Research of Nonlinear Flow Numerical Simulation of Ultra-low

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 Eastern16 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.
Key words 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. λa is called
）
the real starting pressure gradient, and λc 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( λb )[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 λa (the real starting pressure gradient) and λ 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
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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 software
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 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
Figure2.
Fig.1 The curve of the nonlinear porous flow
in ultra-low permeability reservoir
v=
ke (∇p )
µ
⋅ ∇p =
Fig.2 The relationship of permeable capability
coefficient and pressure gradient
Ak (∇p )k
µ
⋅∇p
(1)
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.
3 The application of numerical simulation software
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
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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 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.
Fig3 shows the formation pressure gradient distribution based on different well spacing and
producing time. According to fig3, 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 shown in fig4, 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 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 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 fig3 indicates, all the
producing wells get water injection efficiency in one year under 150-meter well spacing. However, some
150 meters (one years)
200 meters (one years)
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250meters one years)
150 meters (five years)
200 meters (five years)
250meters (five years)
150 meters (ten years)
200 meters (ten years)
250meters (ten years)
Fig.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)
200meters (ten years)
Fig.4 The formation pressure gradient three-dimensional figures of Dong16 block in one, five and ten years of
200 meters producer-injector spacing
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.
3.2 The fluid flow region research of the Eastern 16 block
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 ( λ a ) and the critical starting pressure gradient ( λ c ) as the limits. When
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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 λ a and λ 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.
150 meters (ten years)
200 meters (ten years)
250 meters (ten years)
Fig.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.
4 Conclusion
(1) During the process of exploring the ultra-low 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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