U.S. patent application number 16/336814 was filed with the patent office on 2020-01-16 for system and method for modeling a transient fluid level of a well.
The applicant listed for this patent is Halliburton Energy Services, Inc.. Invention is credited to Avi LIN, Srinath MADASU, Yijie SHEN.
Application Number | 20200018153 16/336814 |
Document ID | / |
Family ID | 62110319 |
Filed Date | 2020-01-16 |
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United States Patent
Application |
20200018153 |
Kind Code |
A1 |
MADASU; Srinath ; et
al. |
January 16, 2020 |
SYSTEM AND METHOD FOR MODELING A TRANSIENT FLUID LEVEL OF A
WELL
Abstract
The disclosed embodiments include a method for determining fluid
level drop and formation permeability during wellbore stimulation
of a shut-in stage in real time. The method includes receiving an
initial permeability value of a formation surrounding a wellbore.
Further, the method includes performing, and if necessary repeating
at a defined time interval, the following steps until a flowrate of
stimulation fluid reaches zero or until a new pumping stage begins.
The steps include solving for the flowrate of the stimulation fluid
in the wellbore and computing hydrostatic pressure and a computed
temperature in the wellbore. Further, the steps include updating a
permeability calculation of the formation based on the flowrate of
the stimulation fluid.
Inventors: |
MADASU; Srinath; (Houston,
TX) ; LIN; Avi; (Houston, TX) ; SHEN;
Yijie; (Houston, TX) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Halliburton Energy Services, Inc. |
Houston |
TX |
US |
|
|
Family ID: |
62110319 |
Appl. No.: |
16/336814 |
Filed: |
November 9, 2016 |
PCT Filed: |
November 9, 2016 |
PCT NO: |
PCT/US2016/061154 |
371 Date: |
March 26, 2019 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
E21B 49/087 20130101;
E21B 47/07 20200501; C09K 8/60 20130101; E21B 47/103 20200501; E21B
43/26 20130101 |
International
Class: |
E21B 47/10 20060101
E21B047/10; E21B 47/06 20060101 E21B047/06; E21B 49/08 20060101
E21B049/08; E21B 43/26 20060101 E21B043/26 |
Claims
1. A method for determining fluid level drop and formation
permeability during wellbore stimulation of a shut-in stage in real
time, comprising: receiving an initial permeability value of a
formation surrounding a wellbore; and performing, and if necessary
repeating at a defined time interval, the following steps until a
flowrate of stimulation fluid reaches zero or until a new pumping
stage begins: solving for the flowrate of the stimulation fluid in
the wellbore; computing hydrostatic pressure and a computed
temperature in the wellbore; and updating a permeability
calculation of the formation based on the flowrate of the
stimulation fluid.
2. The method of claim 1, comprising: receiving a measured
temperature from a distributed temperature sensing (DTS) system;
and updating the flowrate based on a comparison of the computed
temperature and the measured temperature when an accuracy of the
flowrate is not acceptable.
3. The method of claim 2, wherein updating the flowrate when the
accuracy of the flowrate is not acceptable comprises: determining
whether the computed temperature is greater than the measured
temperature; when the computed temperature is greater than the
measured temperature, doubling the flowrate; and when the computed
temperature is less than the measured temperature, dividing the
flowrate by 1.75.
4. The method of claim 2, comprising: determining whether the
accuracy of the flowrate is acceptable, wherein determining whether
the accuracy of the flowrate is acceptable comprises: determining
whether a difference between the computed temperature and the
measured temperature exceeds a tolerance value.
5. The method of claim 1, comprising: computing a fluid level drop
within the wellbore based on the flowrate; and updating stimulation
fluid presence in divisions of the wellbore based on the fluid
level drop.
6. The method of claim 1, wherein the permeability calculation of
the formation is determined based on Darcy's law.
7. The method of claim 1, wherein solving for the flowrate of the
stimulation fluid in the wellbore comprises: calculating an
individual flow rate of each division of the wellbore; and adding
together the individual flow rates of each division of the
wellbore.
8. The method of claim 1, wherein the initial permeability value of
the formation is based on logs produced from core samples of the
formation.
9. The method of claim 1, wherein the stimulation fluid comprises
fracturing fluid or acidizing fluid.
10. The method of claim 1, wherein the defined time steps comprise
one second increments of time.
11. A system for determining formation permeability during wellbore
stimulation, comprising: a distributed temperature sensing (DTS)
system comprising a fiber optic cable extending a length of a
wellbore, wherein the DTS system is configured to provide a
real-time measurement of a measured temperature of the wellbore; a
controller communicatively coupled to the DTS system, the
controller comprising a processor and a memory, wherein the memory
comprises instructions, that when executed, cause the processor to:
receive an initial permeability value of a formation surrounding
the wellbore; and perform, and if necessary repeat at a defined
time interval, the following instructions until a flowrate of
stimulation fluid reaches zero or until a new pumping stage begins:
solve for the flowrate of the stimulation fluid in the wellbore;
compute hydrostatic pressure and computed temperature in the
wellbore; compare the computed temperature to the measured
temperature to determine accuracy of the flowrate; update the
flowrate when the accuracy of the flowrate is not acceptable; and
update a permeability calculation of the formation based on the
flowrate of the stimulation fluid.
12. The system of claim 11, wherein the stimulation fluid comprises
acidizing fluid or fracturing fluid.
13. The system of claim 11, wherein the initial permeability value
of the formation is based on logs produced from core samples of the
formation.
14. The system of claim 11, wherein determining the accuracy of the
flowrate comprises: determining whether a difference between the
computed temperature and the measured temperature exceeds a
tolerance value.
15. The system of claim 11, wherein the instructions that cause the
processor to solve for the flowrate of the stimulation fluid in the
wellbore comprise instructions that cause the processor to:
calculate an individual flow rate of each division of the wellbore;
and add together the individual flow rates of each division of the
wellbore.
16. The system of claim 11, wherein the instructions that cause the
processor to update the flowrate when the accuracy of the flowrate
is not acceptable comprise instructions that cause the processor
to: determine whether the computed temperature is greater than the
measured temperature; when the computed temperature is greater than
the measured temperature, double the flowrate; and when the
computed temperature is less than the measured temperature, divide
the flowrate by 1.75.
17. A non-transitory machine-readable medium comprising
instructions stored therein, which when executed by one or more
processors, causes the one or more processors to perform operations
comprising: receiving an initial permeability value of a formation
surrounding a wellbore; and performing, and if necessary repeating
at a defined time interval, the following operations until a
flowrate of stimulation fluid reaches zero or until a new pumping
stage begins: solving for the flowrate of the stimulation fluid in
the wellbore; computing hydrostatic pressure and computed
temperature in the wellbore; receiving a measured temperature of
the wellbore; comparing the computed temperature to the measured
temperature to determine accuracy of the flowrate; updating the
flowrate when the accuracy of the flowrate is not acceptable; and
updating a permeability calculation of the formation based on the
flowrate of the stimulation fluid.
18. The medium of claim 17, wherein receiving the measured
temperature of the wellbore comprises receiving the measured
temperature in real-time from a distributed temperature sensing
(DTS) system.
19. The medium of claim 17, wherein updating the flowrate when the
accuracy of the flowrate is not acceptable comprises: determining
whether the computed temperature is greater than the measured
temperature; when the computed temperature is greater than the
measured temperature, doubling the flowrate; and when the computed
temperature is less than the measured temperature, dividing the
flowrate by 1.75.
20. The medium of claim 17, comprising recording the permeability
calculation in a memory at each time step.
Description
BACKGROUND
[0001] The present disclosure relates generally to formation
characteristic measurements of formations surrounding a wellbore,
and, more specifically, to systems and methods for modeling
dynamics of flow distribution along a simulated wellbore during a
shut-in process.
[0002] During a shut-in stage of a stimulation process (e.g.,
fracturing or acidizing a formation), no fluids are inserted into
the wellbore at the top of the wellhead. Accordingly, fluid flow
within the wellbore is driven by a difference between wellbore
pressure and reservoir pressure. Because pressure in the wellbore
is often greater than or less than the reservoir pressure, a level
of the fluids within the wellbore during the shut-in stage
dynamically changes based on wellbore and reservoir conditions.
While the level of fluids within the wellbore during the shut-in
stage changes dynamically, traditional measurements of fluid level
within the wellbore only provide static measurement opportunities.
That is, the traditional measurements of the fluid level may only
be available during the shut-in stage after an equilibrium is
reached between the wellbore and reservoir pressures. Such
measurements do not consider time varying fluid level drop.
Additionally, the traditional measurements do not overcome a
no-flow assumption to the reservoir pressure and fluid level
computation. For example, the traditional measurements fail to
account for leakage flow of stimulation fluids from the wellbore to
the reservoir, which results in dynamic decreases in pressure and
fluid level within the wellbore.
BRIEF DESCRIPTION OF THE DRAWINGS
[0003] Illustrative embodiments of the present disclosure are
described in detail below with reference to the attached drawing
figures, which are incorporated by reference herein, and
wherein:
[0004] FIG. 1A is a schematic illustration of a side view of a well
fracturing environment;
[0005] FIG. 1B is a schematic illustration of a side view of a well
acidizing environment;
[0006] FIG. 2 is a schematic illustration of a wellbore during a
shut-in stage including an indication of a flow of stimulation
fluid from the wellbore to a formation;
[0007] FIG. 3 is a schematic illustration of a wellbore during the
shut-in stage at equilibrium and the wellbore during a subsequent
pumping stage;
[0008] FIG. 4 is a flow chart of a method for iteratively
calculating well conditions during a shut-in stage of a well;
[0009] FIG. 5 is a graph of bottom-hole pressure of a wellbore over
time during a shut-in stage and a pumping stage of a well;
[0010] FIG. 6 is a graph of bottom-hole temperature of a wellbore
over time during a shut-in stage and a pumping stage of a well;
and
[0011] FIG. 7 is a flow chart of a method for updating calculations
of permeability of a formation during a shut-in stage of a
well.
[0012] The illustrated figures are only exemplary and are not
intended to assert or imply any limitation with regard to the
environment, architecture, design, or process in which different
embodiments may be implemented.
DETAILED DESCRIPTION
[0013] In the following detailed description of the illustrative
embodiments, reference is made to the accompanying drawings that
form a part hereof. These embodiments are described in sufficient
detail to enable those skilled in the art to practice the
invention, and it is understood that other embodiments may be
utilized and that logical structural, mechanical, electrical, and
chemical changes may be made without departing from the spirit or
scope of the invention. To avoid detail not necessary to enable
those skilled in the art to practice the embodiments described
herein, the description may omit certain information known to those
skilled in the art. The following detailed description is,
therefore, not to be taken in a limiting sense, and the scope of
the illustrative embodiments is defined only by the appended
claims.
[0014] As used herein, the singular forms "a", "an" and "the" are
intended to include the plural forms as well, unless the context
clearly indicates otherwise. It will be further understood that the
terms "comprise" and/or "comprising," when used in this
specification and/or the claims, specify the presence of stated
features, steps, operations, elements, and/or components, but do
not preclude the presence or addition of one or more other
features, steps, operations, elements, components, and/or groups
thereof. In addition, the steps and components described in the
above embodiments and figures are merely illustrative and do not
imply that any particular step or component is a requirement of a
claimed embodiment.
[0015] Unless otherwise specified, any use of any form of the terms
"connect," "engage," "couple," "attach," or any other term
describing an interaction between elements is not meant to limit
the interaction to direct interaction between the elements and may
also include indirect interaction between the elements described.
In the following discussion and in the claims, the terms
"including" and "comprising" are used in an open-ended fashion, and
thus should be interpreted to mean "including, but not limited to".
Unless otherwise indicated, as used throughout this document, "or"
does not require mutual exclusivity.
[0016] The present disclosure relates to measuring formation
characteristics of a formation surrounding a wellbore. More
particularly, the present disclosure relates to systems and methods
for dynamically measuring conditions of a formation surrounding a
wellbore during a shut-in stage of a stimulation process. The
presently disclosed embodiments may be applicable to horizontal,
vertical, deviated, or otherwise nonlinear wellbores in any type of
subterranean formation. Embodiments may be implemented in the
shut-in stage of stimulation processes, such as an acidizing
process or a fracturing process. Further, the embodiments may be
implemented using a distributed temperature sensing (DTS) system to
provide real-time temperature feedback from within the wellbore to
a model that models the formation characteristics.
[0017] Referring to FIG. 1A, a schematic illustration of a side
view of a well fracturing environment 100 including a well 102. In
the embodiment of FIG. 1, a rig 104 is positioned at a surface 106
of the well 102. The well 102 includes a wellbore 108 that extends
from the surface 106 to a subterranean formation 110. A derrick 112
is positioned above the well 102, and the derrick 112 may be used
during formation of the well 102 to support boring equipment and to
hoist and lower pipe into the wellbore 108, among other tasks. Also
depicted is a wellhead 113, which may be used during a shut-in
process to seal the wellbore 108.
[0018] Fractures 114 are illustrated within the formation 110. In
an embodiment, the fractures 114 are produced in the formation by
pumping fracturing fluid into the wellbore 108 at a high pressure
using a pump 116 and a fracturing fluid tank 118. The pump 116
provides the fracturing fluid from the fracturing fluid tank 118 to
the wellbore 108 at a pressure greater than a fracturing pressure
of the formation 110. That is, the fracturing fluid is provided to
the wellbore 108 at a pressure greater than a pressure that results
in the formation 110 fracturing hydraulically. For example, the
fracturing pressure of the formation 110 may be in the range of
6500 to 10,000 psi.
[0019] In an embodiment, the well fracturing environment 100 also
includes a controller 120 that includes a memory 122 and at least
one processor 124. The controller 120 may be used to dynamically
model characteristics of the formation 110, such as porosity and
permeability. The memory 122 may store instructions related to the
dynamic model of the controller 120, and the memory 122 may also
store data used by the controller 120 to dynamically model the
characteristics of the formation 110. In an embodiment, the
processor 124 executes the instructions of the memory to perform
the dynamic modeling. The instructions stored in the memory 122 and
executed by the processor 124 may include, but are not limited to,
machine code instructions, bytecode for a software interpreter,
object code, and source code in a high-level programming language.
The controller 120 may also receive inputs from input devices, such
as a keyboard, a mouse, and a touchscreen, and the controller 120
may also output information to an output device, such as a
monitor.
[0020] In various embodiments, the at least one processor 124 may
be a single-processor system or a multi-processor system including
two or more processors 124 (e.g., two, four, eight, or another
suitable number). The processor 124 may be any processor capable of
executing program instructions. For example, in various
embodiments, the processor 124 may be a general-purpose processor
or an embedded processor implementing any of a variety of
instruction set architectures. Further, the memory 122 may store
program instructions, data, or a combination thereof that are
accessible by the processor 124. In an embodiment, the memory 122
may be implemented using any suitable memory technology, such as
static random access memory (SRAM), nonvolatile memory, or any
other type of memory. In other embodiments, program instructions,
data, or both may be received, sent, or stored in different types
of computer-accessible media or on similar media separate from the
memory 122 or the controller 120.
[0021] A computer-accessible medium may include any tangible or
non-transitory storage media or memory media such as electronic,
magnetic, or optical media coupled to the controller 120. The terms
"tangible" and "non-transitory," as used herein, are intended to
describe a computer-readable storage medium excluding propagating
electromagnetic signals, but the terms are not intended to
otherwise limit the type of physical computer-readable storage
device that is encompassed by the phrase computer-readable medium
or memory. For instance, the terms "non-transitory
computer-readable medium" or "tangible memory" are intended to
encompass types of storage devices that do not necessarily store
information permanently, including, for example, random access
memory (RAM). Program instructions and data stored on a tangible
computer-accessible storage medium in non-transitory form may
further be transmitted by transmission media or signals such as
electrical, electromagnetic, or digital signals, which may be
conveyed via a communication medium such as a network or wireless
link.
[0022] To enhance accuracy of the dynamic model of the formation
characteristics calculated by the controller 120, a distributed
temperature sensing (DTS) system may be provided at the well 102,
and the DTS system includes an optical cable 126 that is coupled to
the controller 120 and extends the length of the wellbore 108. The
optical cable 126 and the DTS system may provide real-time
temperature measurements along the length of the wellbore 108 to
the controller 120. For example, as temperature within the wellbore
108 changes, the temperature change can affect transmission of
light through the optical cable 126. Accordingly, temperature
measurements may be determined at any point along the optical cable
126 by detecting changes in the transmission of light through the
optical cable 126 resulting from the change in temperature. By
providing real-time temperature measurements to the controller 120,
an accuracy of the dynamic model may be checked and compensated for
appropriately, as discussed in detail below with reference to FIG.
7.
[0023] FIG. 1B is a schematic illustration of a side view of a well
acidizing environment 130 within the wellbore 108. The well
acidizing environment 130 is similar to the well fracturing
environment 100 except that the stimulation element is a lower
pressure acidizing fluid, as opposed to the high pressure
fracturing fluid that is provided to the wellbore 108 with
reference to FIG. 1A. The pump 116 pumps acidizing fluid into the
wellbore 108 from an acidizing fluid tank 132.
[0024] In an embodiment, acidizing fluid is used in a formation
stimulation process when a formation 134 has a greater permeability
than the formation 110, which is better suited for a fracturing
process. Using the acidizing fluid, wormholes 136 are produced in
the formation 134 instead of the fractures 114 produced using a
fracturing process. The wormholes 136 result from the acidizing
fluid interacting with the formation 134 to dissolve formation
materials to produce new passageways or to expand existing
passageways for formation fluids to flow. In some embodiments, the
acidizing fluid may include a hydrochloric acid (HCl) base that
dissolves carbonate based materials within the formation 134. In
other embodiments, such as in sandstone formations, hydrofluoric
acid (HF) may be used in combination with HCl as the base of the
acidizing fluid. Additionally, in some embodiments, the acidizing
fluid is provided at a pressure greater than the fracturing
pressure of the formation 134. In such an embodiment, the acidizing
fluid may produce both the fractures 114 and the wormholes 136
within the formation 134.
[0025] FIG. 2 is a schematic illustration of the wellbore 108
during a shut-in stage including an indication of a flow of
stimulation fluid (e.g., fracturing fluid or acidizing fluid) from
the wellbore 108 to the formation 110/134. During the shut-in
stage, pumping of the stimulation fluid at the wellhead 113 ceases,
and a fluid level 202 is established at the onset of the shut-in
stage. Because the stimulation fluid is no longer provided to the
wellbore 108, flow of the stimulation fluids is established by a
difference between hydrostatic pressure within the wellbore 108 and
reservoir pressure of the formation 110/134. As illustrated, the
reservoir pressure of the formation 110/134 is less than the
hydrostatic pressure within the wellbore 108. Accordingly, the
stimulation fluid within the wellbore 108 travels in a direction
204 in the wellbore 108 to establish a new fluid level 206. The new
fluid level 206 is the result of leak-off 208 of the stimulation
fluid in the wellbore 108 to the formation 110/134. In another
embodiment, the reservoir pressure may be greater than the
hydrostatic pressure within the wellbore 108. In such an
embodiment, the reservoir fluids may travel from the formation into
the wellbore 108, which results in the fluid level 202 moving
toward the wellhead 113.
[0026] Because the flow of fluids from or to the wellbore 108 is
transient, the model used to determine characteristics of the
formation may be dynamically altered as the shut-in stage
progresses. Using the model, a pressure, fluid velocity, and
temperature variation along the stimulated wellbore 108 predicts
flow loss or gain of fluid to the formation 110/134. The effects of
the flow of the fluids within the wellbore 108 and temperature
distributions along the wellbore 108 during the shut-in stage
enable an accurate design and analysis of the well production
systems of a reservoir to effectively compute fluid flow or fluid
and proppant flow during production of formation fluids from the
well 102.
[0027] During the shut-in stage, the fluid level 202 within the
wellbore 208 continuously drops or increases to a point where the
hydrostatic pressure of the fluid within the wellbore 208 and the
temperature within the wellbore 208 equilibrate with the reservoir
pressure and temperature of the formation 110/134. The increase or
decrease in the hydrostatic pressure of the fluid within the
wellbore 208 is due to an increase or decrease in the fluid level
202 during the equilibration process. To help illustrate, a net
flow rate in the wellbore 108 is given by the following
equation:
q . w = i = 1 ndivisions q i , ( Equation 1 ) ##EQU00001##
where {dot over (q)}.sub.w is the net flow rate of the wellbore
108, ndivisions is a number of divisions within the wellbore 108,
and q.sub.i is an individual flow rate at a division of the
wellbore 108. The individual divisions (e.g., grid blocks) may be
evenly spaced sections of the wellbore 108. For example, each
division may represent the average conditions of one foot of length
of the wellbore 108 at a specific location within the wellbore 108.
The size and number of divisions within a simulated wellbore may
vary. For example, each division could be larger or smaller than
one foot depending on a desired accuracy of the net flow rate in
the wellbore 108. The individual flow rate in each division is
given by Darcy's Law, but Darcy's law is applied over the entire
reservoir (e.g., formation 110/134) and includes measurements of
the different fluids found within the reservoir. Accordingly, the
following equation provides a volumetric flow rate for any number
of fluids combining the Darcy flow with a hydrostatic pressure
variation:
q . i = 2 .pi. ( .rho. i g ( X i - L S ) - P reservoir ) j = 1
nfronts ln ( r endj r frontj ) k j .mu. j , ( Equation 2 )
##EQU00002##
where {dot over (q)}.sub.i is the individual flow rate at a
division i, .rho..sub.i is a density of the fluid within the
wellbore 108 at the division i, g is the gravitational constant,
X.sub.i is a change in liquid level at the division i, L.sub.s is a
liquid level within the wellbore 108, P.sub.reservoir is the
reservoir pressure, nfronts is a number of fluid fronts within the
wellbore 108 where the fluid fronts are interfaces between fluids,
r.sub.endj is a radius of the wellbore 108 at a deepest point of an
individual fluid front, r.sub.frontj is a radius of the wellbore
108 at a shallowest point of the individual fluid front, k.sub.j is
a permeability of the formation 110/134 at the individual fluid
front, and .mu..sub.j is a viscosity of the fluid at the individual
fluid front. The gravitational constant g, the reservoir pressure
P.sub.reservoir, and the initial permeability k.sub.j are known
values. Further, density .rho..sub.i and viscosity .mu..sub.j are
determined from equations 9 and 10, respectively, which are
provided below. Furthermore, the number of fluid fronts nfronts are
estimated.
[0028] Further, assuming small increments in time, the liquid level
within the wellbore 108 with respect to time, L.sub.s(t), is
provided by the following equation:
L S = i = 1 ndivisions q . i .pi. r w 2 .DELTA. t , ( Equation 3 )
##EQU00003##
where r.sub.w is a radius of the wellbore 108. Using equation 3, an
accurate model of the liquid level within the wellbore 108 at any
time step during the shut-in stage is available. A change in the
liquid level at each time step also provides an indication of the
fluid flow rate to or from the formation 110/134.
[0029] Referring to FIG. 3, a schematic illustration of a wellbore
108A during the shut-in stage at equilibrium and a wellbore 108B
during a subsequent pumping stage is depicted. The wellbores 108A
and 108B include divisions 302A-302E (e.g., grid elements). The
divisions 302A-302E represent equal portions of the wellbore 108.
Calculations related to the individual divisions 302A-302E may
represent each of the divisions 302A-302E as a whole. For example,
when the divisions 302A-302E each represent one foot of the
wellbore 108, individual calculations related to the divisions
302A-302E represent the characteristics of each of the divisions
302A-302E as a sampling point along the length of the wellbore
108.
[0030] As illustrated, the wellbore 108A includes divisions
302A-302C filled with air, while divisions 302D and 302E contain
fluid. Because the wellbore 108A is at equilibrium with the
formation 110/134, the fluid level 202 moved away from the wellhead
113 due to the leakoff 208 of the stimulating fluid into the
formation 110/134. In an embodiment, the leakoff 208 results from
the hydrostatic pressure of the wellbore 108 being greater than the
reservoir pressure of the formation 110/134. As the fluid level 202
moves away from the wellhead 113, the divisions 302A-302C fill with
air.
[0031] At block 304, the wellbore 108 moves to a subsequent pumping
stage. As shown in the wellbore 108B, new stimulating fluid is
pumped into the wellbore 108B from the wellhead 113 to fill the air
space in divisions 302A-302C with the new stimulating fluid. The
wellbore 108B may then enter an additional shut-in stage, and
characteristics of the wellbore 108B may be measured as the
stimulating fluid in the wellbore 108B moves again to equilibrium.
Characteristics of the fluid within the wellbore 108 may also be
tracked. For example, fluid temperature in the wellbore 108 is
constantly changing until the fluid temperature attains equilibrium
with a temperature of the surrounding formation 110/134. Assuming a
steady state and incompressible fluid, the temperature of the
divisions 302A-302E in the wellbore 108 is provided by the
following equation:
T well = T earth + Ag sin .theta. + ( ( T fbh - T earth ) - Ag sin
.theta. ) exp ( L bh - .eta. ) A , ( Equation 4 ) ##EQU00004##
where T.sub.well is the temperature in the wellbore 108,
T.sub.earth is the temperature of the surrounding formation
110/134, g is gravity, .theta. is an angle of the well with respect
to the horizontal axis, T.sub.fbh is a bottom-hole temperature of
the wellbore 108, L.sub.bh is a length of the wellbore 108, .eta.
is a distance of a division from the wellhead 113, and A is
calculated from the following equation:
1 A = + 2 R well 1 R well .rho. C P v [ 1 r tot U tot + f ( t ) k
earth ] - 1 , ( Equation 5 ) ##EQU00005##
where R.sub.well is the resistance of the wellbore 108, .rho. is
the density of the fluid within the wellbore 108, C.sub.p is a
specific heat of the fluid, v is a velocity of the fluid flow,
r.sub.tot is a radius of the wellbore 108, U.sub.tot is the overall
heat transfer coefficient, k.sub.earth is the thermal conductivity
of the formation 110/134, and f(t) is a transient heat conduction
time function. As the velocity of the fluid flow goes to zero, the
temperature in the wellbore 108 approaches the reservoir
temperature of the formation 110/134. Further, .eta.(t) is
represented by the following equation:
f ( t ) = 1.1281 t Dw ( 1 - 0.3 t Dw ) when t Dw .ltoreq. 1.5 (
Equation 6 ) or f ( t ) = [ 0.4063 + 0.5 ln ( t Dw ) ] ( 1 + 0.6 t
Dw ) when t Dw > 1.5 , ( Equation 7 ) ##EQU00006##
where t.sub.Dw is the thermal diffusion coefficient. Additionally,
t.sub.Dw is provided by the following equation:
t Dw = at r w 2 , ( Equation 8 ) ##EQU00007##
where r.sub.w is the radius of the wellbore 108, t is an amount of
time for injection of the fluids into the wellbore, and a is the
thermal diffusivity of the earth. Moreover, the density and the
viscosity of the fluid within the wellbore 108 is a function of
fluid temperature within the wellbore 108, as indicated by the
following equations:
.rho..sub.i=f(T.sub.well) (Equation 9),
.mu..sub.i=f(T.sub.well) (Equation 10),
where f(T.sub.well) for the density and the viscosity are separate
correlations based on experiments that vary from fluid to
fluid.
[0032] In an embodiment, equations 1-9, or any combination thereof,
are iterated at defined time increments. For example, equations 1-9
may be calculated every second, five seconds, ten seconds, twenty
seconds, or more during the shut-in stage to determine various well
characteristics. Iterating equations 1-9 may continue until an
equilibrium condition is reached. In an embodiment, the equilibrium
condition is indicated by
(.rho..sub.ig(X.sub.i-L.sub.S)-P.sub.reservoir) of equation 2, as
calculated at each division of the wellbore 108, being less than or
equal to a tolerance condition. Once the equilibrium condition is
reached, an equilibrium fluid level of the wellbore 108 is given by
equation 3 at the time that the equilibrium condition is
reached.
[0033] To help illustrate, FIG. 4 is a flow chart of a method 400
for iteratively calculating well conditions during a shut-in stage.
Initially, at block 402, a time count is advanced. If the method
400 is initially starting, the time count may be advanced from 0 to
1. Additionally, the time count may be advanced by 1 for all
subsequent actions at block 402.
[0034] At block 404, the flowrate in the reservoir (e.g., the
formation 110/134) is calculated. In an embodiment, the flowrate is
calculated using equation 1, provided above, which is a summation
of the flowrates from the individual divisions of the wellbore 108
that include fluid at the specific time step. Additionally, the
flowrates from the individual divisions of the wellbore 108 are
calculated using equation 2. As the time steps progress, certain
divisions may no longer include fluid as the stimulating fluid
flows out of the wellbore 108 into the formation 110/134 when the
reservoir pressure is less than the hydrostatic pressure of the
wellbore 108. Accordingly, the divisions without fluid do not
contribute to the flowrate in the reservoir of equation 1.
[0035] Using the calculated flowrate, the fluid level drop is
computed at block 406. In an embodiment, the fluid level drop is
calculated using equation 3, which provides the equation to
calculate the liquid level within the wellbore. Accordingly, the
fluid level drop for the individual time step may be calculated by
subtracting the liquid level value of the current time step from
the liquid level value of the previous time step.
[0036] Subsequently, at block 408, grid elements (e.g., divisions)
are updated with appropriate fluid amounts. For example, based on
the liquid level within the wellbore 108 calculated at block 406,
the controller 120 may determine that one or more divisions 302 no
longer include the stimulation fluid and are instead filled with
air. The reduction in fluid within the wellbore 108 may have an
impact on the hydrostatic pressure within the wellbore 108, and the
reduction in fluid within the wellbore 108 may also have an impact
on the overall flow rate provided by equation 1.
[0037] Accordingly, at block 410, the hydrostatic pressure and
temperature within the wellbore 108 are calculated. By way of
example, the hydrostatic pressure may be calculated based on a
function of gravity, density, and a depth of the hydrostatic
pressure measurement. Additionally, the temperature within the
wellbore 108 is calculated using equation 4. As the liquid level
within the wellbore 108 decreases, the hydrostatic pressure within
the wellbore 108 also decreases until the hydrostatic pressure
equilibrates with the reservoir pressure of the formation 110/134.
Similarly, the temperature within the wellbore 108 also increases
or decreases until the temperature reaches an equilibrium with the
reservoir temperature. An increase or decrease in the temperature
within the wellbore 108 may also result in subtle increases or
decreases in hydrostatic pressure within the wellbore 108 as the
temperature of the stimulating fluid and gases within the wellbore
108 increase or decrease. Subsequently at block 412, a next time
step is reached and the time count is advanced at block 402. When
the time count is advanced at block 402, the method 400 repeats the
calculations for the next time step.
[0038] With the information gathered at each time step during the
method 400, the porosity and permeability of the formation 110/134
is calculated. The porosity and permeability of the formation
110/134 may be calculated using Darcy's law to calculate the
permeability and a known correlation between porosity and
permeability to calculate the porosity. With the porosity and
permeability of the formation 110/134, a more accurate prediction
of production from the well 102 is available.
[0039] FIG. 5 is a graph 500 of a bottom-hole pressure of the
wellbore 108 over time during a shut-in stage and a pumping stage
of the well 102. A line 502 represents the bottom-hole pressure of
the wellbore 108 over the course of the pumping stage, the shut-in
stage, and the beginning of a subsequent pumping stage. An abscissa
504 provides an indication of time, and an ordinate 506 provides an
indication of the bottom-hole pressure of the wellbore 108 in
pounds per square inch (psi). Point 508 represents initialization
of the bottom-hole pressure measurement. At point 510, which occurs
just after point 508, a pumping stage begins. During the pumping
stage, stimulating fluid, such as acidizing fluid or fracturing
fluid, is pumped into the wellbore 108 from the wellhead 113. As
shown in the graph 500, the bottom-hole pressure of the wellbore
108 increases from point 510 to point 512.
[0040] Subsequently, at point 512, the shut-in stage begins. During
the shut-in stage, the stimulating fluid is no longer pumped into
the wellbore 108 at the wellhead 113. Accordingly, the bottom-hole
pressure rapidly declines once the shut-in stage begins.
Additionally, as the shut-in stage approaches point 514, the rapid
decline of the bottom-hole pressure begins to level off as a
difference in reservoir pressure of the formation 110/134 and the
hydrostatic pressure of the wellbore 108 decreases. The
equalization of the reservoir pressure and the hydrostatic pressure
is a result of the stimulation fluid leak off into the formation
110/134. When the stimulation fluid leaks off, the fluid level
within the wellbore 108 decreases, and the bottom-hole pressure, as
shown in the graph 500, decreases until equalization with the
reservoir pressure is achieved.
[0041] In an embodiment, at point 514, a new pumping stage begins.
The new pumping stage includes pumping additional stimulation fluid
into the wellbore 108 to occupy empty space within the wellbore 108
resulting from fluid leak off into the formation 110/134. As shown,
the bottom-hole pressure of the wellbore 108 during the new pumping
stage increases rapidly as stimulation fluid is pumped into the
wellbore 108 from the wellhead 113. Once a desired pressure is
reached, such as a fracturing pressure, a new shut-in stage may
begin (not shown), and the process may repeat itself. This process
may be repeated until indications of permeability and porosity
within the formation 110/134 is sufficient for reservoir fluid
production. Further, as the shut-in stages occur, the controller
120 may use equations 1-9 to calculate the permeability and the
porosity of the formation 110/134 and estimate production
parameters of the well 102.
[0042] FIG. 6 is a graph 600 of a bottom-hole temperature of the
wellbore 108 over time during a shut-in stage and a pumping stage
of the well 102. A line 602 represents the bottom-hole temperature
of the wellbore 108 over the course of the shut-in stage and the
beginning of the pumping stage. An abscissa 604 provides an
indication of time, and an ordinate 606 provides an indication of
the bottom-hole temperature of the wellbore 108 in degrees
Fahrenheit. As in FIG. 5, point 508 also represents initialization
of the bottom-hole temperature measurement. At point 510, which
occurs just after point 508, a pumping stage begins. During the
pumping stage, stimulating fluid, such as acidizing fluid or
fracturing fluid, is pumped into the wellbore 108 from the wellhead
113. As shown in the graph 600, the bottom-hole temperature of the
wellbore 108 decreases from point 510 to point 512 as the
stimulating fluid is pumped into the wellbore 108 from the wellhead
113. In the illustrated embodiment, the decrease in temperature is
a result of the stimulating fluid having an initial temperature
that is less than a temperature of the formation 110/134
surrounding the wellbore 108.
[0043] Subsequently, at point 512, the shut-in stage begins. During
the shut-in stage, the stimulating fluid is no longer pumped into
the wellbore 108 at the wellhead 113. Accordingly, the bottom-hole
temperature increases as the stimulation temperature equilibrates
with the reservoir temperature during the shut-in stage. As the
shut-in stage approaches point 514, the increase in the bottom-hole
temperature begins to level off as a difference in the reservoir
temperature of the formation 110/134 and the temperature of the
fluid within the wellbore 108 decreases. The equalization of the
reservoir temperature and the fluid temperature within the wellbore
108 is a result of the stimulation fluid leak off into the
formation 110/134 and a surface area of the fluid within the
wellbore 108 that is in contact with the formation 110/134
decreasing. When the stimulation fluid leaks off, the fluid level
within the wellbore 108 decreases, and the bottom-hole temperature,
as shown in the graph 500, increases until equalization with the
reservoir temperature is achieved. In another embodiment, the
reservoir temperature is less than the stimulation fluid
temperature. In such an embodiment, the equilibration of the
bottom-hole temperature results in a decrease in the bottom-hole
temperature of the wellbore 108 during the shut-in stage.
[0044] At point 514, a new pumping stage begins. The new pumping
stage includes pumping additional stimulation fluid into the
wellbore 108 to occupy empty space within the wellbore 108
resulting from fluid leak off into the formation 110/134. As shown,
the bottom-hole temperature of the wellbore 108 during the new
pumping stage decreases rapidly as stimulation fluid is pumped into
the wellbore 108 from the wellhead 113. As discussed above with
reference to FIG. 5, once a desired bottom-hole pressure is
reached, such as a fracturing pressure, a new shut-in stage may
begin (e.g., as indicated by a rise in temperature), and the
process may repeat itself. This process may be repeated until
indications of permeability and porosity within the formation
110/134 are sufficient for production. Further, as the shut-in
stages occur, the controller 120 may use equations 1-9 to calculate
the permeability and the porosity of the formation 110/134 and
estimate production parameters of the well 102.
[0045] FIG. 7 is a flow chart of a method 700 for updating
calculations of permeability of the formation 110/134 during a
shut-in stage. Initially, at block 702, a permeability value of the
formation 110/134 is initialized. In an embodiment, the initial
permeability value of the formation 110/134 may be determined based
on logs of the formation 110/134 that are generated during core
sampling processes.
[0046] After the permeability value is initialized, a flowrate in
the reservoir (e.g., the formation 110/134) is calculated at block
704. In an embodiment, the flowrate is calculated using equation 1,
provided above, which is a summation of the flowrates from the
individual divisions of the wellbore 108 that include stimulation
fluid at a specific time step during which the method occurs.
Additionally, the flowrates from the individual divisions of the
wellbore 108 are calculated using equation 2. As the method 700
iterates, certain divisions of the wellbore 108 may no longer
include fluid as the stimulating fluid flows out of the wellbore
108 into the formation 110/134 when the reservoir pressure is less
than the hydrostatic pressure of the wellbore 108. Accordingly, the
divisions without fluid do not contribute to the flowrate in the
reservoir of equation 1.
[0047] Using the calculated flowrate, the fluid level drop is
computed at block 706. In an embodiment, the fluid level drop is
calculated using equation 3, which provides the equation to
calculate the liquid level within the wellbore 108. Accordingly,
the fluid level drop for an iteration of the method 700 may be
calculated by subtracting the liquid level value of the current
iteration from the liquid level value of the previous
iteration.
[0048] Subsequently, at block 708, grid elements (e.g., divisions)
are updated with appropriate fluid amounts. For example, based on
the liquid level within the wellbore calculated at block 706, the
controller 120 may determine that one or more divisions 302 no
longer include the stimulation fluid and are instead filled with
air. The reduction in fluid within the wellbore 108 may have an
impact on the hydrostatic pressure within the wellbore 108.
[0049] At block 710, the hydrostatic pressure and temperature
within the wellbore 108 are calculated. As mentioned above, the
hydrostatic temperature is measured based on a function of the
gravity, the density, and the bottom-hole depth. The temperature
within the wellbore 108 is calculated using equation 4. As the
liquid level within the wellbore 108 decreases, the hydrostatic
pressure within the wellbore 108 also decreases until the
hydrostatic pressure equilibrates with the reservoir pressure of
the formation 110/134. Similarly, during the shut-in stage, the
temperature within the wellbore 108 increases or decreases until
the temperature reaches an equilibrium with the reservoir
temperature. An increase or decrease in the temperature within the
wellbore 108 may also result in subtle increases or decreases in
hydrostatic pressure within the wellbore 108 as the temperature of
the stimulating fluid within the wellbore 108 increases or
decreases.
[0050] At block 712, a difference is determined between the
computed temperature within the wellbore 108 and a distributed
temperature sensing (DTS) system temperature measurement received
from block 714. The DTS system temperature measurement provides
real-time temperature sensing within the wellbore 108 to the
controller 120. The controller 120 uses the DTS system temperature
measurements to improve an accuracy of the model provided by the
flow rate and temperature models (e.g., equations 1 and 4) when the
DTS system is available. At block 712, the controller 120, for
example, compares a difference between the computed temperature
provided by equation 4 and the measured temperature from the DTS
system to a tolerance value. By way of example, the tolerance value
may be 1 degree Fahrenheit, 1 degree Celsius, or any other value
that is determined to be sufficiently accurate. By way of example,
the tolerance value may be established based on the DTS system
measurement resolution. In an embodiment with a 1 degree Celsius
tolerance value, the DTS temperature resolution may be between
approximately 0.5 and 1 degree Celsius.
[0051] If the difference between the computed temperature and the
DTS system measured temperature is greater than the tolerance
value, then a determination is made as to whether the computed
temperature is greater than the DTS system measured temperature at
block 716. If the computed temperature is not greater than the DTS
system measured temperature, then a new flow rate is established at
block 718. In an embodiment, the new flow rate is equal to the
previous flow rate, as calculated at block 704 or as calculated in
a previous iteration, divided by 1.75. The divider of 1.75 is used
as an example, but it may be appreciated that a larger or smaller
divider is also contemplated. For example, the divider may be as
low as 1.25 or as high as 2 to efficiently determine a more
accurate flow rate.
[0052] Further, if the computed temperature is greater than the DTS
system measured temperature, then a new flow rate is establish at
block 720. In an embodiment, the new flow rate is equal to the
previous flow rate, as calculated at block 704 or as calculated in
a previous iteration, multiplied by two. The multiplier of two is
used as an example, but it may be appreciated that a larger or
smaller multiplier is also contemplated. For example, the
multiplier may be as low as 1.25 or as high as 3 to efficiently
determine a more accurate flow rate.
[0053] After the new flow rate is established in either blocks 718
or 720, a new fluid level drop is calculated, at block 706, based
on the new flow rate. A loop including blocks 706-720 may iterate
until the difference between the computed temperature and the DTS
system measured temperature is within an acceptable tolerance value
at block 712. Once confirmation is established that the difference
is within the acceptable tolerance value, the new flow rate is
accepted at block 722. Using the accepted flow rate, the
permeability of the formation 110/134 is updated at block 724 using
Darcy's law. It may be appreciated that the method 700 may be
iterated during the shut-in stage such that the permeability of the
formation 110/134 is monitored at near real-time. The permeability
at each iteration of the method 700 may be stored in the memory 122
of the controller 120 for use in determining production
capabilities of the well 102.
[0054] The above-disclosed embodiments have been presented for
purposes of illustration and to enable one of ordinary skill in the
art to practice the disclosure, but the disclosure is not intended
to be exhaustive or limited to the forms disclosed. Many
insubstantial modifications and variations will be apparent to
those of ordinary skill in the art without departing from the scope
and spirit of the disclosure. For instance, although the flowcharts
depict a serial process, some of the steps/processes may be
performed in parallel or out of sequence, or combined into a single
step/process. The scope of the claims is intended to broadly cover
the disclosed embodiments and any such modification. Further, the
following clauses represent additional embodiments of the
disclosure and should be considered within the scope of the
disclosure:
[0055] Clause 1, a method for determining fluid level drop and
formation permeability during wellbore stimulation of a shut-in
stage in real time, comprising: receiving an initial permeability
value of a formation surrounding a wellbore; and performing, and if
necessary repeating at a defined time interval, the following steps
until a flowrate of stimulation fluid reaches zero or until a new
pumping stage begins: solving for the flowrate of the stimulation
fluid in the wellbore;
[0056] computing hydrostatic pressure and a computed temperature in
the wellbore; and updating a permeability calculation of the
formation based on the flowrate of the stimulation fluid.
[0057] Clause 2, the method of clause 1, comprising: receiving a
measured temperature from a distributed temperature sensing (DTS)
system; and updating the flowrate based on a comparison of the
computed temperature and the measured temperature when an accuracy
of the flowrate is not acceptable.
[0058] Clause 3, the method of clause 2, wherein updating the
flowrate when the accuracy of the flowrate is not acceptable
comprises: determining whether the computed temperature is greater
than the measured temperature; when the computed temperature is
greater than the measured temperature, doubling the flowrate; and
when the computed temperature is less than the measured
temperature, dividing the flowrate by 1.75.
[0059] Clause 4, the method of at least one of clauses 2-3,
comprising: determining whether the accuracy of the flowrate is
acceptable, wherein determining whether the accuracy of the
flowrate is acceptable comprises: determining whether a difference
between the computed temperature and the measured temperature
exceeds a tolerance value.
[0060] Clause 5, the method of at least one of clauses 1-4,
comprising: computing a fluid level drop within the wellbore based
on the flowrate; and updating stimulation fluid presence in
divisions of the wellbore based on the fluid level drop.
[0061] Clause 6, the method of at least one of clauses 1-5, wherein
the permeability calculation of the formation is determined based
on Darcy's law.
[0062] Clause 7, the method of at least one of clauses 1-6, wherein
solving for the flowrate of the stimulation fluid in the wellbore
comprises: calculating an individual flow rate of each division of
the wellbore; and adding together the individual flow rates of each
division of the wellbore.
[0063] Clause 8, the method of at least one of clauses 1-7, wherein
the initial permeability value of the formation is based on logs
produced from core samples of the formation.
[0064] Clause 9, the method of at least one of clauses 1-8, wherein
the stimulation fluid comprises fracturing fluid or acidizing
fluid.
[0065] Clause 10, the method of at least one of clauses 1-9,
wherein the defined time steps comprise one second increments of
time.
[0066] Clause 11, a system for determining formation permeability
during wellbore stimulation, comprising: a distributed temperature
sensing (DTS) system comprising a fiber optic cable extending a
length of a wellbore, wherein the DTS system is configured to
provide a real-time measurement of a measured temperature of the
wellbore; a controller communicatively coupled to the DTS system,
the controller comprising a processor and a memory, wherein the
memory comprises instructions, that when executed, cause the
processor to: receive an initial permeability value of a formation
surrounding the wellbore; and perform, and if necessary repeat at a
defined time interval, the following instructions until a flowrate
of stimulation fluid reaches zero or until a new pumping stage
begins: solve for the flowrate of the stimulation fluid in the
wellbore; compute hydrostatic pressure and computed temperature in
the wellbore; compare the computed temperature to the measured
temperature to determine accuracy of the flowrate; update the
flowrate when the accuracy of the flowrate is not acceptable; and
update a permeability calculation of the formation based on the
flowrate of the stimulation fluid.
[0067] Clause 12, the system of clause 11, wherein the stimulation
fluid comprises acidizing fluid or fracturing fluid.
[0068] Clause 13, the system of clause 11 or 12, wherein the
initial permeability value of the formation is based on logs
produced from core samples of the formation.
[0069] Clause 14, the system of at least one of clauses 11-13,
wherein determining the accuracy of the flowrate comprises:
determining whether a difference between the computed temperature
and the measured temperature exceeds a tolerance value.
[0070] Clause 15, the system of at least one of clauses 11-14,
wherein the instructions that cause the processor to solve for the
flowrate of the stimulation fluid in the wellbore comprise
instructions that cause the processor to: calculate an individual
flow rate of each division of the wellbore; and add together the
individual flow rates of each division of the wellbore.
[0071] Clause 16, the system of at least one of clauses 11-15,
wherein the instructions that cause the processor to update the
flowrate when the accuracy of the flowrate is not acceptable
comprise instructions that cause the processor to: determine
whether the computed temperature is greater than the measured
temperature; when the computed temperature is greater than the
measured temperature, double the flowrate; and when the computed
temperature is less than the measured temperature, divide the
flowrate by 1.75.
[0072] Clause 17, a non-transitory machine-readable medium
comprising instructions stored therein, which when executed by one
or more processors, causes the one or more processors to perform
operations comprising: receiving an initial permeability value of a
formation surrounding a wellbore; and performing, and if necessary
repeating at a defined time interval, the following operations
until a flowrate of stimulation fluid reaches zero or until a new
pumping stage begins; solving for the flowrate of the stimulation
fluid in the wellbore; computing hydrostatic pressure and computed
temperature in the wellbore; receiving a measured temperature of
the wellbore; comparing the computed temperature to the measured
temperature to determine accuracy of the flowrate; updating the
flowrate when the accuracy of the flowrate is not acceptable; and
updating a permeability calculation of the formation based on the
flowrate of the stimulation fluid.
[0073] Clause 18, the medium of clause 17, wherein receiving the
measured temperature of the wellbore comprises receiving the
measured temperature in real-time from a distributed temperature
sensing (DTS) system.
[0074] Clause 19, the medium of clause 17 or 18, wherein updating
the flowrate when the accuracy of the flowrate is not acceptable
comprises: determining whether the computed temperature is greater
than the measured temperature; when the computed temperature is
greater than the measured temperature, doubling the flowrate; and
when the computed temperature is less than the measured
temperature, dividing the flowrate by 1.75.
[0075] Clause 20, the medium of at least one of clauses 17-19,
comprising recording the permeability calculation in a memory at
each time step.
[0076] While this specification provides specific details related
to certain components related to dynamically modeling a formation
surrounding a wellbore, it may be appreciated that the list of
components is illustrative only and is not intended to be
exhaustive or limited to the forms disclosed. Other components
related to dynamically modeling the formation will be apparent to
those of ordinary skill in the art without departing from the scope
and spirit of the disclosure. Further, the scope of the claims is
intended to broadly cover the disclosed components and any such
components that are apparent to those of ordinary skill in the
art.
[0077] It should be apparent from the foregoing disclosure of
illustrative embodiments that significant advantages have been
provided. The illustrative embodiments are not limited solely to
the descriptions and illustrations included herein and are instead
capable of various changes and modifications without departing from
the spirit of the disclosure.
* * * * *