnical Engineering
12th Issue, Sep. 2013
Research of Nonlinear Flow Numerical Simulation of
Ultra-low Permeability Reservoir in Yushulin Oilfield
YU Rongze, YANG Zhengming
Institute of Porous Flow & Fluid Mechanics of Chinese Academy of Sciences
[email protected]
ABSTRACT: According to the seepage characteristics of ultra-low permeability reservoir, the nonlinear
flow numerical simulation software for ultra-low permeability reservoir is developed. The unit of the
inverted nine spot well pattern of Eastern 16 block of Daqing Yushulin Oil field is taken as the research
object. Under the condition of keeping the bottom hole flowing pressure of the production wells and
water injection wells constant, the simulation of the formation pressure gradient distribution is made
under different Producer-injector Spacing by using the numerical simulation software. At last, different
fluid flow region, effective driving pressure system and reasonable well pattern deployment are achieved
to provide references to the well pattern arrangement of the injection and production wells for this kind
of ultra-low permeability reservoir.
KEYWORDS: Ultra-low permeability reservoir, Nonlinear flow, Reservoir numerical simulation,
Seepage, Well pattern
1 INTRODUCTION
In 1856, a French hydraulician named H.Darcy presented
Darcy law, which laid the foundation of seepage mechanics.
The subsequent experimental results and field reality
indicate that Darcy Law has some limitations and only
applicable to the middle and high permeability reservoir [1].
Until 1924, a Russian scholar put forward the theory that the
flow in the porous medium occurs only when the pressure
gradient exceeds a certain pressure gradient. And from then
on, the research of non-Darcy flow started. The non-Darcy
flow here refers to the model which takes the starting
pressure gradient into consideration. Many scholars at home
and abroad (e.g. B.A. Florin; Miller; Pascal; Irmay; Huang
Yanzhang; Yan Qinglai; etc.)make some related research on
this theory and gain some achievements which applies well
to the development of the normal low permeability reservoir.
Recent years, with the development of ultra-low
permeability reservoir, the limitations of non-Darcy flow
are becoming more and more obvious. The fluid seepage of
ultra-low permeability reservoir has its own distinctive
characteristics, and the feature of its flow curve is shown in
graph 1. Generally, the flow curve consists of two parts: the
concave nonlinear part at low seepage velocity and the
straight line part at high seepage velocity. When the pressure
gradient is smaller than a special value, the flow curve is a
concave and nonlinear curve. With the increase of the
pressure gradient, the seepage curve transforms into linear
seepage segment. a is called the real starting pressure
gradient, and c is called the critical starting pressure
gradient. The cross point between the extension of the
straight line segment and the pressure gradient is quasi
starting pressure gradient( b )[10].
In the process of exploring the ultra-low permeability
reservoir, the nonlinear part become more and more obvious,
and there are great differences between a (the real
© ST. PLUM-BLOSSOM PRESS PTY LTD
starting pressure gradient) and b (the quasi starting
pressure gradient). The application of non-Darcy model in
the exploitation of ultra-low permeability reservoir will
result in a big deviation. But the nonlinear flow model can
describe the seepage law of reservoir fluid in a more
accurate way. This paper takes advantage of the seepage
characteristics of the ultra-low permeability reservoir, and
compiles reservoir numerical simulation software which
accords with nonlinear flow law. In order to investigate the
effective driving pressure system and reasonable well
pattern deployment in the ultra-low permeability reservoir,
the numerical simulation software is used to simulate the
unit of the inverted nine spot well pattern of Eastern16 block
of Yushulin oil field in Daqing oilfield. Under the condition
of keeping the bottom hole flowing pressure of the
production wells and water injection wells constant, the
formation pressure gradient distribution is stimulated when
the Producer-Injector Spacing is changed. At last, different
fluid flow region, effective driving pressure system and
reasonable well pattern deployment are achieved to provide
references to the well pattern arrangement of the injection
and production wells for this kind of ultra-low permeability
reservoir.
2 NONLINEAR PROCESSING OF THE
RESERVOIR
NUMERICAL
SIMULATION
SPFTWARE
In order to describe the nonlinear flow phenomenon of
ultra-low permeability reservoir in mathematical sense,
experimental correction is used on the basis of classical
Darcy law. Permeability k is a constant in Darcy law. The
permeability has square length dimension. There is a clear
definition about permeability in classical seepage
mechanics, namely a property of porous media. It
represents the easiness of fluid flow through porous media
Research of Nonlinear Flow Numerical Simulation of Ultra-low Permeability Reservoir in Yushulin Oilfield
DOI:10.5503/J.PNSGE.2013.12.011
under different pressure gradient. It is the fluid conductivity
of porous media. As for the nonlinear flow of ultra-low
permeability reservoir, the equivalent percolation ability ke
is introduced, which is the function of pressure gradient. In
the process of mathematical treatment, permeability is
always in proportion with viscosity. So in terms of
mathematics, viscosity can be considered as a fixed value,
and then the change of percolation ability caused by
viscosity is attributed to the change of permeability. Thus
the relationship of equivalent percolation ability ke and
pressure gradient is established. The percolation ability
coefficient is defined as AK  ke k , in which Ak is the
function of pressure gradient, k is the absolute permeability,
and then the relation of the percolation ability coefficient
and pressure gradient is achieved, as is shown in Figure 2.
Figure 1 The curve of the nonlinear porous flow in
ultra-low permeability reservoir
Figure 2 The relationship of permeable capability
coefficient and pressure gradient
A (p )k
(1)
p  k
p


The relation curve of velocity and driving pressure
gradient can be gained from core experiment, then the
relation curve of equivalent percolation ability ke and
pressure gradient can be obtained. And finally, the relation
curve of percolation ability coefficient and pressure
gradient is built. In the calculation process of numerical
stimulation, on the basis of black-oil model numerical
simulation algorithm, the value of permeability is modified
according to the change of formation pressure gradient in
every time step, enabling the porous flow process to
approach the nonlinear flow curve.
v
ke (p )
3 THE APPLICATION OF
SIMULATION SOFTWARE
liquid-producing capacity and injection wells under the
steady liquid-injecting. The producer-injector spacing is
changing from 150 meters to 250meters.
3.1 The formation pressure gradient distribution under
different well spacing and producing time
Fig.3 shows the formation pressure gradient distribution
based on different well spacing and producing time.
According to Fig.3, high pressure gradient region appears
in the vicinity of producing and injecting well bore because
of the oil output and water injection. Combining the
three-dimensional formation pressure gradient distribution
was shown in Fig.4, the highest pressure gradient appears
in the vicinity of water injecting well because of water
injection. Secondly, the higher pressure gradient appears in
the vicinity of four edge wells. The relatively low pressure
gradient appears in the vicinity of four corner wells. The
lowest pressure gradient region is between the edge well
and corner well where is the remaining oil enriched zones.
The water injecting well is not fractured, and the profile of
the pressure gradient is evenly spread to the nearby strata of
the wells.
Because of the horizontal fracture made by fracturing
measures, the highest pressure gradient appears in the two
edge wells of water well line. The low pressure gradient
area between the edge wells of oil well line and the corner
wells is obviously smaller than the low pressure gradient
area between the edge wells of water wells line and the
corner wells. Because of the small percolating resistance in
horizontal direction caused by the fracture, the edge wells
of water well line obtain more effective energy complement
and high pressure gradient strip is formed in horizontal
direction between water injection well and two edge wells
of water well line. It shows that the pressure gradient
NUMERICAL
The numerical simulation software is used to simulate
Eastern16 block of Yushulin ultra-low permeability
reservoir in Daqing oilfield. The different fluid flow region,
effective driving pressure system and reasonable well
pattern deployment are achieved. Eastern16 block is a
major producing block of Yushulin ultra-low permeability
reservoir. The reservoir physical property of this block is
comparatively well, the average effective porosity is 15%,
the average effective permeability is 4.47×10-3μm2, the oil
viscosity underground is about 4.662mPa•s, the oil bearing
area is about 11.0km2, and the geological reserves of this
block is about 80 million tons. Eastern16 block was put
into production in 1993, using the 300×300 meters square
well pattern, and inverted nine spot geometrical pattern
flooding form in the reservoir development. All the
production wells are fractured. During the numerical
simulation, keep the production wells under the steady
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Physical and Numerical Simulation of Geotechnical Engineering
12th Issue, Sep. 2013
profiles propagate faster in horizontal direction and the
water flow is large in this direction. Secondly, the high
pressure gradient strip is also formed in vertical direction
between water injection well and two edge wells of oil well
line. The four corner wells get the least effective energy
complement. All these fit well with the actual situation.
In view of different well spacing at the same
150 meters (one years)
development time, the smaller the well spacing is, the faster
the pressure gradient profiles propagate. And the bigger the
well spacing is, the larger the remaining oil enriched area
between edge wells and corner wells become. As Fig.3
indicates, all the producing wells get water injection
efficiency in one year under 150-meter well spacing.
200 meters (one years)
250 meters (one years)
150 meters (five years)
200 meters (five years)
250 meters (five years)
150 meters (ten years)
200 meters (ten years)
250 meters (ten years)
Figure 3 The formation pressure gradient planar figure of Dong16 block in one, five and ten years under the condition
of different producer-injector spacing
200 meters (one year)
200 meters (five years)
200 meters (ten years)
Figure 4 The formation pressure gradient three-dimensional figures of Dong16 block in one, five and ten years of 200
meters producer-injector spacing
51
Research of Nonlinear Flow Numerical Simulation of Ultra-low Permeability Reservoir in Yushulin Oilfield
DOI:10.5503/J.PNSGE.2013.12.011
Low pressure gradient areas appears between the corner
well and the water injection well under 250-meter well
spacing, that is to say, the corner well does not get good
water injection efficiency. Under the same well spacing,
pressure gradient profiles propagate to the surrounding area
with the time. By comparing different well spacing, it can
be concluded that the whole formation is effectively
employed under 150-meter and 200-meter well spacing.
But the relatively low pressure gradient area still appears
near the four corner wells. So it can be considered that the
effective driving pressure system does not established
under 250-meter well spacing. Finally, the conclusion can
be drawn that the reasonable well spacing of Eastern 16
block is about 200 meters.
Fig.2 is the relation curve of the percolation ability
coefficient and pressure gradient of Eastern 16 block.
Based on the curve, the real starting pressure gradient is
0.02MPa/m, and the critical starting pressure gradient is
0.08MPa/m. The formation fluid flow region is divided into
three parts, taking the real starting pressure gradient (  a )
and the critical starting pressure gradient (  c ) as the limits.
When the pressure gradient is smaller than the real starting
pressure gradient, there will be no fluid in the formation,
and that area is not employed, which is called the dead oil
zone. When the pressure gradient is bigger than the critical
starting pressure gradient, linear flow occurs in the
formation. When the formation pressure gradient is
between  a and  c , nonlinear flow occurs. Based on the
research of the fluid flow region, the distribution of the
remaining oil, the effective driving of the well pattern, and
the nonlinear flow region can be studied effectively.
3.2 The fluid flow region research of the Eastern 16
block
150 meters (ten years)
200 meters (ten years)
250 meters (ten years)
Figure 5 The formation fluid flow region distribution figure of Eastern 16 block under different producer-injector
spacing in ten years
Fig.5 shows the distribution of the formation fluid region
under different producer-injector spacing when the
producing time is ten years. The red part represents the
region where the pressure gradient is bigger than the
critical starting pressure gradient and linear flow occurs.
Suppose the pressure gradient of the blue part is smaller
than the critical starting pressure gradient, and there is no
flow in this area. The nonlinear flow occurs in the
remaining region. Judging from Fig.5, there appears dead
oil zone between the edge wells of the water well line and
the neighboring corner wells under the 250-meter spacing
only. Thus, the reasonable producer-injector spacing of
Eastern 16 block is about 200 meters. With the increase of
the well spacing, the area of the nonlinear flow region
becomes larger and larger. During the process of exploring
the ultra-low permeability reservoir, nonlinear flow occurs
in a very large area of the formation. The research on the
nonlinear flow numerical stimulation can help to describe
the seepage law of that kind of reservoir fluid more
precisely.
permeability reservoir, linear flow only occurs in a small
area near the wellhead. But nonlinear flow occurs in a very
large area of the formation, playing the leading role of the
formation seepage. Therefore, the description of the
seepage law of the reservoir fluid is more accurate when
considering nonlinear flow.
(2) When exploring the ultra-low permeability reservoir,
the bigger the well spacing is, the percolating resistance is
larger. Under the condition of keeping the output of the
production well to a certain level, the well spacing can be
decreased to improve the development effect of the
reservoir.
(3) The reasonable well spacing of Eastern 16 block in
Daqing Yushulin ultra-low permeability reservoir is about
200 meters.
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4 CONCLUSIONS
(1) During the process of exploring the ultra-low
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Physical and Numerical Simulation of Geotechnical Engineering
12th Issue, Sep. 2013
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