Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
IS11.0593-WO-PCT
SYSTEM AND METHOD FOR PERFORMING
WELLBORE FRACTURE OPERATIONS
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims priority to US Provisional Application No.
61/574,521 filed on
August 4,2011 and US Provisional Application No. 61/574,131 filed on July 28,
2011, the entire
contents of which is hereby incorporated by reference.
BACKGROUND
[0002] The present disclosure relates generally to methods and systems for
performing wellsite
operations. More particularly, this disclosure is directed to methods and
systems for performing
fracture operations, such as investigating subterranean formations and
characterizing hydraulic
fracture networks in a subterranean formation.
[0003] In order to facilitate the recovery of hydrocarbons from oil and gas
wells, the
subterranean formations surrounding such wells can be hydraulically fractured.
Hydraulic
fracturing may be used to create cracks in subsurface formations to allow oil
or gas to move
toward the well. A formation is fractured by introducing a specially
engineered fluid (referred to
as "fracturing fluid" or "fracturing slurry" herein) at high pressure and high
flow rates into the
formation through one or more wellbore. Hydraulic fractures may extend away
from the
wellbore hundreds of feet in two opposing directions according to the natural
stresses within the
formation. Under certain circumstances, they may form a complex fracture
network.
[0004] The fracturing fluids may be loaded with proppants, which are sized
particles that may be
mixed with the fracturing fluid to help provide an efficient conduit for
production of
hydrocarbons from the formation/reservoir to the wellbore. Proppant may
comprise naturally
occurring sand grains or gravel, man-made or specially engineered proppants,
e.g. fibers, resin-
coated sand, or high-strength ceramic materials, e.g. sintered bauxite. The
proppant collects
heterogeneously or homogenously inside the fracture to "prop" open the new
cracks or pores in
the formation. The proppant creates planes of permeable conduits through which
production
fluids can flow to the wellbore. The fracturing fluids are preferably of high
viscosity, and
therefore capable of carrying effective volumes of proppant material.
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
[0005] The fracturing fluid may be realized by a viscous fluid, sometimes
referred to as a "pad"
that is injected into the treatment well at a rate and pressure sufficient to
initiate and propagate a
fracture in hydrocarbon formation. Injection of the "pad" is continued until a
fracture of
sufficient geometry is obtained to permit placement of the proppant particles.
After the injection
of the "pad," the fracturing fluid may consist of a fracturing fluid and
proppant material. The
fracturing fluid may be a gel, oil based, water based, brine, acid, emulsion,
foam or any other
similar fluid. The fracturing fluid can contain several additives, viscosity
builders, drag reducers,
fluid-loss additives, corrosion inhibitors and the like. In order to keep the
proppant suspended in
the fracturing fluid until such time as all intervals of the formation have
been fractured as
desired, the proppant may have a density close to the density of the
fracturing fluid utilized.
[0006] Proppants may be comprised of any of the various commercially available
fused
materials such as silica or oxides. These fused materials can comprise any of
the various
commercially available glasses or high-strength ceramic products. Following
the placement of
the proppant, the well may be shut-in for a time sufficient to permit the
pressure to bleed off into
the formation. This causes the fracture to close and exert a closure stress on
the propping agent
particles. The shut-in period may vary from a few minutes to several days.
[0007] Current hydraulic fracture monitoring methods and systems may map where
the fractures
occur and the extent of the fractures. Some methods and systems of
microseismic monitoring
may process seismic event locations by mapping seismic arrival times and
polarization
information into three-dimensional space through the use of modeled travel
times and/or ray
paths. These methods and systems can be used to infer hydraulic fracture
propagation over time.
[0008] Conventional hydraulic fracture models may also assume a bi-wing type
induced fracture.
These bi-wing fractures may be short in representing the complex nature of
induced fractures in
some unconventional reservoirs with preexisting natural fractures. Published
models may map
the complex geometry of discrete hydraulic fractures based on monitoring
microseismic event
distribution.
[0009] In some cases, models may not be constrained by accounting for either
the amount of
pumped fluid or mechanical interactions between fractures and injected fluid
and among the
fractures. Some of the constrained models may provide a fundamental
understanding of involved
mechanisms, but may be complex in mathematical description and/or require
computer
2
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
processing resources and time in order to provide accurate simulations of
hydraulic fracture
propagation.
[0010] Unconventional formations, such as shales are being developed as
sources of
hydrocarbon production. Once considered only as source rocks and seals, shale
formations are
now considered as tight-porosity and low-permeability unconventional
reservoirs. Patterns of
hydraulic fractures created by the fracturing stimulation may be complex and
may form a
fracture network as indicated by the distribution of associated microseismic
events. Complex
hydraulic fracture networks have been developed to represent the created
hydraulic fractures.
Examples of fracture models are provided in US Patent/Application Nos.
6101447, 7363162,
7788074, 20080133186, 20100138196, and 20100250215.
[0011] Hydraulic fracturing of shale formation may be used to stimulate and
produce from the
reservoir. Production simulation has been developed to estimate production
from reservoirs.
Various production simulation techniques have been used with conventional
reservoirs.
Examples of production simulation are provided in Warren et al., "The Behavior
of Naturally
Fractured Reservoirs, Soc.Pet.Eng.J., Vol. 3(3): pp. 245-255 (1963) (hereafter
"Warren &
Root"); Basquet et al., "Gas Flow Simulation in Discrete Fracture Network
Models". Paper SPE
79708 presented at the SPE Reservoir Simulation Symposium, Houston, Texas, 3-5
February
2003 (hereafter "Basquet"); Gong et al., "Detailed Modeling of the Complex
Fracture Network
of Shale Gas Reservoirs", SPE paper 142705 presented at the SPE Middle East
Unconventional
Gas Conference and Exhibition held in Muscat, Oman, 31 January 2011 (hereafter
"Gong");
Cinco-Ley et al., "Pressure Transient Analysis for Naturally Fractured
Reservoirs", SPE paper
11026 presented at the Annual Fall Technical Conference and Exhibition held in
New Orleans,
LA, Sept 26, 1982 (hereafter "Cinco-Ley"); Xu et al., "Quick Estimate of
Initial Production from
Stimulated Reservoirs with Complex Hydraulic Fracture Network", Paper SPE
146753 presented
at the SPE Annual Technical Conference and Exhibition held in Denver,
Colorado, USA, 30
October 2011 (hereafter "Xu 2011"); and C.E. Cohen et al. "Production Forecast
After Hydraulic
Fracturing in Naturally Fractured Reservoir: Coupling a Complex Fracturing
Simulator and a
Semi-Analytical Production Model", Paper (SPE 152541) presented at the SPE
Hydraulic
Fracturing Technology Conference and Exhibition held in The Woodlands, Texas,
USA, 8th of
February 2012, the entire contents of which are hereby incorporated by
reference. However, the
3
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
reservoirs may be unconventional and/or have natural fractures, such as those
with shale.
SUMMARY
[0012] In at least one aspect the present disclosure relates to a method of
performing a
production operation about a wellbore penetrating a subterranean formation.
The subterranean
formation has a plurality of fractures thereabout. The method involves
generating a flow rate
through a discrete fracture network defined by the plurality of fractures in
the subterranean
formation. The discrete fracture network includes a plurality of fracture
branches with
intersections therebetween and a plurality of matrix blocks. The method
further involves
generating a pressure profile of the discrete fracture network for an initial
time based on the flow
rate, and generating a production rate based on the pressure profile.
[0013] In another aspect, the disclosure relates to a method of performing an
oilfield operation
about a wellbore penetrating a subterranean formation. The method involves
performing a
fracture operation comprising generating fractures about the wellbore. The
fractures define a
hydraulic fracture network about the wellbore. The method also involves
generating a discrete
fracture network about the wellbore by extrapolating fracture data from the
hydraulic fracture
network. The discrete fracture network includes a plurality of fracture
branches with
intersections therebetween and a plurality of matrix blocks. The method
further involves
generating a depth of drainage through the discrete fracture network, defining
at least one
production parameter, and performing a production operation to produce fluids
from the
subterranean formation based on the depth of drainage and the at least one
production parameter.
[0014] Finally, in another aspect, the disclosure relates to a method of
performing an oilfield
operation about a wellbore penetrating a subterranean formation. The method
involves
stimulating the wellbore by injecting fluid into the subterranean formation
such that fractures are
generated about the wellbore, measuring the fractures and defining a hydraulic
fracture network
based on the measured fractures.
[0015] The method also involves generating a discrete fracture network about
the wellbore by
extrapolating fracture data from the hydraulic fracture network. The discrete
fracture network
includes a plurality of fracture branches with intersections therebetween and
a plurality of matrix
blocks. The method also involves generating a depth of drainage through the
discrete fracture
4
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
network, defining at least one production parameter, estimating a production
rate over time based
on the depth of drainage and the production parameter(s), and producing fluids
from the
subterranean formation based on the estimated production rate.
[0016] This summary is provided to introduce a selection of concepts that are
further described
below in the detailed description. This summary is not intended to identify
key or essential
features of the claimed subject matter, nor is it intended to be used as an
aid in limiting the scope
of the claimed subject matter.
BRIEF DESCRIPTION OF THE DRAWINGS
[0017] Embodiments of the system and method for characterizing wellbore
stresses are
described with reference to the following figures. The same numbers are used
throughout the
figures to reference like features and components.
[0018] Figs. 1.1-1.4 are schematic views illustrating various oilfield
operations at a wellsite;
[0019] Figs. 2.1-2.4 are schematic views of data collected by the operations
of Figures 1.1-1.4;
[0020] Fig. 3 is a schematic illustration of a hydraulic fracturing site
depicting a fracture
operation;
[0021] Figs. 4.1 and 4.2 are flow charts depicting methods of performing an
oilfield operation
and a production operation, respectively;
[0022] Fig. 5 is a schematic illustration of a production simulation of a
discrete fracture network
(DFN) extracted from a hydraulic fracturing simulation;
[0023] Fig. 6 is a schematic illustration of the DFN of Fig. 5 having a
plurality of matrix blocks;
[0024] Fig. 7. is a schematic illustration of a an approximation of flow
through a matrix block;
[0025] Figs. 8.1 ¨ 8.3 are graphs illustrating production, cumulated
production and pressure,
respectively, of a well;
[0026] Fig. 9 is a schematic diagram depicting coordinates of fractures of a
matrix block;
[0027] Fig. 10 is a schematic diagram depicting flow rate from a matrix block
to a branch of a
DFN;
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
[0028] Figs. 11.1 and 11.2 are graphs depicting pressure versus time over time
for a highly
conductive DFN;
[0029] Fig. 12 is a graph of normalized pressure and time delay over time for
a highly
conductive DFN;
[0030] Fig. 13 is a graph of cumulated production over time for a highly
conductive DFN;
[0031] Figs. 14.1 and 14.2 are graphs depicting pressure versus time over time
for a low
conductivity DFN;
[0032] Fig. 15 a graph of normalized pressure and time delay over time for a
low conductivity
DFN;
[0033] Fig. 16 is a graph of cumulated production over time for a low
conductivity DFN;
[0034] Fig. 17 is a graph of normalized pressure and time delay over time for
a low conductivity
DFN using an Unconventional Production Model (UPM);
[0035] Fig. 18 is a graph of cumulated production over time for a low
conductivity DFN using a
UPM;
[0036] Fig. 19 is a table of graphs of pressure and time delay over time;
[0037] Fig. 20 is a graph comparing simulated production over time using a
reservoir simulator
and the UPM;
[0038] Figs. 21.1 and 21.2 are schematic diagrams depicting of a DFN as
depicted by a reservoir
simulator and the UPM, respectively;
[0039] Fig. 22 is a graph comparing simulated production over time for
different fracture
conductivities using a reservoir simulator and the UPM; and
[0040] Figs. 23.1 and 23.2 are graphs of flow rate and cumulated production,
respectively, over
time by a reservoir simulator, the UPM and the UPM without delay.
DETAILED DESCRIPTION
[0041] The description that follows includes exemplary systems, apparatuses,
methods, and
instruction sequences that embody techniques of the subject matter herein.
However, it is
6
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
understood that the described embodiments may be practiced without these
specific details.
[0042] The present disclosure relates to techniques for performing fracture
operations to estimate
and/or predict production. The fracture operations involve fracture modeling
that utilize elliptical
and wire mesh modeling to estimate production.
[0043] Figures 1.1-1.4 depict various oilfield operations that may be
performed at a wellsite, and
Figures 2.1-2.4 depict various information that may be collected at the
wellsite. Figures 1.1-1.4
depict simplified, schematic views of a representative oilfield or wellsite
100 having subsurface
formation 102 containing, for example, reservoir 104 therein and depicting
various oilfield
operations being performed on the wellsite 100. FIG. 1.1 depicts a survey
operation being
performed by a survey tool, such as seismic truck 106.1, to measure properties
of the subsurface
formation. The survey operation may be a seismic survey operation for
producing sound
vibrations. In FIG. 1.1, one such sound vibration 112 generated by a source
110 reflects off a
plurality of horizons 114 in an earth formation 116. The sound vibration(s)
112 may be received
in by sensors, such as geophone-receivers 118, situated on the earth's
surface, and the geophones
118 produce electrical output signals, referred to as data received 120 in
FIG. 1.1.
[0044] In response to the received sound vibration(s) 112 representative of
different parameters
(such as amplitude and/or frequency) of the sound vibration(s) 112, the
geophones 118 may
produce electrical output signals containing data concerning the subsurface
formation. The data
received 120 may be provided as input data to a computer 122.1 of the seismic
truck 106.1, and
responsive to the input data, the computer 122.1 may generate a seismic and
microseismic data
output 124. The seismic data output may be stored, transmitted or further
processed as desired,
for example by data reduction.
[0045] FIG. 1.2 depicts a drilling operation being performed by a drilling
tool 106.2 suspended
by a rig 128 and advanced into the subsurface formations 102 to form a
wellbore 136 or other
channel. A mud pit 130 may be used to draw drilling mud into the drilling
tools via flow line 132
for circulating drilling mud through the drilling tools, up the wellbore 136
and back to the
surface. The drilling mud may be filtered and returned to the mud pit. A
circulating system may
be used for storing, controlling or filtering the flowing drilling muds. In
this illustration, the
drilling tools are advanced into the subsurface formations to reach reservoir
104. Each well may
target one or more reservoirs. The drilling tools may be adapted for measuring
downhole
7
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
properties using logging while drilling tools. The logging while drilling tool
may also be adapted
for taking a core sample 133 as shown, or removed so that a core sample may be
taken using
another tool.
[0046] A surface unit 134 may be used to communicate with the drilling tools
and/or offsite
operations. The surface unit may communicate with the drilling tools to send
commands to the
drilling tools, and to receive data therefrom. The surface unit may be
provided with computer
facilities for receiving, storing, processing, and/or analyzing data from the
operation. The surface
unit may collect data generated during the drilling operation and produce data
output 135 which
may be stored or transmitted. Computer facilities, such as those of the
surface unit, may be
positioned at various locations about the wellsite and/or at remote locations.
[0047] Sensors (S), such as gauges, may be positioned about the oilfield to
collect data relating
to various operations as described previously. As shown, the sensor (S) may be
positioned in one
or more locations in the drilling tools and/or at the rig to measure drilling
parameters, such as
weight on bit, torque on bit, pressures, temperatures, flow rates,
compositions, rotary speed
and/or other parameters of the operation. Sensors (S) may also be positioned
in one or more
locations in the circulating system.
[0048] The data gathered by the sensors may be collected by the surface unit
and/or other data
collection sources for analysis or other processing. The data collected by the
sensors may be used
alone or in combination with other data. The data may be collected in one or
more databases
and/or transmitted on or offsite. All or select portions of the data may be
selectively used for
analyzing and/or predicting operations of the current and/or other wellbores.
The data may be
historical data, real time data or combinations thereof. The real time data
may be used in real
time, or stored for later use. The data may also be combined with historical
data or other inputs
for further analysis. The data may be stored in separate databases, or
combined into a single
database.
[0049] The collected data may be used to perform analysis, such as modeling
operations. For
example, the seismic data output may be used to perform geological,
geophysical, and/or
reservoir engineering analysis. The reservoir, wellbore, surface and/or
processed data may be
used to perform reservoir, wellbore, geological, and geophysical or other
simulations. The data
outputs from the operation may be generated directly from the sensors, or
after some
8
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
preprocessing or modeling. These data outputs may act as inputs for further
analysis.
[0050] The data may be collected and stored at the surface unit 134. One or
more surface units
may be located at the wellsite, or connected remotely thereto. The surface
unit may be a single
unit, or a complex network of units used to perform the necessary data
management functions
throughout the oilfield. The surface unit may be a manual or automatic system.
The surface unit
134 may be operated and/or adjusted by a user.
[0051] The surface unit may be provided with a transceiver 137 to allow
communications
between the surface unit and various portions of the current oilfield or other
locations. The
surface unit 134 may also be provided with or functionally connected to one or
more controllers
for actuating mechanisms at the wellsite 100. The surface unit 134 may then
send command
signals to the oilfield in response to data received. The surface unit 134 may
receive commands
via the transceiver or may itself execute commands to the controller. A
processor may be
provided to analyze the data (locally or remotely), make the decisions and/or
actuate the
controller. In this manner, operations may be selectively adjusted based on
the data collected.
Portions of the operation, such as controlling drilling, weight on bit, pump
rates or other
parameters, may be optimized based on the information. These adjustments may
be made
automatically based on computer protocol, and/or manually by an operator. In
some cases, well
plans may be adjusted to select optimum operating conditions, or to avoid
problems.
[0052] FIG. 1.3 depicts a wireline operation being performed by a wireline
tool 106.3 suspended
by the rig 128 and into the wellbore 136 of FIG. 1.2. The wireline tool 106.3
may be adapted for
deployment into a wellbore 136 for generating well logs, performing downhole
tests and/or
collecting samples. The wireline tool 106.3 may be used to provide another
method and
apparatus for performing a seismic survey operation. The wireline tool 106.3
of FIG. 1.3 may,
for example, have an explosive, radioactive, electrical, or acoustic energy
source 144 that sends
and/or receives electrical signals to the surrounding subsurface formations
102 and fluids
therein.
[0053] The wireline tool 106.3 may be operatively connected to, for example,
the geophones 118
and the computer 122.1 of the seismic truck 106.1 of FIG. 1.1. The wireline
tool 106.3 may also
provide data to the surface unit 134. The surface unit 134 may collect data
generated during the
wireline operation and produce data output 124 which may be stored or
transmitted. The wireline
9
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
tool 106.3 may be positioned at various depths in the wellbore to provide a
survey or other
information relating to the subsurface formation.
[0054] Sensors (S), such as gauges, may be positioned about the wellsite 100
to collect data
relating to various operations as described previously. As shown, the sensor
(S) is positioned in
the wireline tool 106.3 to measure downhole parameters which relate to, for
example porosity,
permeability, fluid composition and/or other parameters of the operation.
[0055] FIG. 1.4 depicts a production operation being performed by a production
tool 106.4
deployed from a production unit or Christmas tree 129 and into the completed
wellbore 136 of
FIG. 1.3 for drawing fluid from the downhole reservoirs into surface
facilities 142. Fluid flows
from reservoir 104 through perforations in the casing (not shown) and into the
production tool
106.4 in the wellbore 136 and to the surface facilities 142 via a gathering
network 146.
[0056] Sensors (S), such as gauges, may be positioned about the oilfield to
collect data relating
to various operations as described previously. As shown, the sensor (S) may be
positioned in the
production tool 106.4 or associated equipment, such as the Christmas tree 129,
gathering
network, surface facilities and/or the production facility, to measure fluid
parameters, such as
fluid composition, flow rates, pressures, temperatures, and/or other
parameters of the production
operation.
[0057] While only simplified wellsite configurations are shown, it will be
appreciated that the
oilfield or wellsite 100 may cover a portion of land, sea and/or water
locations that hosts one or
more wellsites. Production may also include injection wells (not shown) for
added recovery or
for storage of hydrocarbons, carbon dioxide, or water, for example. One or
more gathering
facilities may be operatively connected to one or more of the wellsites for
selectively collecting
downhole fluids from the wellsite(s).
[0058] It should be appreciated that FIGS. 1.2-1.4 depict tools that can be
used to measure not
only properties of an oilfield, but also properties of non-oilfield
operations, such as mines,
aquifers, storage, and other subsurface facilities. Also, while certain data
acquisition tools are
depicted, it will be appreciated that various measurement tools (e.g.,
wireline, measurement
while drilling (MWD), logging while drilling (LWD), core sample, etc.) capable
of sensing
parameters, such as seismic two-way travel time, density, resistivity,
production rate, etc., of the
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
subsurface formation and/or its geological formations may be used. Various
sensors (S) may be
located at various positions along the wellbore and/or the monitoring tools to
collect and/or
monitor the desired data. Other sources of data may also be provided from
offsite locations.
[0059] The oilfield configuration of FIGS. 1.1-1.4 depict examples of a
wellsite 100 and various
operations usable with the techniques provided herein. Part, or all, of the
oilfield may be on land,
water and/or sea. Also, while a single oilfield measured at a single location
is depicted, reservoir
engineering may be utilized with any combination of one or more oilfields, one
or more
processing facilities, and one or more wellsites.
[0060] FIGS. 2.1-2.4 are graphical depictions of examples of data collected by
the tools of FIGS.
1.1-1.4, respectively. FIG. 2.1 depicts a seismic trace 202 of the subsurface
formation of FIG. 1.1
taken by seismic truck 106.1. The seismic trace may be used to provide data,
such as a two-way
response over a period of time. FIG. 2.2 depicts a core sample 133 taken by
the drilling tools
106.2. The core sample may be used to provide data, such as a graph of the
density, porosity,
permeability or other physical property of the core sample over the length of
the core. Tests for
density and viscosity may be performed on the fluids in the core at varying
pressures and
temperatures. FIG. 2.3 depicts a well log 204 of the subsurface formation of
FIG. 1.3 taken by
the wireline tool 106.3. The wireline log may provide a resistivity or other
measurement of the
formation at various depts. FIG. 2.4 depicts a production decline curve or
graph 206 of fluid
flowing through the subsurface formation of FIG. 1.4 measured at the surface
facilities 142. The
production decline curve may provide the production rate Q as a function of
time t.
[0061] The respective graphs of FIGS. 2.1, 2.3, and 2.4 depict examples of
static measurements
that may describe or provide information about the physical characteristics of
the formation and
reservoirs contained therein. These measurements may be analyzed to define
properties of the
formation(s), to determine the accuracy of the measurements and/or to check
for errors. The plots
of each of the respective measurements may be aligned and scaled for
comparison and
verification of the properties.
[0062] FIG. 2.4 depicts an example of a dynamic measurement of the fluid
properties through
the wellbore. As the fluid flows through the wellbore, measurements are taken
of fluid
properties, such as flow rates, pressures, composition, etc. As described
below, the static and
dynamic measurements may be analyzed and used to generate models of the
subsurface
11
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
formation to determine characteristics thereof. Similar measurements may also
be used to
measure changes in formation aspects over time.
OILFIELD OPERATIONS
[0063] The production operations may be simulated before, during or after
production is
generated from a wellbore. Simulating the production from complex fractured
reservoir may be
performed using various techniques. Dual porosity models may be used to
address differences of
properties between the fracture and the rest of the reservoir (matrix). Dual
porosity may consider
two coarse grids connected to each other, one for the fracture network and
another one for the
matrix. This method may also involve averaging of properties (e.g., for the
fracture network) and
simplifications to model the exchange term between the two medium. This method
may be used,
for example, for naturally fractured reservoirs. Additional analysis may be
provided for near
wellbore effects of the fracture network, such as in cases with networks
created by hydraulic
fracturing. Dual porosity techniques are described in Warren & Root,
previously incorporated by
reference herein.
[0064] Another approach involves using one medium that contains both the
fracture and the
reservoir, and a refined numerical grid. Additional computational time may be
needed for
processing. Flexibility on the gridding (e.g., unstructured mesh generation)
may be provided
using, for example, a specialized reservoir simulator.
[0065] Yet another approach involves the use of dual porosity equations on a
discrete-fracture-
network (DFN). An example of DFN is provided in Basquet, previously
incorporated by
reference herein. Additional methods may be used to simulate the flow from the
matrix to the
fractures. In some cases, such as with compressive reservoir fluids (e.g.,
gas), the production
history from each matrix block into the DFN may be considered. The matrix
block may be
gridded using additional unknowns in the system of equations. Examples of
gridding are
provided by Gong, previously incorporated by reference herein. Analytical
solutions may also be
provided to simulate the flow. Solutions may be derived from a Laplace
transform of the
continuity equation. Examples of analytical solutions are provided by Cinco-
Ley and Xu 2011,
previously incorporated by reference herein.
[0066] Transient fracture pressure may be considered to obtain a complex
expression that may
12
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
use numerical integration in time. Constant fracture pressure may also be
considered, and an
expression of the flow rate between the matrix and the fracture that is linear
in pressure may also
be obtained. This solution may be used, for example, in conductive fractures
where the variations
of pressure inside the DFN are negligible (e.g., at constant wellbore
pressure). The present
disclosure may employ one or more of the approaches to generate an analytical
solution. This
solution may extend over a range of fracture conductivity, in cases of
hydraulic fracturing, and/or
in naturally fractured reservoirs.
[0067] The present disclosure provides an analytical solution over a range of
fracture
conductivity in cases of hydraulic fracturing in naturally fractured
reservoirs. Such simulation
may apply to unconventional reservoirs, such as shale gas, although it can be
applicable to other
subterranean formations as well. These unconventional reservoirs have two main
features: low
rock permeability and a dense network of natural fractures. A stimulation
approach may be
provided to address potential differences in the production mode of
unconventional or other
reservoirs which may involve horizontal wells and large hydraulic fracturing
treatment to
produce. In some cases, these treatments initiate hydraulic fractures that
interact with natural
fractures, and may result in complex fracturing network that connect the well
to the reservoir.
[0068] This disclosure discloses a methodology to simulate the production from
reservoirs, such
as unconventional (naturally fractured) reservoir after a complex network of
hydraulic fractures
has been created. The disclosed method first extrapolates the results from an
unconventional
fracture model (UFM) simulation and then process it with a methodology that
would give to the
user a forecast of the production of the well for several years, within a time
limit and accuracy
range. The method of the current application extends the validity of the semi-
analytical model
for a full range of fracture conductivities to consider in real cases. The
simulator may be
validated against simulations by reservoir simulations, such as ECLIPSETM
commercially
available from Schlumberger Technology Corporation (see: www.s1b.corn), to
illustrate the
capabilities of the algorithm to provide accurate results for a given range of
fracture
conductivity.
[0069] The current disclosure also discloses a method to simulate the
production from a
naturally fractured reservoir that has been stimulated by hydraulic
fracturing. Portions of the
method may be implemented into a software program that simulates hydraulic
fracture
13
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
treatments. The method may first extrapolate the results from the simulation
to re-create an
adapted hydraulic fracture network with averaged properties between
intersections of the
network, and then estimate equivalent block depth in front of each fracture
face. Finally,
parameters may be input for the production condition and the production
simulator run. The
production from each matrix block in contact with a fracture uses an analytic
expression that can
be extended to a full range of realistic values for the problem parameters
(conductivity,
permeability, etc.) This is accomplished by updating at each time step and for
each fracture face,
the initial production time in order to accounts for delays in the production
of each matrix block,
and in a way to preserve mass balance of reservoir fluid in place/produced.
The update is carried
by a search algorithm that calculates this initial time so the mass really
produced from each side
of a matrix block is equal to the same mass if the current pressure conditions
in the adjacent
fracture would have been constant in time and had started at the updated
initial time. The method
may be compared with simulations by existing reservoir simulators, such as
ECLIPSETM. Results
over a range of fracture conductivity may be performed and cross-checked with
a reservoir
simulator.
[0070] Figure 3 illustrates an exemplary operational setting for hydraulic
fracturing of a
subterranean formation (referred to herein as a "fracture site") in accordance
with the present
disclosure. The fracture site 300 can be located on land or in a water
environment and includes a
treatment well 301 extending into a subterranean formation as well as a
monitoring well 303
extending into the subterranean formation and offset from the treatment well
301. The
monitoring well 303 includes an array of geophone receivers 305 (e.g., three-
component
geophones) spaced therein as shown.
[0071] During the fracturing operation, fracturing fluid is pumped from the
surface 311 into the
treatment 301 causing the surrounding formation in a hydrocarbon reservoir 307
to fracture and
form a hydraulic fracture network 308. Such fracturing produces microseismic
events 310, which
emit both compressional waves (also referred to as primary waves or P-waves)
and shear waves
(also referred to as secondary waves or S-waves) that propagate through the
earth and are
recorded by the geophone receiver array 305 of the monitoring well 303.
[0072] The distance to the microseismic events 310 can be calculated by
measuring the
difference in arrival times between the P-waves and the S-waves. Also,
hodogram analysis,
14
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
which examines the particle motion of the P-waves, can be used to determine
azimuth angle to
the event. The depth of the event 310 is constrained by using the P- and S-
wave arrival delays
between receivers of the array 305. The distance, azimuth angle and depth
values of such
microseismic events 310 can be used to derive a geometric boundary or profile
of the fracturing
caused by the fracturing fluid over time, such as an elliptical boundary
defined by a height h,
elliptic aspect ratio e and major axis a as illustrated in Figure 3.
[0073] The site 301 also includes a supply of fracturing fluid and pumping
means (not shown)
for supplying fracturing fluid under high pressure to the treatment well 301.
The fracturing fluid
can be stored with proppant (and possibly other special ingredients) pre-mixed
therein.
Alternatively, the fracturing fluid can be stored without pre-mixed proppant
or other special
ingredients, and the proppant (and/or other special ingredients) mixed into
the fracturing fluid in
a controlled manner by a process control system as described in U.S. Patent
No. 7,516,793,
herein incorporated by reference in its entirety. The treatment well 301 also
includes a flow
sensor S as schematically depicted for measuring the pumping rate of the
fracturing fluid
supplied to the treatment well and a downhole pressure sensor for measuring
the downhole
pressure of the fracturing fluid in the treatment well 301.
[0074] A data processing system 309 is linked to the receivers of the array
305 of the monitoring
well 303 and to the sensor S (e.g., flow sensor and downhole pressure sensor)
of the treatment
well 301. The data processing system 309 may be incorporated into and/or work
with the surface
unit 134. The data processing system 309 carries out the processing set forth
in Figure 4 and
described herein. As will be appreciated by those skilled in the art, the data
processing system
309 includes data processing functionality (e.g., one or more microprocessors,
associated
memory, and other hardware and/or software) to implement the disclosure as
described herein.
[0075] The data processing system 309 can be realized by a workstation or
other suitable data
processing system located at the site 301. Alternatively, the data processing
system 309 can be
realized by a distributed data processing system wherein data is communicated
(preferably in
real time) over a communication link (typically a satellite link) to a remote
location for data
analysis as described herein. The data analysis can be carried out on a
workstation or other
suitable data processing system (such as a computer cluster or computing
grid). Moreover, the
data processing functionality of the present disclosure can be stored on a
program storage device
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
(e.g., one or more optical disks or other hand-holdable non-volatile storage
apparatus, or a server
accessible over a network) and loaded onto a suitable data processing system
as needed for
execution thereon as described herein.
[0076] Figure 4.1 is a flow chart depicting a method 400.1 of performing an
oilfield operation.
The method involves 420 performing a fracture operation (actual or simulated),
422 generating a
DFN about the wellbore, 424 generating a depth of drainage through the DFN,
426 defining at
least one production parameter, and 428 performing a production operation.
[0077] Figure 4.2 depicts a method 400.2 of performing a production operation.
This production
operation may be the same as the production operation 428 of Figure 4.1. In
the version of
method 400.2, the production operation is simulated. As indicated in Figure
4.2, the method
400.2 involves 421 generating a flow rate through a discrete fracture network,
423 generating a
pressure profile of the discrete fracture network based on the flow rate, and
425 generating a
production rate based on the pressure profile. The method may also involve 427
validating the
production rates. The method may be provided with other features, and
performed in any order.
[0078] The performing a fracture operation 420 involves generating fractures
about the wellbore
and defining a hydraulic fracture network about the wellbore. This fracture
operation may be
performed by actual injection of fluid as shown, for example, in Figure 3.
Hydraulic fracturing of
the well may also be simulated using hydraulic fracture simulators.
Simulations may involve
generating a fracture network about the wellbore. Discrete fracture network
techniques are
provided in US Patent Application No. 20100307755. Data from the actual or
simulated
hydraulic fracturing may be used to generate data describing the resulting
DFN.
[0079] A hydraulic fracture simulation 530 may be visually depicted by
computer generated
images as shown in Figure 5. The hydraulic fracture simulation 530 includes a
plurality of
fractures 534 that form a hydraulic fracture network 536. Features of the
fracture network 536,
such as slurry 538, fluid 540 and bank 542, are depicted in the fracture
network 536.
[0080] Generating a DFN 422 involves extrapolating fracture data from the
hydraulic fracture
network. The DFN may be generated by extrapolation of fracture data. The
fracture data may be
extrapolated from the hydraulic fracture simulation 530. This data may be
exported
automatically to form a production network visualization 532 as schematically
depicted by arrow
16
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
533. Figure 5 shows an example of a data export from the hydraulic fracture
simulation 530 to
the production network visualization 532. The production network visualization
532 provides an
example of the creation of a simulated hydraulic fracture network from
measured fracture data
into an equivalent DFN network. The export may be performed to create a DFN
535 in a format
that can be used by a production model.
[0081] In the example shown in Figure 5, the DFN 535 includes branches 544 and
intersections
(or fracture tips) 546. These fracture branches 544 and intersections 546
extract portions of the
hydraulic fracture simulation 530 that depict fluid flow through the fracture
network 536. The
remainder of the fractures 534 has been eliminated.
[0082] The format of the DFN 535 considers a unique averaged value for each
property at each
fracture branch 544. The fracture branches 544 are defined as the plane that
connects two
intersections 536. These intersections 536 may be a fracture intersection, or
a fracture
intersection and a fracture tip. The properties at each fracture branch 544
may be, for example,
spatial coordinates at an extremity of the branch, the averaged conductivity,
the averaged height,
the averaged reservoir pressure at the branch location, and/or the averaged
reservoir permeability
at the branch location.
[0083] The description of the DFN 535 by the intersections 546 and branches
544 may be used
by the present model to calculate the pressure at the intersections 546. This
description may also
use the branches 544 to both connect the intersections 546 and to calculate
production from
adjacent matrix blocks.
[0084] Referring back to Figure 4, the generating 424 a depth of drainage
through the DFN 535
may be carried out using matrix blocks. As shown in figure 6, the production
network
visualization 532 of Figure 5 has been modified to a production network
visualization 532
depicting a modified DFN 535' with a matrix block 648 in front of each
fracture branch 544 as
shown in Figure 6. Each of the matrix blocks has a depth 650.
[0085] The production network visualization 532' provides an example of the
generation of
matrix depth 650 to be depleted on each side of all branches 544. The modified
DFN 535' may
be used to automatically or manually generate a depth of drainage 650 for each
matrix block 648.
This may be done in such way that the total and actual volume of a given
matrix block (not in
17
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
contact with any reservoir boundaries) may be drained.
[0086] Figure 7 schematically depicts flow of fluid through a matrix block.
This figure illustrates
the definition of equivalent block length, and the calculation of equivalent
block depth. In the
example shown, for a square matrix block 648.1 surrounded by four fracture
branches 544 of
equal length, an assumption may be made that each quarter 752 of the matrix
block 648 can be
depleted by the fracture branch 544 it contacts. A volume 754.1 of the matrix
block 648 that is
depleted and an equivalent block depth 755 to be depleted depicted.
[0087] Assuming a linear flow from the matrix block 648.1 to the fracture
branch 544 (as will be
described in further detail herein), it may also be assumed that this quarter
752 of the matrix
block 648 has the length L of the fracture branch 544. Therefore, the depth of
this "quarter" 752
of the matrix block 648.2 has to be equal to one-fourth of the block length L
(or L/4) for the total
volume to be depleted to be the same. As indicated by the arrow 733, using
linear flow
approximation, an equivalent block depth L/4 for a volume 754.2 of the matrix
block 648.2 to be
depleted may be determined. More complicated block shapes may be used, but may
involve
techniques that are more complex.
[0088] Referring again to Figure 4, the defining 426 one or more production
parameters may be
performed by obtaining user input. The user may define one or more production
parameters for
consideration in the simulation. The user may select such production
parameters based on some
criteria or as desired. Examples of production parameters that may be selected
include bottom
hole pressure (BHP), reservoir fluid viscosity at reservoir conditions,
reservoir fluid
compressibility at reservoir conditions, and duration over which production is
to be simulated,
among others.
[0089] The performing a production operation 428 involves producing fluids
from the
subterranean formation based on the depth of drainage and the at least one
production parameter.
The production operation may be actual or simulated. Actual production
operations involve
producing fluids to the surface as shown in Figure 1.4. Simulated production
may be performed
using production simulations. Visualization of the production results may also
be provided. Such
visualization may allow a user to visualize production decline and cumulated
production, but
also dynamics of pressure fields in the fracture network and the matrix
blocks. Figures 8.1-8.3
provide examples of visualization of the production data in time (e.g., 140
days).
18
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
[0090] Fig. 8.1 is a graph 800.1 depicting production rate 856.1. The graph
800.1 plots
production per day (Mscf/d) (y-axis) versus time t in days (x-axis). Fig. 8.2
is a graph 800.2
depicting cumulated production 856.2. The graph 800.2 depicts cumulated
production P
(MMscf) (y-axis) versus time t (x-axis). Fig. 8.3 is a three dimensional graph
800.3 depicting
reservoir pressure (z-axis) versus distance x (m) (x-axis) and distance y (m)
(y-axis), and
pressure in the fracture network 858 and in the matrix blocks 848. These and
other depictions
may be provided. The production operation may be adjusted based on the
production estimates.
PRODUCTION OPERATIONS
[0091] The production operation (428 and/or 400.2) will be described in three
parts. First,
equations used in the analysis and their analytical solutions are presented.
Second, the effect of
conductivity on the model is provided, together with an example involving a
single fracture
branch for both high and low conductivities. Third, validity of the model and
ways to address
issues, such as conductivity, are provided.
1. ANALYTICAL SOLUTION
[0092] Production rate may be determined using governing equations and
analytical solutions.
The continuity equation for compressible fluid in porous media is applied to
both the matrix and
the fractures. Inside the fracture network, the continuity equation can be re-
written as follows:
(1)
a
(3Qf (xf, t)) = ¨pQmf (xf,
oxf
[0093] Qmf is the flow rate from the matrix to the reservoir, Qf is the flow
rate inside the fracture,
p is the fluid density and xf is the axis along the fracture. It is assumed
that the fracture
permeability (conductivity divided by the width) is so large that the
transient term of the
continuity equation may be neglected over the time scale considered for
production simulation
(from days to years). Darcy flow inside the fracture network may also be
assumed.
a ammo) (2)
pQmf (xf, = ¨ ¨ ¨ HC
2RT dxf oxf
19
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
[0094] Pf is the pressure inside the fracture, C the conductivity, T the
temperature. The function
m is the pseudo pressure. See Al-Hussainy et al., "The Flow of Real Gases
Through Porous
Media", Journal of Petroleum Technology, 1966, pp. 624-36.
(3)
pf P
_______________________ dP
m(Pf) = 2
[0095] Inside the matrix, the continuity equation for a compressible fluid
takes the following
form.
(4)
a ( knym apm) vnict(Pm)p _a pm
ax WPHOZ(Pm) ax ) Z(Pm) m at
[0096] Pm is the pressure inside the matrix, km is the matrix permeability, ct
is the fluid
compressibility, Ix is the viscosity, Z is the volume factor and ym is the
porosity of the matrix. For
simplification, Eq. 4 can be re-written as follows:
a2m _ 1 am (5)
ax,i, ¨ a at
a is defined in Eq. 6.
km (6)
a = ____________
(PmR(Pm)ct(Pm)
[0097] To calculate Qmf, Eq. (5) may be solved, with xm the coordinate along
an axis orthogonal
to the fracture 964 and its coordinate xf. Figure 9 provides an illustration
of the coordinates in the
fracture 964 and matrix block 648.
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
[0098] The solution of Eq. 5 may be found by using a Laplace transform, such
as explained in
Jeannot, Yves. "Thansfert Thermique", Textbook, Ecole des Mines de Nancy,
2009.
http://www.thermique55.com/principal/thermique.pdf; and Bello, R.O., "Rate
Transient Analysis
in Shale Gas Reservoirs with Transient Linear Behavior", PhD Thesis, 2009. A
detailed list of
equations, implementation, algorithm and variables for the presented method
are provided
herein.
[0099] The pressure profile in the matrix may be determined for constant
fracture pressure. The
first assumption of the model is that the gas behavior can be described by the
following real gas
equation:
M P
P = ¨ ( n ) inside the matrix (7)
RT Z(Pm)
M Pf
p = ¨RT (-Z(Pf)) inside the fracture network (8)
[0100] The basis equation for the linear gas flow inside the matrix block is
a ( pm apm) _ 13(pmct(Pm) a pm
(9)
axm WPHOZ(Pm) axm) ¨ Z(Pm)km at
with
1 1 az(pm)
(P )=--= (10)
Pm Z) (Pm apm
[won The following definition of a pseudo pressure will simplify the
resolution previous
equation
Pm p
__________________________ dP (11)
m(Pm) = 2 IPLB 11(P)Z(P)
[0102] Equation (11) then becomes
am21 am,,
_ , (12)
ax ,ii a at
with
km
a = __________________________________________________________________ (13)
(PmR(Pm) ct (Pm)
21
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
In. = In(Pm) ¨ In(Pm_0) = In(Pm) ¨ Inm_o
(14)
and boundary conditions:
ni,,(xõ, = L, t) = mjxn, = ¨L, t) = mf ¨ mm_o
(15)
am,,
(16)
axm
m,, (xõõ to) = 0
(17)
[0103] The Laplace transform of equation (15) gives
4302
(18)
õ20 = 0
axm2 ¨ '1
with
S
(19)
q2 = -a
[0104] For the solution as the form
0 (xm, s) = Acosh(qxm) + Bsinh(qxm)
(20)
the Laplace transform of equation (16) is
ao
(21)
¨ (0, s) = 0
axm
that gives B = 0, so
13(xm, s) = Acosh(qxm)
(22)
[0105] For now it is assumed that the pressure in the fracture network is
almost constant.
mf(xf,t) = mf(xf)
[0106] Therefore, the Laplace transform of equation (15) gives
22
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
9(xm = L, s) = 0(xm = ¨L, s) = mf __ -mm
(23)
S
that gives
mf ¨ nlmo
A= _
(24)
s cosh(qL)
and
mf_mm 0 eqx+e-qx
(25)
13(xm,$) = mf-rnm-o cosh(qxm) = ___ - _______
s cosh(qL) s eqL(1+e-2qx)
[0107] By using a Taylor series development of 1, the following can be
provided:
1+e-2qxm
9(Xm, s) = mf
¨Mm- (e-(L-m) + e-(m)) Enco 0(-1)n e-2nqL
(26)
s
[0108] The inverse Laplace Transform gives
m(Pm) ¨ mm_o =
(27)
(mf ¨ mm_0) 1 ( [(2n + 1)L ¨ xml [(2n + 1)L +
xml)
(-1)n erfc + erf c
2,1a(t ¨ to) 2,1a(t ¨ to)
])
n=0
[0109] Flow rate from the matrix to fracture with constant fracture pressure
may then be
determined. Flow rate from the matrix to the fracture is given by Darcy's law:
MHkm z2 0m(Pm) ,1
(28)
PQmf(xfg t) = --2RT k=1
a-m xm=-Lk,L=Lk
[0110] Lk corresponds to the maximum length of drainage on the side k of the
fracture.
2 \ 2 \
(29)
/ 7(2n+1)L¨xm 7(2n+1)L-Fxm 1 '
am(pm) (mf-mm_0)znoo(1) (_ir e 2 ja(t¨t0) _ e 2 ja(t¨t0) j
Oxm Vna(t-to) -
\ I
23
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
which gives
PQmf(xf, =
(30)
\ 2
( (n+1)Lk
2
MHlim v 1 Ua(t-to,k))
(mf min_o) 2RT 1-\/[a
to,k) n=0
2 \nLk
¨ e \la(t-to,k)/
[0111] Flow inside the fracture branch between intersection i and j may also
be determined. The
flow inside the fracture network is described by the following equation:
a
¨ pQf(xf,t)) = ¨pQmf (xf, t)
(31)
dxf
with Qmf the flow rate (m3/s) from the matrix to the fracture and Qf the flux
(m2/s) from the
fracture. Under the assumption that the gas behavior can be described by the
following real gas
equation, this equation becomes:
a (¨Hc ani(Pf))
(32)
dxf = ¨pQmf(xf,t)
2RT dxf
with the following boundary conditions:
m(Pf(xf = 0)) ¨ mm_o = mf (xf = 0) ¨ mm_o = mf,1 ¨ mm_o =
(33)
m(Pf (xf = Lf)) ¨ mm_o = mf (xf = Lf) ¨ mm_o = mf,j ¨ mm_o =
with Lf the length of the fracture between two intersections. Using the
following:
nif* = nif (Xf) Mini)
(34)
24
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
and introducing equation (30) into equation (32), the following is obtained:
(amf*
(35)
_ y2mf* = 0
dxf dxf
with
\ 2
( nõ ( (n+1)Lk
(36)
2
1 ,la(,k)) \la(,k))
y2 = CV m ___________ /(-1)11 t-to ¨ e t-to
k=1 \i(t ¨ to,k) n=0
[0112] Solution to equation (35) has the form
mf* = AeYxf + Be-Yxf
(37)
and equations (34) gives
mf*je-YLf ¨ mf*J mf*J ¨ mf* jeYLf
(38)
mf(xf) = mm_o +exf + ______________________________________ e-Yxf
e-yLf _ eyLf e-yLf _ eyLf
[0113] Flow rate may also be determined at intersection, for example, i from
branch i,j.
MHCiJ amt.
(39)
= 2RT dxf I r,
- xf=.
[0114] When introducing equation (48) in equation (39)
yMHCij mf*,i(e-YLf+eYLO ¨ 2mf*J
(40)
= _______________
2RT e-yLf _ eyLf
if this is an element from the tubing, the equation becomes
MHCi ¨
(41)
= 2RT Lf
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
[0115] Mass balance may also be determined at an intersection between
fractures
Nij
(42)
= 0
with N_ij the number of branches reaching this intersection.
N
yijHijCijM (mci ¨ mmo jj)(e-YLtij+eYLtij) ¨ 2(mcj ¨ mmom)
(43)
=
2RT¨ e -yLf = = yLf ==
e
J-1 j=1
=0
[0116] This can be rearranged as follows
Nij Nij
Yij Hij Cij (e YLtii )
(44)
Mt'
e-yLtij eyLtijmf,-yL == yL ==
e ¨ e
yijHijCij(e YLtij+eY1-1,ij ¨ 2)
= m
-yLf = =
e ¨ eyLf = =
j=1
[0117] The time function to,k(t) of fluid flow through the matrix block may
also be updated.
Objective function F may be defined as the difference between the real mass
produced so far
from each face of each matrix block, and the mass that would have been
produced if the current
pressure field inside the DFN had been constant and the initial time
considered in the analytical
solution had been constant and equal to to,k(t).
26
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
Fk (t, to,k (0) (45)
t
= f PQtot,ij,k (T, P(T), tO,k(T)) dT
0
t
¨ f PQtot,ij,k (T, P (t), to,k(t)) dT
to,k(t)
or
t Lf
Fk(t, to,k (0) = Mtot,k(t) ¨ f f pQmck (T, Pf (Xf, t), to,k(t)) dTdXf
to,k(t) 0
[0118] Initial time to,k(t) may be calculated by finding the value of to,k(t)
that would give F,,,k(t) =
0. Thus, the total mass produced from face k of the branch is equal to the
mass that would have
been produced so far by the same branch under certain conditions, such as if
the current pressure
condition in the fracture would have been the same and constant from initial
production time
to,k(t), and/or if there would have been no production from this face before
the initial time to,k(t).
[0119] This search for the value of to,k(t) is done with the iterative
algorithm of Newton:
0 li
tall (t) = tg,k(t) F,11(1(tell)'k(t))\ with Fn (t, tg,k(t)) =
F(t,t ril,,k ( 0 ) (46)
Fk'ni _______________ t,tbi,ii (0) K1*(0
[0120] The derivative OFilii(t,tg'k(t)) is calculated using a numerical
gradient
atgo)
where:
a = variable
ct = compressibility (Pa-1)
C =conductivity (m2.m)
Fo,k = objective function (m3)
H = fracture height (m)
km = matrix permeability (m2)
L = maximum length of drainage (m)
27
CA 02843469 2014-01-27
WO 2013/016733
PCT/US2012/048871
m = real gas pseudo pressure (Pals)
m = normalized real gas pseudo pressure (Pals)
mf = real gas pseudo pressure in the fractures (Pals)
mf = normalized real gas pseudo pressure in the fractures (Pals)
mm = real gas pseudo pressure in the matrix(Pals)
mm = normalized real gas pseudo pressure in the matrix(Pals)
mm 0 = initial real gas pseudo pressure in the matrix(Pals)
M = molar mass (kg/mol)
Pm = matrix pressure (Pa)
Pm() = initial matrix pressure (Pa)
Pf = initial fracture pressure (Pa)
PLB = low base pressure (Pa)
Q0( = total flow rate from a matrix block into a fracture (m3/s)
Qmf = local flow rate from a matrix block into a fracture (m2/s)
Qf = flow rate inside the matrix (m3/s)
R = universal gas constant (J/mol/K)
t = time (s)
to* = initial production time (s)
T = Temperature (K)
xf = coordinate in the fracture (m)
xm = coordinate in the matrix (m)
Z = volume factor
Ix = viscosity (Pa.$)
(pm = porosity
p = reservoir fluid density (kg/m3)
y = variable
[0121] With to,k(t) known, the pressure distribution may then be calculated as
follows:
pQmf (xf, t) = (mt. (47)
2
7 ( (n+1)Lk
2 co
MHkm v 1 ,la(t-to,k)/
¨ _________________________________________ m 1(-1)11 e
In) 2 RT- -0/ra Li
k=1 ,\I'(-t ¨ to,k) n=0
\
7 2 \
nLk
¨ e Qa(t¨to,k)/
I
28
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
[0122] This solution being linear in pressure, Eq. 2 may be integrated and
solved.
¨ ¨
(48)
mf(xf) = mm_o + ______________ eYxf + ____________ e-Yxf
e-yLf _ eyLf e-yLf _ eyLf
\2\
(49)
( ____________________________________________ ( (n+1)Lk
2 co
y2 = km v 1
____________________ 1(-1)11 Ua(t-to,k))
¨ e Qa(t-to,k))
C 1-\/[a
k=1 \i(t ¨ to,k) n=0
[0123] Knowing the pressure distribution inside the network, the production
rate can be
calculated with Darcy's law.
[0124] The calculation may be implemented into various fracture networks
without a constraint
on the time step. In some cases, such as where production is done at a
constant BHP and the
conductivity is high, the flow from the matrix may be based on the assumption
that the pressure
inside the fracture stays constant. But in reality, only a fraction of the
fracture branches of the
network may have high conductivities. Examples of calculations are provided in
Cipolla, C. L.,
Lolon, E. P., Mayerhofer, M. J., "Reservoir Modeling and Production Evaluation
in shale-Gas
Reservoirs", SPE paper 13185 presented at the International Petroleum
Technology Conference
held in Doha, Qatar, December 7th 2009.
VALIDITY OF THE ANALYTICAL SOLUTION
[0125] The analytical solution may be validated 427 by analyzing the solution
to determine its
application in a given formation. To study the validity of the analytical
model for different values
of fracture conductivity, the evolution of the pressure and production at a
single fracture branch
of a complex network may be analyzed. This study may consist of two sets of
equally spaced
parallel fractures as shown in Fig. 10. This figure describes a single branch
1070 in a DFN 1072
about a wellbore 1074 that will be analyzed. A matrix block 1048 of the DFN
1072 is depicted as
29
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
having a flow rate 1076 from the matrix block 1048 to the fracture branch
1070.
[0126] For a high conductivity (finite) in the fracture network (e.g., about
2,500 mD.ft (762
mD.m)) in a reservoir of about 0.0001 mD, the BHP is almost instantaneously
diffused inside the
network and from there the variation of pressure inside the DFN can be
neglected, compared to
the pressure differential between the initial reservoir pressure and the BHP.
[0127] Figures 11.1 and 11.2 are three dimensional graphs 1100.1 and 1100.2
depicting reservoir
pressure P (z-axis) versus distance x (m) (x-axis) and distance y (m) (y-axis)
for 1 and 365 days,
respectively. This figure depicts pressure of the DFN and an initial reservoir
pressure 1178 at
two different times of production for a high-conductivity DFN. These and other
depictions may
be provided. The production operation may be adjusted based on the production
estimates.
[0128] As shown in Figure 12, the pressure inside a selected fracture branch
(such as the branch
1070 of Fig. 10) can be considered constant during ten years of production.
This figure depicts a
graph 1200 of pressure (Pm,0 - PO (left y-axis) and initial time T in days
(right y-axis) over time t
in days (e.g., during three years of production) (x-axis) in a case of high
conductivities.
Generated lines for pressure 1280 and time delay 1281 are nearly flat.
[0129] The consequence of this almost constant pressure in the DFN is shown in
Fig. 13 where
the cumulated volume produced (from the matrix block into fracture branch
(e.g., 1048 to 1070
in Fig. 10) converges towards the maximum volume recoverable as defined by
mass balance (or
initial volume of gas in place). Figure 13 is a graph 1300 depicting cumulated
production P (y-
axis) versus time t (x-axis), resulting in a production curve 1384 that
reaches toward a maximum
recoverable volume 1382. This figure depicts cumulated production from a
fracture branch
versus time in case of high-conductivities. Because we are considering
compressible fluids, in
this example, the measure of volume may be done at surface conditions. This
convergence
indicates that the analytical solution verifies mass balance in this case of a
high-conductivity
DFN. The same analysis for a low-conductivity (or finite conductivity) DFN (50
mD.ft (15.24
mD.ft)) may have a different conclusion.
[0130] As shown in Figs. 14.1 and 14.2, the pressure in the DFN may vary
compared to the
pressure range of the problem (e.g., BHP, initial reservoir pressure, etc.)
This figure depicts
pressure inside the DFN at two different times of production for low-
conductivity DFN. Figures
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
14.1 and 14.2 are three dimensional graphs 1400.1 and 1400.2 depicting
reservoir pressure P (z-
axis) versus distance x (x-axis) and distance y (y-axis) for 1 and 365 days,
respectively. This
figure depicts pressure inside the DFN at two different times of production
for a high-
conductivity DFN. An initial reservoir pressure 1478 and a pressure of the DFN
1435 are also
depicted.
[0131] This pressure variation may be seen on the pressure recorded in the
fracture branch
versus time as shown in Figure 15. As shown in Figure 15, where the pressure
inside a selected
fracture branch (such as the branch 1070 of Fig. 10) can be considered
constant during ten years
of production. This figure depicts a graph 1500 of pressure (Pm,0- PO (left y-
axis) and time delay
T in days (right y-axis) over time t in days (e.g., during three years of
production) (x-axis) in a
case of low conductivities (infinite). Generated lines for normalized pressure
1580 and time
delay 1581 are nearly flat. Variation of boundary condition 1584 is also
depicted.
[0132] This variation of the pressure in the DFN means that the assumption of
constant pressure
boundary condition in the analytical solution may require further analysis to
confirm validity.
The consequence is that the calculated flow rate from the matrix may be
underestimated and the
mass balance may be incorrect as illustrated in Fig. 16. Figure 16 is a graph
1600 depicting
cumulated production P (y-axis) versus time t (x-axis), resulting in a
production curve 1684 that
reaches toward a maximum recoverable volume 1682. This figure depicts
cumulated production
from a fracture branch versus time in case of low conductivities. An error
1686 between the
production curve 1684 and the maximum recoverable volume 1682 is also
depicted.
[0133] The low diffusivity in the fracture network may result in a "delay" in
the production of
the block depending on how far (or how connected) it is from the wellbore.
This observation is a
starting point for the method to extend the validity of the analytical
solution to low conductivity
fractures.
EXTENSION OF THE VALIDITY OF THE ANALYTICAL SOLUTION
[0134] The validity of this analytical solution may be extended to modify the
"initial" time to (or
to,k(t)) in such a way that the volume produced so far from the matrix block
is equal to the
volume that would have been produced according to the analytical solution
under current
pressure conditions inside the DFN. By doing this search at every time step
and on each side of
31
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
each fracture branch, the analytical solution is forced to satisfy mass
balance. The search for the
to begins by defining the objective function F to minimize.
t Lf (50)
Fk (t, to,k(t)) = Mtot,k(t) ¨ f f pQmck (T, Pf, (Xf, t), to,k(t)) dTdXf = 0
0 0
M0 t is the volume produced at time t from the matrix block on the side k of
the fracture branch.
It is compared to the integration of the flow rate from the matrix over the
length of the fracture
branch and from the initial time to* to t. The search for to* such that F
equals to zero, the iterative
algorithm of Newton-Raphson as described in Eq. 51 may be used.
t1(t) = tak(t) Ri(t, ticii,k (0 ________________ with Fir
(t,tak(t)) =
) a Fit: (t, tg,k (0) (51)
LO,k
Fkn (t, trolA (0) atg,k(t)
[0135] The derivative of the function Fo* is calculated by a numerical
gradient. If to* meets its
time boundaries the optimization uses the bisection method. This optimization
algorithm is very
efficient because the solution from the previous time step is used as the
initial guess for the next
iteration. From a numerical point of view, the calculation of the approximated
volume requires
integration in time, which is the most CPU intensive part of the simulation.
The optimization
algorithm is applied for each side of each branch with minimal dependencies
between the
variables, making this part of the algorithm a candidate for parallel
computing.
[0136] To illustrate the mechanism behind this approach, the analysis above
may be used on a
single fracture branch of a DFN with low conductivity (or finite conductivity)
(50 mD.ft (15.24
mD.ft)). This pressure variation may be seen on the pressure recorded in the
fracture branch
versus time as shown in Figure 17. As shown in Figure 17, where the pressure
inside a selected
fracture branch (such as the branch 1070 of Fig. 10) can be considered
constant during ten years
of production. This figure depicts a graph 1700 of normalized pressure (Pm,0-
Pf) (left y-axis) and
time delay T in days (right y-axis) over time tin days (e.g., during three
years of production) (x-
axis) in a case of low conductivities. The resulting lines for normalized
pressure 1780 and time
delay 1781 incline.
[0137] Fig. 17 also shows the computed pressure inside the fracture and the
initial time to,k
32
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
updated with the proposed method. The increase of to* with time may be
necessary to sustain the
flow rate from the matrix and the cumulated production as shown in Fig. 18.
Figure 18 is a graph
1800 depicting cumulated production (y-axis) versus time (x-axis), resulting
in a production
curve 1884 that reaches toward a maximum recoverable volume 1882. This figure
depicts
cumulated production from a fracture branch versus time in case of low
conductivities.
[0138] This figure indicates that the method reduces the error on the mass
balance, because the
cumulated production converges close to the maximum recoverable volume in Fig.
18 in
comparison to Fig. 16, thereby indicating that the validity of the method may
extend with the
analytical solution.
[0139] Fig. 19 is a chart 1900 depicting the distribution of pressure P and
the initial time delay T
as calculated by the algorithm on the entire fracture network at different
time steps ti (1 day), t2
(200 days) and t3 (3 years). The chart includes DFNs 1935.1, 1935.2 and 1935.3
for pressure and
DFNs 1935.4, 1935.5 and 1935.6 for time delay at the time steps ti, t2 and t3,
respectively. This
figure shows pressure and initial time (or "delay') in the reservoir at
different times of
production. The "pressure" column shows the pressure inside the reservoir
blocks and the
pressure inside the fracture network. The "initial time" T column shows the
initial time for each
block calculated by the algorithm.
[0140] The analysis above may be performed using an unconventional production
model (UPM).
To illustrate the capabilities of the UPM, simulations have been compared with
those from a
commercial reservoir simulator. The comparison is done with two different
fracture geometries:
a single bi-wing and a "wire-mesh" fracture network.
[0141] In an example involving a single bi-wing fracture, the hydraulic
fracture is a single
symmetrical fracture with a half-length of 1263 ft (384.96 m) and a fracture
height of 98.4 ft
(19.99 m). The permeability of the reservoir is 0.0001 mD with a porosity of
8%, the initial
reservoir pressure is 4000 psi (281.29 kg/cm) and the bottom-hole pressure is
1000 psi (70.32
kg/cm). In this example, the volume factor Z and the gas viscosity were
constant and equal to 1
and 0.02 cP, respectively.
Fig. 20 is a comparison of the simulated cumulated production between the
reservoir simulation
and the UPM, for different fracture conductivities varying between 0.005 and
5000 mD.ft (1524
33
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
mD.m), and for a bi-wing fracture. Fig. 20 shows that the greater the distance
from the
perforations (center of the grid), the smaller the initial time.
[0142] The Figure 20 is a graph 2000 of cumulated production at surface
condition (y-axis)
versus time t (x-axis). This figure depicts a validation by comparison with a
reservoir simulator.
The resulting solid lines 2088.1-2088.7 and resulting dashed lines 2089.1-
2089.7 show
production based on reservoir simulator and the production model,
respectively, at various
locations. This graph 2000 indicates that the greater the distance is from the
perforations, the
longer it takes for the BHP to diffuse up to that location.
[0143] For a wire-mesh fracture network, this case represents a complex
fracture network made
up of 13 identical fractures in each orthogonal direction with a vertical well
in the middle. In this
example, the permeability of the reservoir is about 0.001 mD with a porosity
of about 8%, the
initial reservoir pressure is about 4000 psi (281.29 kg/cm) and the bottom-
hole pressure is 1000
psi (70.32 kg/cm). As also shown in this example, the volume factor Z and the
gas viscosity were
constant and equal to 1 and 0.02 cP, respectively.
[0144] Figures 21.1 and 21.2 provide various visualizations of a DFN performed
by various
simulators. This figure show a reservoir and DFN used in a comparison between
simulations
done with a commercial reservoir simulator and the UPM. Figure 21.1 shows an
example of
DFNs 2135.1 and 2135.2 as depicted by a reservoir simulator, such as
ECLIPSETM. Figure 21.2
shows a DFN 2135.3 generated using the UPM. Each of the DFNs depicted may be
the same
DFN resulting in the different images as shown.
[0145] Figs. 22-24 compare results generated by a reservoir simulator and the
UPM in examples
where conductivities of DFN may vary. Fig. 22 is a comparison of the simulated
cumulated
production between the reservoir simulation and the UPM, for different
fracture conductivities
varying between 0.082 mD.ft (24.99 mD.mm) to about 8200 mD.ft (2499.36 mD.m),
and for a
bi-wing fracture.
[0146] Fig. 22 shows that the greater the distance from the perforations
(center of the grid), the
smaller the initial time. The Figure 22 is a graph 2200 of cumulated
production at surface
condition (y-axis) versus time t (x-axis). This figure depicts a validation by
comparison with a
reservoir simulator. The resulting solid lines 2288.1-2288.6 and resulting
dashed lines 2289.1-
34
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
2289.6 show production based on reservoir simulator and the UPM, respectively,
at various
locations. This graph 2200 indicates that the greater the distance is from the
perforations, the
longer it takes for the BHP to diffuse up to that location.
[0147] As used herein, UPM without "delay" means that the UPM simulator uses
the analytical
part of the model, with a constant initial time equal to 0. When the fracture
conductivity is
increased, the difference between the reservoir simulator and the UPM
simulation without
"delay" may be reduced.
[0148] These comparisons show reasonably good agreement between the two
simulators, in
particular in the case of low conductivity where the algorithm to update the
initial time plays a
major role. To illustrate the importance of the algorithm correcting the
initial time, Figs. 23.1 and
23.2 compare the simulation results for the case of fracture conductivity
equal to 82 mD.ft (24.99
mD.m).
[0149] Fig. 23.1 is a graph 2300.1 depicting flow rate at surface conditions.
Production (y-axis)
is plotted versus time t (x-axis). The resulting lines 2390.1-290.3 depict the
simulation generated
by a reservoir simulator, the UPM and the UPM without delay, respectively.
Figure 23.2 is a
graph 2300.2 depicting current production at surface conditions. Cumulated
production P (y-
axis) is plotted versus time t (x-axis). The resulting lines 2390.4-290.6
depict the simulation
generated by a reservoir simulator, the UPM and the UPM without delay,
respectively. These
figures depict a comparison of the rate (Fig. 23.1) and cumulated production
(Fig. 23.2) between
a commercial reservoir simulator, the UPM and the UPM without "delay".
[0150] It should be noted that in the development of any such actual
embodiment, numerous
implementation¨specific decisions must be made to achieve the developer's
specific goals, such
as compliance with system related and business related constraints, which will
vary from one
implementation to another. Moreover, it will be appreciated that such a
development effort might
be complex and time consuming but would nevertheless be a routine undertaking
for those of
ordinary skill in the art having the benefit of this disclosure. In addition,
the composition
used/disclosed herein can also comprise some components other than those
cited. In the
summary and the detailed description, each numerical value should be read once
as modified by
the term "about" (unless already expressly so modified), and then read again
as not so modified
unless otherwise indicated in context. Also, in the summary and the detailed
description, it
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
should be understood that a concentration range listed or described as being
useful, suitable, or
the like, is intended that any and every concentration within the range,
including the end points,
is to be considered as having been stated. For example, "a range of from 1 to
10" is to be read as
indicating each and every possible number along the continuum between about 1
and about 10.
Thus, even if specific data points within the range, or even no data points
within the range, are
explicitly identified or refer to only a few specific, it is to be understood
that inventors appreciate
and understand that any and all data points within the range are to be
considered to have been
specified, and that inventors possessed knowledge of the entire range and all
points within the
range.
[0151] The statements made herein merely provide information related to the
present disclosure
and may not constitute prior art, and may describe some embodiments
illustrating the disclosed
subject matter. All references cited herein are incorporated by reference into
the current
application in the entirety.
[0152] The preceding description has been presented with reference to some
embodiments.
Persons skilled in the art and technology to which this disclosure pertains
will appreciate that
alterations and changes in the described structures and methods of operation
can be practiced
without meaningfully departing from the principle, and scope of this
application. Accordingly,
the foregoing description should not be read as pertaining only to the precise
structures described
and shown in the accompanying drawings, but rather should be read as
consistent with and as
support for the following claims, which are to have their fullest and fairest
scope.
[0153] Although only a few example embodiments have been described in detail
above, those
skilled in the art will readily appreciate that many modifications are
possible in the example
embodiments without materially departing from the system and method for
performing wellbore
stimulation operations. Accordingly, all such modifications are intended to be
included within
the scope of this disclosure as defined in the following claims. In the
claims, means-plus-
function clauses are intended to cover the structures described herein as
performing the recited
function and not only structural equivalents, but also equivalent structures.
Thus, although a nail
and a screw may not be structural equivalents in that a nail employs a
cylindrical surface to
secure wooden parts together, whereas a screw employs a helical surface, in
the environment of
fastening wooden parts, a nail and a screw may be equivalent structures. It is
the express
36
CA 02843469 2014-01-27
WO 2013/016733 PCT/US2012/048871
intention of the applicant not to invoke 35 U.S.C. 112, paragraph 6 for any
limitations of any of
the claims herein, except for those in which the claim expressly uses the
words 'means for'
together with an associated function.
37
