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1169
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Development of hydraulic fractures mainly
occurs along the axes of the regional stress field assuming fracturing operations are conducted in areas lacking a significant alteration of pressure and temperature, i.e. new exploration wells
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[1]
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.
Modern pumping units which are employed for hydraulic fracturing operations
achieve wellhead pressures of up to 20 MPa during the injection of fracturing fluid into
the reservoir. Spontaneous hydraulicfracturing growth in the horizon of interest is initiated as soon as injection pressure exceeds yield strength of the particular reservoir
rock [2–8].
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1541
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Modern pumping units which are employed for hydraulic fracturing operations
achieve wellhead pressures of up to 20 MPa during the injection of fracturing fluid into
the reservoir. Spontaneous hydraulicfracturing growth in the horizon of interest is initiated as soon as injection pressure exceeds yield strength of the particular reservoir
rock
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[2–8]
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. Realtime data acquisition of wellhead pressures from active and observation
wells and the results of interference testing confirm that in some cases hydraulic fractures may achieve a length of up to 1 000 m [8].
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1757
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Realtime data acquisition of wellhead pressures from active and observation
wells and the results of interference testing confirm that in some cases hydraulic fractures may achieve a length of up to 1 000 m
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[8]
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.
S. Ekie et al. [9] present a mathematical model for the fracture formation for two vertical wells — one active well and one observation well. Conducting pulsetests for the
tracking of registration response pressures in several vertical observation wells can be
used to determine the orientation of the fracture originating from the active fracture well.
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1776
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Realtime data acquisition of wellhead pressures from active and observation
wells and the results of interference testing confirm that in some cases hydraulic fractures may achieve a length of up to 1 000 m [8].
S. Ekie et al.
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[9]
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present a mathematical model for the fracture formation for two vertical wells — one active well and one observation well. Conducting pulsetests for the
tracking of registration response pressures in several vertical observation wells can be
used to determine the orientation of the fracture originating from the active fracture well.
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2134
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Conducting pulsetests for the
tracking of registration response pressures in several vertical observation wells can be
used to determine the orientation of the fracture originating from the active fracture well.
N. Mousli et al.
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[10]
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, D. Meehan et al. [11] presented analytical solutions of modeling
interference test for wells with parallel. D. Tiab and E. Abobise [12] discussed the design of pulse testing of a fractured active well and vertical observation well (without
fractures), presenting correlations for fracture orientation, average permeability and other parameters of the reservoir on the response amplitude and the
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2157
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Conducting pulsetests for the
tracking of registration response pressures in several vertical observation wells can be
used to determine the orientation of the fracture originating from the active fracture well.
N. Mousli et al. [10], D. Meehan et al.
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[11]
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presented analytical solutions of modeling
interference test for wells with parallel. D. Tiab and E. Abobise [12] discussed the design of pulse testing of a fractured active well and vertical observation well (without
fractures), presenting correlations for fracture orientation, average permeability and other parameters of the reservoir on the response amplitude and the response time in the
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2271
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Conducting pulsetests for the
tracking of registration response pressures in several vertical observation wells can be
used to determine the orientation of the fracture originating from the active fracture well.
N. Mousli et al. [10], D. Meehan et al. [11] presented analytical solutions of modeling
interference test for wells with parallel. D. Tiab and E. Abobise
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[12]
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discussed the design of pulse testing of a fractured active well and vertical observation well (without
fractures), presenting correlations for fracture orientation, average permeability and other parameters of the reservoir on the response amplitude and the response time in the
observation well.
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2620
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Abobise [12] discussed the design of pulse testing of a fractured active well and vertical observation well (without
fractures), presenting correlations for fracture orientation, average permeability and other parameters of the reservoir on the response amplitude and the response time in the
observation well. In the same year K. Cooper and R. Collins
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[13]
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applied of a mathematical model which is based on interference test of a twowell system with a fractured (one
fracture) and another nonfracture well that was used to interpret the results of a field
case and to estimate underlying parameters of the system.
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2921
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Collins [13] applied of a mathematical model which is based on interference test of a twowell system with a fractured (one
fracture) and another nonfracture well that was used to interpret the results of a field
case and to estimate underlying parameters of the system. The article of H. Najurieta et
al.
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[14]
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presents a twodimensional model for heterogeneous anisotropic reservoirs; demonstrating the mathematical modeling for all wells. It can be used to calculate 2D pressure maps, transmissivity and diffusivity between active and observation wells estimated.
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3268
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It can be used to calculate 2D pressure maps, transmissivity and diffusivity between active and observation wells estimated.
Reservoir case studies with conductive faults were also presented in the article
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[15]
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.
Contrary to the abovementioned papers we elaborate a case that consists of the active
fractured well and the observation fractured well (fractures are oriented along the regional stress) either having a lowpermeability porous bridge between the fracture tips,
or two wells which are being directly connected through intersecting fracture planes
without a porous media bridge.
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3796
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well (fractures are oriented along the regional stress) either having a lowpermeability porous bridge between the fracture tips,
or two wells which are being directly connected through intersecting fracture planes
without a porous media bridge. Furthermore, we want to highlight the results of interfe56 Нефть и газ No 6, 2017
rence test from the work
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[8]
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by interpreting the chosen data model and providing an estimation of the fracture and reservoir characteristics. Formulating the abovementioned
problem, injection pressure is assumed to surpass the fracture closure pressure, i. e. its
geometry (height, length, width) is treated constant.
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7889
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The system of equations (1)–(4) and the corresponding boundary conditions
(5)–(8) for the geometry, as shown in Figure 1, were solved using the finite difference
method for the Newton iteration scheme on a nonuniform rectangular difference grid
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[16]
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. The accuracy of the approximation was tested against an analytical solution for the
case of wells with a single vertical fracture of finite conductivity [17]. An example of
calculation was performed using the following parameters of the system:
km = 1∙10
15 m2;
μ= 0,3 mPa∙s; L=500 m; h= 21,23 m; mφ= 0,17; fφ=0,414;
cmt= 3,6687∙10
9 1/Pa;
cft= 9,4845∙10
9 1/Pa; d= 1, 3, 5, 10,
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8047
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(1)–(4) and the corresponding boundary conditions
(5)–(8) for the geometry, as shown in Figure 1, were solved using the finite difference
method for the Newton iteration scheme on a nonuniform rectangular difference grid
[16]. The accuracy of the approximation was tested against an analytical solution for the
case of wells with a single vertical fracture of finite conductivity
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[17]
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. An example of
calculation was performed using the following parameters of the system:
km = 1∙10
15 m2;
μ= 0,3 mPa∙s; L=500 m; h= 21,23 m; mφ= 0,17; fφ=0,414;
cmt= 3,6687∙10
9 1/Pa;
cft= 9,4845∙10
9 1/Pa; d= 1, 3, 5, 10, 30, 100, 200, 500, 800 m;
xdf−=9001 m; 2fx=100 m; kfwf ≈ 10∙1012 m2∙m; ip= 27∙106 Pa.
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11223
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The presence of a small porous medium bridges having low filtration properties leads
to a significant loss of pressure response between the active and the observation wells.
The field case which are
presented by A. Davletbaev et
al.
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[8]
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show that pressure is
responding almost instantaneous between the active and observation wells. Furthermore,
the pressure difference between
the wells is much smaller than
in the results which are shown
in Figures 2–4.
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13049
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The Figure emphasizes that higher fracture conductivities result in a better match for
both pressure changes and absolute values
of pressures in the active and the observation wells.
Field case interpretation. The mathematical model, which is presented by A.
Davletbaev et al.
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[8]
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, was used to interpret interferencetest pressure data for
wells pair (active well and observation
well) and to acquire refined fracture parameters. History of injected water volumes into the active well was included in
the mathematical model.
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