Note: Descriptions are shown in the official language in which they were submitted.
CA 02858319 2015-12-17
SYSTEM AND METHOD FOR SIMULATION OF GAS DESORPTION IN A
RESERVOIR USING A MULTI-POROSITY APPROACH
Background
Reservoir simulation is an area of reservoir engineering that employs computer
models to predict the transport of fluids, such as petroleum, water, and gas,
within a
reservoir. Reservoir simulators are used by petroleum producers in determining
how best
to develop new fields, as well as in generating production forecasts on which
investment
decisions are based in connection with developed fields.
Fractured reservoirs present special challenges for simulation because of the
multiple porosity systems or structures that may be present in these types of
reservoirs.
Fractured reservoirs are traditionally modeled by representing the porous
media using two
co-exiting pore systems or structures interconnected by flow networks, in what
is referred
to as dual porosity analysis. One type of pore system used in the prior art is
the rock
matrix, defined with matrix nodes, is characterized by high pore volume and
low
conductivity. The other type of pore system used in the prior art are induced
fractures, and
defined with fracture nodes, is characterized by low pore volume and high
conductivity.
These prior art reservoir simulation methods and systems typically treat
absorbed gas
within the reservoir as residing in the rock matrix pores of the reservoir.
For example, in
one simulated representation, referred to as dual-porosity, single-
permeability ("DPSP"),
matrix simulation nodes communicate only with fracture simulation nodes, and
the analysis
focuses on mass transfer and fluid flow of hydrocarbons between matrix nodes
and fracture
nodes. In DPSP, fracture nodes can also communicate with other fractures,
which
communicate with both matrix simulation nodes as well as other fracture
simulation nodes.
In another simulated representation, referred to as dual-porosity, dual-
permeability
("DPDP"), matrix simulation nodes communicate with both fracture simulation
nodes and
as well as other matrix simulation nodes, and the analysis focuses on mass
transfer and
fluid flow of hydrocarbons between matrix nodes and fracture nodes as well as
between
matrix nodes and other matrix nodes.
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Those of ordinary skilled in the art will appreciate that "nodes" as used
herein refer
to an elemental representation of pore structures within a simulated
reservoir, while
"zones" refer to a collection nodes within the simulated reservoir. Unknowns
such as
pressures and composition are solved for, typically on a node by node basis,
at desired time
and/or depth increments.
One particular type of reservoir encountered in oil and gas reservoir
simulation is a
shale reservoir. Shale reservoirs typically include large pores or vugs. Vugs
are pore
spaces that are comparatively larger than pore spaces of the rock matrix.
Kerogen resides
in this system of vugs within the porous rock matrix.
Vugs may or may not be connected to one another. "Separate vugs" are vugs that
are interconnected only through the interparticle porosity, i.e., the rock
matrix porosity, and
are not interconnected to one another (as are matrix pore volumes and fracture
pore
volumes). "Touching vugs" are vugs that are interconnected to one another.
Because of
their separate physical and mechanical characteristics, the fluid retention
and transport
.. properties of vug pore systems are different from those of both the matrix
and fracture
systems, and have not heretofore been adequately addressed with analysis
utilizing only
matrix porosity systems and induced porosity systems. In other words, because
of the
geologic complexities of shale reservoirs, traditional dual porosity reservoir
modeling
techniques do not adequately predict mass transfer and fluid flow
characteristics of shale
reservoirs.
Brief Description of the Drawings
A more complete understanding of the present disclosure and advantages thereof
may be acquired by referring to the following description taken in conjunction
with the
accompanying figures, wherein:
Fig. 1 illustrates an example of a reservoir simulation model comprising
multiple
wells.
Fig. 2 illustrates a representation of an example formation comprising a
complex
network of artificially-induced fractures.
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Fig. 3 illustrates a simulation grid of a formation comprising a highly
deviated
wellbore surrounded by natural fractures and a complex network of artificially-
induced
fractures.
Fig. 4 illustrates steps in an exemplary process utilized to model flow
characteristics of a reservoir.
Detailed Description
To overcome the above-noted and other limitations of the current approaches,
one
or more embodiments described herein comprise a reservoir simulator including
a unique
manner of handling gas desorption in shale gas reservoir simulations by
rigorously
simulating the flow mechanism that occurs therein.
It has been found that the mechanism for desorption of gas in a shale gas
reservoir
is based on the existence of four separate porosity systems, each of which is
incorporated
in the method and system of the invention. In the method and system of the
invention,
each of these four porosity systems is separately characterized and
incorporated into the
model. The four porosity systems are the matrix porosity system, the induced
fracture
porosity systems, the natural fracture porosity system and the vug porosity
system. As
explained above, heretofore, only the matrix porosity system and the induced
fracture
porosity systems have been used in reservoir modeling in the past. The method
and system
of the invention incorporate natural fracture porosity systems and vug
porosity systems.
The innermost of these porosity systems is the kerogen vugs, which contain the
gas
saturation as wetting fluid. The other porosity systems, which are the rock
matrix, the
induced fracture network and the natural fracture network, function as
conduits for the gas
contained in the kerogen of the shale. Rather than residing in pores
throughout the porous
rock matrix, the adsorbed gas is generally found only in the kerogen vugs.
Natural
fractures exist near the vugs, which natural fractures may or may not be open.
The
framework rock matrix of the porous medium connects the complex natural
fractures to the
hydraulic induced fractures near the well. The only accurate way to treat this
system in
accordance with the flow characteristics thereof, and in particular to account
for the vugs
throughout the matrix, requires a multiple porosity simulation system in which
the vuggy
portions of the formation containing the kerogen are connected to the rock
matrix and the
natural fracture system. The matrix and natural fractures are connected to the
induced
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fractures near the wellbore, which fractures will in turn have different
properties than the
natural fractures due to the presence of fracking fluid and perhaps proppant,
and hence one
reason why natural fractures pore systems and induced fracture pore systems
are
characterized and separately analyzed in the method and system of the
invention.
The equations provided hereinbelow are transfer functions derived from field
observations and laboratory measurements of the desorption process from the
kerogen
vugs, matrix and fractures of a reservoir. The transfer functions are then
utilized by the
simulation system to simulate the complex fracture system for the shale as
reservoir
coupled with the kerogen desorption. In one embodiment of the invention, vuggy
porosity
is used to model the kerogen desorption from within a complex fracture system
comprised
of both induced and natural fractures.
Fig. 1 is a block diagram of an exemplary computer system 100 adapted for
implementing a reservoir simulation system as described herein. In one
embodiment, the
computer system 100 includes at least one processor 102, storage 104, I/O
devices 106, and
a display 108 interconnected via a system bus 109. Software instructions
executable by the
processor 102 for implementing a reservoir simulation system 110 in accordance
with the
embodiments described herein, may be stored in storage 104. Although not
explicitly
shown in Fig. 1, it will be recognized that the computer system 100 may be
connected to
one or more public and/or private networks via appropriate network
connections. It will
also be recognized that the software instructions comprising the reservoir
simulation
system 110 may be loaded into storage 104 from a CD-ROM or other appropriate
storage
media.
In one embodiment, a portion of the reservoir simulation system 110 is
implemented using reservoir simulation software. In this embodiment, a
"subgrid" data
type is used to offer a generalized formulation design. In one embodiment,
this data type
may be Fortran. The subgrid defines the grid domain and interconnectivity
properties of
the nodes of the various porosity structures. It also tracks various node
variables, such as
pressure, composition, fluid saturation, etc. Subgrids are designated as being
of a
particular porosity type, e.g., natural fracture, matrix, induced fracture and
vug. The nodes
that constitute these grids are correspondingly referred to as natural
fracture nodes, matrix
nodes, induced fracture nodes and vug nodes. Subgrids of different porosity
types
occupying the same physical space are said to be "associated". Connections
between
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porosity types, and in particular, the nodes of the porosity types, are
represented as external
connections, subgrid to associated subgrids. Internal (or intragrid)
connections, and in
particular, the nodes of a subgrid, represent flow connections within a
porosity type.
The modeling of a shale gas reservoir generally involves defining one or more
elongated, highly deviated production wellbore, typically thousands of feet in
length, with
multiple hydraulic fracture zones disposed substantially perpendicular to the
wellbore,
depending on the stress field in the formation. For certain formations, the
stress field is
such that a complex fracture system is induced between the large fractures
emanating from
the well. One representation of such fractures for an example formation is
presented in
Fig. 2 and designated by a reference numeral 200. The representation 200 has
been
derived from a finite element model of the porous media of the formation
following high
pressure injection of fracture fluid and proppant. Heavier lines, such as
those designated
by reference numeral 202, represent fractures induced by hydraulic fracturing,
as described
above, and which have been modeled in the prior art, i.e., induced fracture
porosity
systems. Narrower lines and triangular features, such as those designated by
reference
numerals 204 and 206, respectively, represent a possible finite volume grid
with which to
model the flow of fluid (primarily gas and water) in the complex fracture
network and
eventually to a horizontal production wellbore via the induced fracture, as
illustrated in
Fig. 3. Specifically, Fig. 3 illustrates a simulation grid 300 for an
elongated, substantially
horizontal wellbore 302, surrounded by induced fractures 304 and a complex
natural
fracture network 306.
It has been found that there are two features of the physics in reservoir
simulation
that are required to properly model shale gas flow to a wellbore in a
reservoir: non-Darcy
flow and gas desorption. In the method and system of the invention, these two
features are
considered when modeling mass transfer and fluid flow between the matrix
nodes, natural
fracture nodes, induced fracture nodes and vug nodes.
Non-Darcy flow is fluid flow that deviates from Darcy's assumption that fluid
flow
in the formation will be laminar. Non-Darcy flow is typically observed in high-
velocity
gas flow induced pressure differentials between the formation and the
wellbore.
Specifically, when the flow at the wellbore reaches velocities in excess of
the Reynolds
number for Darcy (or laminar) flow, turbulent flow results and non-Darcy
analysis must be
utilized. The effect of non-Darcy flow is a rate-dependent skin effect. That
is, as the
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velocity within the wellbore increases, there is an increase in the pressure
drop between the
wellbore and the fracture.
Thus, the typical equation for flow in the reservoir is modified to account
for the
effects of non-Darcy flow using the Forchheimer parameter 13 as shown in
equation (1)
below:
a
(1) /3 '14 ) q + Op( ¨q )2
öx KkrA A
Where:
P=pressure
ap
¨= pressure drop in a direction x
ax
= viscosity
K = permeability
kr = relative permeability
A = cross sectional area to flow
= Forchheimcr parameter
p = density
q = flow rate
For high velocity flow occurring in the fractures and near the wellbore, non-
Darcy
flow results in a significant increase in the pressure drop and therefore
plays an important
role in properly modeling shale gas production. Because prior art techniques
did not tend
to model natural fracture pore systems, to the extent non-Darcy flow analysis
has been
used in the past for reservoir modeling, it has only been utilized to model
flow in matrix
pore systems and induced fracture systems.
Unfortunately, inclusion of the effect of equation (1) in reservoir fluid flow
represents significantly more effort than was required for the skin factor.
Since velocity
depends not only on pressure drop but also on viscosity and relative
permeability, a highly
non-linear dependence is added to the flow equations for gridblock-to-
gridblock or
fracture-to-fracture non-Darcy flow treatment. The skin factor only requires a
minor
modification to the coefficient for the pressure loss between the wellbore and
the reservoir
or fractures. Inclusion of the non-Darcy effect adds a significant non-linear
term to the
pressure equations and requires that this term be included in the
linearization for the
Newton-Raphson iteration to solve for the flow in the wellbore and reservoir.
In turn, this
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may increase the number of non-linear iterations and therefore increase
overall
computation time for the reservoir simulation.
Gas desorption for shale development is an important, heretofore underutilized
parameter in shale formation modeling. It is estimated that in some shale
formations, more
than 50% of the gas production will be due to desorption. To the extent gas
desorption has
been modeled in shale reservoirs, its use has been limited to desorption from
the shale
matrix. It has not heretofore been applied to desorption analysis from kerogen
vugs.
Because economics are highly dependent on ultimate recovery from the
formation, gas
desorption must be treated for a shale gas reservoir simulation system to have
any
credibility. Moreover, it must be applied in a way that accounts for the
existence of
kerogen vugs within the reservoir. Desorption is described by the Langmuir
equation
(equation (2) below) for isothermal desorption characteristics:
P
(2) v = V L=
g PL+13
Where:
Vg = volume of gas contained in the porous medium
VL = asymptotic adsorption volume
PL = pressure at which the adsorbed volume reaches VL
P ¨ reservoir pressure
Use of equation (2) in the simulator results in a modification similar to that
for dual
porosity, single permeability ("DPSP"), in which a source of gas, i.e., vug
nodes, are
included in each grid, the volume of which depends on the change in matrix
pressure over
a timestep in the simulator.
For more rigorous treatment of the physics, consideration of sorption time and
desorption effects on formation permeability may also be necessary. Sorption
time is the
time it takes for 63.2% of the gas to be desorbed as calculated using equation
(2). In the
case of shale gas, this time is generally extremely short and can be ignored.
Similarly, the
effect of desorption on matrix permeability is generally very small for shale
gas and can
also be easily ignored.
In practice, when pressure is lowered in the horizontal production wellbore
302
(Fig. 3), the pressure is almost instantaneously lowered in all of the
fracture system
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(including both induced fracture and natural fractures) to which the wellbore
is connected.
For those fractures connected directly to a kerogen vug, the pressure is also
reduced from
the initial pressure. From equation (2) above, the kerogen must release gas
into the
surrounding reservoir fractures and matrix based on the Langmuir equation.
Although the
Vi. and PL parameters can be experimentally determined, often these are
estimated by
analogy and rules of thumb. Flow through the multiple fractures and matrix
represents a
significant difference with conventional treatment in which only the matrix
contains the
adsorbed gas which is directly in contact with fractures. The more complex
treatment
using vugs should allow a more realistic simulation of desorption than is
currently
achieved since the complex geometry of the porous medium is correctly
characterized.
With reference to Figure 4, a flowchart is shown illustrating the steps of the
process
of the invention. The process is utilized to model flow characteristics to a
wellbore of a
shale reservoir having kerogen vugs and is preferably performed in conjunction
with a
three dimensional model of a reservoir. In step 400, reservoir
characterization is undertake
in which at least three, and preferably four different pore types are
described based on
fractured shale characteristics. In one embodiment, at least three different
pore types are
identified, selected from the group consisting of natural fracture pore
systems, matrix pore
systems, induced fracture pore systems and vug pore systems. In one
embodiment, four
different pore types are identified, namely natural fracture pore systems,
matrix pore
systems, induced fracture pore systems and vug pore systems. In any event, in
step 402,
the pore types are utilized to create one or more subgrids that represent a
zone within the
reservoir. Each zone includes a plurality of nodes of at least one of the pore
types. In one
embodiment, a subgrid for at least three different pore types is created for a
zone. In one
embodiment, a subgrid for each of the four pore types is created for a zone.
In step 404, once the shale reservoir has been described sufficiently,
connectivities
or transfer terms, if any, between the nodes are identified and assigned. This
may include
connectivity between similar nodes within the same subgrid, such as between
matrix nodes
within a subgrid, or may include connectivity between the nodes of one subgrid
and the
nodes of another associated subgrid, such as between vug nodes and natural
fracture nodes
or between matrix nodes and vug nodes. These transfer terms are the parameters
that effect
flow rates among the various porosity types, such as, for example, initial
pore pressures,
fluid distributions and volumes. These transfer terms are preferably assigned
on a nodal
basis to the nodes of the subgrids. In one embodiment, the model consists of
at least three
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different pore types and associated volumes which contain fluids which are to
be modeled. In
one embodiment, the model consists of at least four different pore types and
associated
volumes which contain fluids which are to be modeled.
In step 406, know magnitudes for the transfer terms may be assigned, such as,
for
example, densities, volumes, flow rates and compressibilitics.
In step 408, source terms are now incorporated as boundary conditions to the
model in
such a way that extraction of the gas is consistent with the wellbore's
induced fractures. Put
another way, to initiate flow in the simulation, a wellbore pressure is
selected and
incorporated into the model. This pressure affects the flow in the induced
fractures, which, in
turn by virtue of the transfer terms, affects flow between the other porosity
types.
In step 410, a linear solver is utilized to solve for any unknown magnitudes
of the
transfer terms associated with the nodes. In one embodiment, non-linear
equations are
selected to model the reservoir and the subgrids and nodes thereof. In one
embodiment, the
linear solver methodology is applied by subgrid or associated subgrids. The
Newton-
Raphson method is then applied to linearize these non-linear equations. The
linear solver then
can be applied to the linear equations to solve for the unknowns. In one
embodiment, this
step may be iterated utilizing the resultant magnitudes until a desired degree
of convergence
is achieved between the linear and non-linear equations.
In step 412, optionally, once a desired degree of convergence is obtained and
the
magnitudes of the unknowns are identified, time may be incremented and/or the
wellbore
parameters, such as the boundary conditions of pressure, may be altered to
achieve a desired
level of mass transfer and fluid flow for the modeled reservoir.
The foregoing methods and systems described herein are particularly useful in
drilling
wellbores in shale reservoirs. First a shale reservoir is modeled as described
herein to design
a well completion plan for a well. In an embodiment, the drilling well
completion plan
includes the selection of a fracturing plan, which may include the selection
of fracture zones
and their positioning, fracturing fluids, proppants and fracturing pressures.
In other
embodiments, the drilling well completion plan may include selecting a
particular trajectory
of the wellbore or selecting a desired wellbore pressure to facilitate mass
transfer and fluid
flow to the wellbore. Based on the model, a drilling plan may be implemented
and a
wellbore drilled in accordance with the plan. Thereafter, in one
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embodiment, fracturing may be carried out in accordance with the model to
enhance flow
from the reservoir to the wellbore. In another embodiment, wellbore pressure
may be
adjusted in accordance with the model to achieve a desired degree of mass
transfer and
fluid flow. Those of ordinary skilled in the art will appreciate that while
the method of the
invention has been described statically as part of implementation of a
drilling plan, the
method can also be implemented dynamically. Thus, a drilling plan may be
implemented
and data from the drilling process, and in particular, the actual flow
characteristics of the
reservoir, may be used to update the model for the drilling of additional
wellbores within
the reservoir. After implementing the drilling plan, the system of the
invention may be
utilized during the drilling process on the fly or iteratively to calculate
and re-calculate
connectivity characteristics of the reservoir over a period of time as
parameters change or
are clarified or adjusted. In either case, the results of the dynamic
calculations may be
utilized to alter a previously implemented drilling plan. For example, the
dynamic
calculations may result in the utilization of heavier or lighter fracturing
fluids.
While certain features and embodiments of the invention have been described in
detail herein, it will be readily understood that the invention encompasses
all modifications
and enhancements within the scope of the following claims. Furthermore, no
limitations
are intended in the details of construction or design herein shown, other than
as described
in the claims below. Moreover, those skilled in the art will appreciate that
description of
various components as being oriented vertically or horizontally are not
intended as
limitations, but are provided for the convenience of describing the invention.
It is therefore evident that the particular illustrative embodiments disclosed
above
may be altered or modified and all such variations are considered within the
scope of the
present invention. Also, the terms in the claims have their plain, ordinary
meaning unless
otherwise explicitly and clearly defined by the patentee.
