U.S. patent application number 14/987120 was filed with the patent office on 2017-07-06 for modeling to characterize fractures network in homogeneous petroleum reservoirs.
The applicant listed for this patent is Saudi Arabian Oil Company. Invention is credited to Faisal M. AlThawad, Mahmoud Jamiolahmady.
Application Number | 20170191348 14/987120 |
Document ID | / |
Family ID | 57915077 |
Filed Date | 2017-07-06 |
United States Patent
Application |
20170191348 |
Kind Code |
A1 |
AlThawad; Faisal M. ; et
al. |
July 6, 2017 |
MODELING TO CHARACTERIZE FRACTURES NETWORK IN HOMOGENEOUS PETROLEUM
RESERVOIRS
Abstract
Models of complex reservoir systems including fracture networks
and faults are provided from pressure transient test data obtained
from a well in a region of interest in the reservoir. An analytic
solution methodology is provided to interpret well test data
signature from the pressure transient test data based on model data
formed of simulated flow geometry and pressure data behavior.
Inventors: |
AlThawad; Faisal M.;
(Dammam, SA) ; Jamiolahmady; Mahmoud; (Edinburgh,
GB) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Saudi Arabian Oil Company |
Dhahran |
|
SA |
|
|
Family ID: |
57915077 |
Appl. No.: |
14/987120 |
Filed: |
January 4, 2016 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
E21B 41/0092 20130101;
E21B 43/26 20130101; E21B 49/008 20130101; G01V 99/005
20130101 |
International
Class: |
E21B 41/00 20060101
E21B041/00 |
Claims
1. A computer implemented method of deter wining a model of a
subsurface earth formation, having a well intersecting a complex
geological network of a fault and a fracture in the formation,
based on a pressure transient test of the formation, the computer
implemented method comprising the steps of: obtaining a test
measure of bottom hole pressure in the well; obtaining a test
pressure derivative of well pressure in the well at sampled
instants of measurement during the pressure transient test of the
formation; receiving an estimated reference type-curve set of a
plurality of type-curves of well pressures in the well and pressure
derivatives for selected test values of fracture conductivity and
fault conductivity in the formation; determining a model well
pressure of the formation based on the test measure of well
pressure and an estimated value of fracture conductivity and an
estimated value of fault conductivity in the formation; determining
a model pressure derivative based on the test measure of well
pressure and the estimated value of fracture conductivity and the
estimated value of fault conductivity in the formation; forming a
model type-curve of the determined model well pressure of the
formation and the model pressure derivative based on the determined
model well pressure of the formation; comparing the model
type-curve of the determined model well pressure of the formation
and the model pressure derivative with the plurality of type-curves
of the estimated reference type-curve set; and if the model
type-curve matches one of the plurality of type-curves of the
estimated reference type-curve set within an acceptable limit of
accuracy, storing the estimated value of fracture conductivity and
the estimated value of fault conductivity in the formation of the
matched type-curve of the estimated reference type-curve set as
models of the fracture conductivity and the fault conductivity of
the formation; and if not, adjusting one or both of the estimated
value of fracture conductivity and the estimated value of fault
conductivity in the formation; and repeating the steps of
determining a model well pressure, determining a model pressure
derivative, forming a model type-curve and comparing based on the
adjusted estimated value of fracture conductivity and fault
conductivity of the formation until an acceptable match is
achieved.
2. The computer implemented method of claim 1, further including
the step of forming a measure of the formation permeability based
on the stored models of the fracture conductivity and the fault
conductivity of the formation.
3. The computer implemented method of claim 1, further including
the step of forming an output display of the stored models of the
fracture conductivity and the fault conductivity of the
formation.
4. The computer implemented method of claim 1, further including
the step of forming an output display of the stored model of the
fracture conductivity as dimensional fracture conductivity of the
formation.
5. The computer implemented method of claim 1, further including
the step of forming an output display of the stored model of the
fracture conductivity as dimensionless fracture conductivity of the
formation.
6. The computer implemented method of claim 1, further including
the step of forming an output display of the stored model of the
fault conductivity as dimensional fault conductivity of the
formation.
7. The computer implemented method of claim 1, further including
the step of forming an output display of the stored model of the
fault conductivity as dimensionless fault conductivity of the
formation.
8. A data processing system for determining a model of a subsurface
earth formation, having a well intersecting a complex geological
network of a fault and a fracture in the formation, based on a
pressure transient test of the formation, the data processing
system comprising: a processor performing the steps of: obtaining a
test measure of bottom-hole pressure in the well; obtaining a test
pressure derivative of well pressure in the well at sampled
instants of measurement during the pressure transient test of the
formation; receiving an estimated reference type-curve set of a
plurality of type-curves of well pressures in the well and pressure
derivatives for selected test values of fracture conductivity and
fault conductivity in the formation; determining a model well
pressure of the formation based on the test measure of well
pressure and an estimated value of fracture conductivity and an
estimated value of fault conductivity in the formation; determining
a model pressure derivative based on the test measure of well
pressure and the estimated value of fracture conductivity and the
estimated value of fault conductivity in the formation; forming a
model type-curve of the determined model well pressure of the
formation and the model pressure derivative based on the determined
model well pressure of the formation; comparing the model
type-curve of the determined model well pressure of the formation
and the model pressure derivative with the plurality of type-curves
of the estimated reference type-curve set; and if the model
type-curve matches one of the plurality of type-curves of the
estimated reference type-curve set within an acceptable limit of
accuracy, storing the estimated value of fracture conductivity and
the estimated value of fault conductivity in the formation of the
matched type-curve of the estimated reference type-curve set as
models of the fracture conductivity and the fault conductivity of
the formation; and if not, adjusting one or both of the estimated
value of fracture conductivity and the estimated value of fault
conductivity in the formation; and repeating the steps of
determining a model well pressure, determining a model pressure
derivative, forming a model type-curve and comparing based on the
adjusted estimated value of fracture conductivity and fault
conductivity of the formation until an acceptable match is
achieved; and a memory storing the estimated value of fracture
conductivity and the estimated value of fault conductivity in the
formation of the matched type-curve of the estimated reference
type-curve set as models of the fracture conductivity and the fault
conductivity of the formation.
9. The data processing system of claim 8, further including the
processor performing the step of: forming a measure of the
formation permeability based on the stored models of the fracture
conductivity and the fault conductivity of the formation.
10. The data processing system of claim 8, further including: an
output display forming of the stored models of the fracture
conductivity and the fault conductivity of the formation.
11. The data processing system of claim 8, further including: the
output display forming an output record of the stored model of the
fracture conductivity as dimensional fracture conductivity of the
formation.
12. The data processing system of claim 8, further including: the
output display forming an output record of the stored model of the
fracture conductivity as dimensionless fracture conductivity of the
formation.
13. The data processing system of claim 8, further including: the
output display forming an output record of the stored model of the
fault conductivity as dimensional fault conductivity of the
formation.
14. The data processing system of claim 8, further including: the
output display forming an output record of the stored model of the
fault conductivity as dimensionless fault conductivity of the
formation.
15. A data storage device having stored in a non-transitory
computer readable medium computer operable instructions for causing
a data processing system to determine a model of a subsurface earth
formation, having a well intersecting a complex geological network
of a fault and a fracture in the formation, based on a pressure
transient test of the formation, the instructions stored in the
data storage device causing the data processing system to perform
the following steps: obtaining a test measure of bottom-hole
pressure in the well; obtaining a test pressure derivative of well
pressure in the well at sampled instants of measurement during the
pressure transient test of the formation; receiving an estimated
reference type-curve set of a plurality of type-curves of well
pressures in the well and pressure derivatives for selected test
values of fracture conductivity and fault conductivity in the
formation; determining a model well pressure of the formation based
on the test measure of well pressure and an estimated value of
fracture conductivity and an estimated value of fault conductivity
in the formation; determining a model pressure derivative based on
the test measure of well pressure and the estimated value of
fracture conductivity and the estimated value of fault conductivity
in the formation; forming a model type-curve of the determined
model well pressure of the formation and the model pressure
derivative based on the determined model well pressure of the
formation; comparing the model type-curve of the determined model
well pressure of the formation and the model pressure derivative
with the plurality of type-curves of the estimated reference
type-curve set; and if the model type-curve matches one of the
plurality of type-curves of the estimated reference type-curve set
within an acceptable limit of accuracy, storing the estimated value
of fracture conductivity and the estimated value of fault
conductivity in the formation of the matched type-curve of the
estimated reference type-curve set as models of the fracture
conductivity and the fault conductivity of the formation; and if
not, adjusting one or both of the estimated value of fracture
conductivity and the estimated value of fault conductivity in the
formation; and repeating the steps of determining a model well
pressure, determining a model pressure derivative, forming a model
type-curve and comparing based on the adjusted estimated value of
fracture conductivity and fault conductivity of the formation until
an acceptable match is achieved.
16. The data storage device of claim 15, wherein the instructions
cause the data processing system to perform the step of: forming a
measure of the formation permeability based on the stored models of
the fracture conductivity and the fault conductivity of the
formation.
17. The data storage device of claim 15, wherein the instructions
cause the data processing system to perform the step of: forming an
output display of the stored models of the fracture conductivity
and the fault conductivity of the formation.
18. The data storage device of claim 15, wherein the instructions
cause the data processing system to perform the step of: forming an
output display of the stored model of the fracture conductivity as
dimensional fracture conductivity of the formation.
19. The data storage device of claim 15, wherein the instructions
cause the data processing system to perform the step of: forming an
output display of the stored model of the fracture conductivity as
dimensionless fracture conductivity of the formation.
20. The data storage device of claim 15, wherein the instructions
cause the data processing system to perform the step of: forming an
output display of the stored model of the fault conductivity as
dimensional fault conductivity of the formation.
21. The data storage device of claim 15, wherein the instructions
cause the data processing system to perform the step of: forming an
output display of the stored model of the fault conductivity as
dimensionless fault conductivity of the formation.
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] The present invention relates to modeling the structure of
subsurface reservoirs, and more particularly to forming models of
fracture networks in a reservoir based on pressure transient test
measurements obtained from a formation layer of interest in the
reservoir.
[0003] 2. Description of the Related Art
[0004] In reservoir engineering, accurate modeling of subsurface
reservoirs and formations, and numerical simulation of fluid flow
related processes through computer processing, are widely used for
accurate oil and gas reservoir management and development plans.
Both direct and indirect methods are used to assess the nature of
the rock containing hydrocarbon fluids.
[0005] Direct methods use direct measuring tools such as well
logging tools. However, the ability of such tools to obtain data
measurements as a function of depth into the reservoir from the
tools is shallow, typically on the order of a few inches. For
indirect measurements tools such as pressure gauges are used to
record pressure changes due to well rate variations. Indirect
measurements involve flowing the well and recording the pressure
changes with time. The pressure data obtained are then processed in
a number of different ways to describe the reservoir and model the
fluid flow processes.
[0006] Reservoir modeling is, to a great extent, an art and has its
benefits and restraints. There are two main methods to model the
reservoirs namely; numerical and analytical. Numerical modeling is
flexible, however, it can be inaccurate due to instability of
computer processing to solve multiple, multi-variable non-linear
differential equations expressing the physical relationships of
reservoir rock and fluid phenomena and characteristics.
Furthermore, since reservoirs of interest are quite large and there
is an increasing need for accuracy, hence, numerical models of a
reservoir are organized into a large number of individual cells.
The number of cells can be from tens to hundreds of millions for
typical reservoirs. Instability in the modeling and the gridding
effect make numerical modeling unsuitable to address the more
complex cases.
[0007] Conversely, analytical methods are exact, accurate, stable
solutions and serves as a platform to address more general/complex
cases. Moreover, generating Type-Curves for unlimited scenarios is
a byproduct of the solution. Although, analytical models are more
accurate than numerical models, yet, they are much harder to
develop especially with complex geology and well geometries, as the
number of variables increase and hence, become hard to solve.
Therefore, developers tend to simplify such a complex problem by
dividing the problem into segments, replacing the real variables
with dimensionless variables and also use mathematical
transformations should they need to. This approach results in a set
of equations comprising important parameters that are solved
analytically or so called semi-analytically.
[0008] In current oil production operation ventures, it is becoming
increasingly likely to encounter complex geology such as natural
and/or man-made fractures. In particular, in transient well test
pressure data (derivative plots) from complex fractured carbonate
and sandstone reservoirs, a unique flow pattern has been observed
indicating complex geology characterized by a fracture flow
signature in the flow pattern at early times and a conductive fault
indicator in late times. The presence of such complex geology and
well geometry in formations of interest is also widely identifiable
through the growing number of image and production logs. The
identification, characterization and modelling of reservoirs with
such pressure signatures have, therefore, become increasingly
important. However, so far as is known, there is no analytical
solution to interpret such well test data signatures and hence,
numerical simulation of the flow has so far been done, which is
known to be cumbersome and impractical.
SUMMARY OF THE INVENTION
[0009] Briefly, the present invention provides a new and improved
computer implemented method of determining a model of a subsurface
earth formation, having a well intersecting a complex geological
network of a fault and a fracture in the formation, based on a
pressure transient test of the formation. The computer implemented
method obtains a test measure of bottom-hole pressure and also
obtains a test pressure derivative at sampled instants of
measurement during a pressure transient test of the formation. An
estimated reference type-curve set of a plurality of type-curves of
well pressures in the well and pressure derivatives for selected
test values of reservoir capacity, fracture conductivity, fault
conductivity value and distance from the tested well and the
formation capacity are received. A model well pressure of the
formation is determined based on the test measure of well pressure
and an estimated value of fracture conductivity, fault
conductivity, distance and the formation capacity. A model pressure
derivative is then determined based on the test measure of well
pressure and the estimated values in the formation. A model
type-curve is then formed of the determined model well pressure of
the formation and the model pressure derivative. The model
type-curve of the determined model well pressure of the formation
and the model pressure derivative are then determined with the
plurality of type-curves of the estimated reference type-curve set.
If the model type-curve matches one of the plurality of type-curves
of the estimated reference type-curve set within an acceptable
limit of accuracy, the estimated value of fracture conductivity and
the estimated value of fault conductivity in the formation in
addition to its proximity and reservoir capacity of the matched
type-curve of the estimated reference type-curve set are stored as
models of the fracture conductivity and the fault conductivity of
the formation. If not, the estimated values are adjusted, and the
steps of determining a model well pressure, determining a model
pressure derivative, forming a model type-curve and comparing are
repeated based on the adjusted estimated value of fracture
conductivity, fault conductivity and its remoteness from the tested
well along with the formation capacity.
[0010] The present invention also provides a new and improved data
processing system for determining a model of a subsurface earth
formation, having a well intersecting a complex geological network
of a fault and a fracture in the formation, based on a pressure
transient test of the formation. The data processing system
includes a processor, which obtains a test measure of bottom-hole
pressure in the well and also a test pressure derivative at sampled
instants of measurement during the pressure transient test of the
formation. The processor receives an estimated reference type-curve
set of a plurality of type-curves of well pressures in the well and
pressure derivatives for selected test values of fracture
conductivity fault conductivity in the formation. The processor
then determines a model well pressure of the formation based on the
test measure of well pressure and an estimated value of fracture
conductivity and an estimated value of fault conductivity and its
proximity along with the reservoir capacity in the formation, and
also determines a model pressure derivative based on the test
measure of well pressure and the estimated value of fracture
conductivity and the estimated value of fault conductivity in the
formation. The processor then forms a model type-curve of the
determined model well pressure of the formation and the model
pressure derivative. The processor next compares the model
type-curve of the determined model well pressure of the formation
and the model pressure derivative with the plurality of type-curves
of the estimated reference type-curve set. If the model type-curve
matches one of the plurality of type-curves of the estimated
reference type-curve set within an acceptable limit of accuracy,
the processor stores the estimated value of fracture conductivity
and the estimated value of fault conductivity in the formation of
the matched type-curve of the estimated reference type-curve set as
models of the fracture conductivity and the fault conductivity and
distance to fault in the formation. If not, the processor adjusts
one or all of the estimated value of fracture conductivity,
estimated value of fault conductivity and distance to the fault in
the formation from the tested well and the quality of formation,
and repeats the steps of determining a model well pressure,
determining a model pressure derivative, forming a model type-curve
and comparing based on the adjusted estimated value of fracture
conductivity, fault conductivity and distance of the formation and
other values. A memory of the data processing system stores the
estimated value of fracture conductivity and the estimated value of
fault conductivity in the formation of the matched type-curve of
the estimated reference type-curve set as models of the fracture
conductivity and the fault conductivity of the formation.
[0011] The present invention further provides a new and improved
data storage device having stored in a non-transitory computer
readable medium computer operable instructions for causing a data
processing system to determine a model of a subsurface earth
formation, having a well intersecting a complex geological network
of a fault and a fracture in the formation, based on a pressure
transient test of the formation, the instructions stored in the
data storage device causing the data processing system to perform a
sequence of processing steps. A test measure of bottom-hole
pressure is obtained, and a test pressure derivative is also
obtained. An estimated reference type-curve set of a plurality of
type-curves of well pressures in the well and pressure derivatives
for selected test values of fracture conductivity, fault
conductivity and distance with reservoir capacity in the formation
are received. A model well pressure of the formation is determined
based on the test measure of well pressure and an estimated value
of fracture conductivity, fault conductivity, distance and
reservoir capacity in the formation. A model pressure derivative is
then determined based on the test measure of well pressure and the
estimated value of fracture conductivity, the estimated value of
fault conductivity and distance with reservoir capacity in the
formation. A model type-curve is then formed of the determined
model well pressure of the formation and the model pressure
derivative based on the determined model well pressure of the
formation. The model type-curve of the determined model well
pressure of the formation and the model pressure derivative are
then determined with the plurality of type-curves of the estimated
reference type-curve set. If the model type-curve matches one of
the plurality of type-curves of the estimated reference type-curve
set within an acceptable limit of accuracy, the estimated value of
fracture conductivity and the estimated value of fault conductivity
in the formation of the matched type-curve of the estimated
reference type-curve set are stored as models of the fracture
conductivity and the fault conductivity of the formation. If not,
one or both of the estimated value of fracture conductivity, an
estimated value of fault conductivity and distance with reservoir
capacity in the formation are adjusted, and the steps of
determining a model well pressure, determining a model pressure
derivative, forming a model type-curve and comparing are repeated
based on the adjusted estimated value of fracture conductivity,
fault conductivity and distance with reservoir capacity of the
formation.
BRIEF DESCRIPTION OF THE DRAWINGS
[0012] FIG. 1 is a schematic view, taken in cross-section, of a
producing fractured well in a reservoir formation in the earth
having a geologic fault nearby.
[0013] FIG. 2 is a plan view of the flow geometry of the well and
reservoir formation of FIG. 1.
[0014] FIG. 3 is a functional block diagram of a flow chart of data
processing steps for developing type-curves of pressure and
pressure derivatives as functions of time for different fracture
and fault conductivities according to the present invention.
[0015] FIG. 4 is a functional block diagram of a flow chart of data
processing steps for modeling to characterize fractures networks
according to the present invention.
[0016] FIG. 5 is a schematic diagram of a data processing system
for modeling to characterize fractures networks according to the
present invention.
[0017] FIG. 6 is a plot of a type-curve of dimensionless pressure
and its log pressure derivative as functions of dimensionless time
for a range of different fracture and fault conductivities
according to the present invention.
[0018] FIG. 7 is a plot of a type-curve of dimensionless log
pressure derivative as functions of dimensionless time for a range
of different fracture and fault conductivities and reflecting an
early fracture linear flow according to the present invention.
[0019] FIG. 8 is a plot of a type-curve of dimensionless pressure
and its log pressure derivative as functions of dimensionless time
obtained according to the present invention for a well intersecting
a fracture network as compared to a synthetic numerical model of
the same well and fracture network.
[0020] FIG. 9 is a plot of a type-curve of dimensionless pressure
and its log pressure derivative as functions of dimensionless time
obtained according to the present invention for a well intersecting
a fracture network as compared to a field example data for such a
well.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0021] In the drawings, FIGS. 1 and 2 illustrate a reservoir
formation layer R of interest in an example subsurface hydrocarbon
producing reservoir with complex flow geometry. A hydrocarbon
producing well 10 in a well bore 12 has been drilled into and
through the reservoir as well as through subsurface formations
above the depth of the reservoir. The producing well is located in
a fracture or fracture matrix 14 in the layer R. The fracture 14 is
one component of the complex flow geometry. As indicated at 16, the
fracture 14 has a fracture width w.sub.f.
[0022] A fault indicated schematically at 18 is also present in the
layer R composed of Region 1, Region 2, and Region 3 nearby the
well 10 and the fracture 14. The fault 18 juxtaposes different
geometry across a fault between regions identified as Region 2 and
Region 3, which are same quality zones in the reservoir. The fault
18 is another component of the complex flow geometry. As indicated
at 20, the fault 18 has a fault width W.sub.f.
[0023] FIG. 2 illustrates schematically the complex flow geometry
in the reservoir layer R. The flow domain of the reservoir layer R
is composed of three areas: (i) the reservoir layer R with its
specific rock and fluid parameters and properties), which defines
flow as indicated schematically by arrows 22 into and around the
fracture network 14, the fractured well 10 and the nearby fault 18;
(ii) the fracture 14 (with its specific fracture properties), which
allows fluids to flow as indicated by arrows 24 along and into the
fracture 14 and towards the well 10; and (iii) the nearby fault 18
(with its specific properties), which allows fluids to flow as
indicated by arrows 26 along, across and towards the fractured well
10. The flow per unit area is defined to be positive from above and
negative from below. It should be noted that the present invention
provides indications to reservoir engineers and analysts
information with regard to the reservoir pressure conditions as
functions of both time and space in general, and wellbore pressure
conditions with regard to time in particular.
[0024] To overcome the aforementioned difficulties, the present
invention provides a computer implemented methodology of modeling
of subsurface reservoirs and formations, and reservoir simulation
of such models. The present invention provides improvements to the
existing technological processes of characterizing and modeling of
subsurface hydrocarbon reservoirs, where complex flow geometry with
fractures and faults are present in order to evaluate their
development. The present invention is also potentially capable of
improving the functioning of computers in performance of reservoir
simulation, by reducing the processing time lost due to instability
in the simulator processing of the reservoir model.
Nomenclature
[0025] Set forth below are nomenclature and the major working
equations of the analytical solution, also interchangeably referred
to as the model, which are used in calculating pressures and
pressure derivatives. In this model, the well is considered to be
producing at a constant rate of g STB/d, while the pressures and
pressure derivatives and the crossflow rates are determined for the
three regions. The Laplace and Fourier transforms have been
performed on the equations governing the two dimensional flow in
these three regions. These transformations are with respect to
dimensionless time (t), in terms of transform parameters (s) and a
space variable (x) in terms of transform parameter (p),
respectively. The equations (with the associated boundary
conditions) are solved in the Laplace space and inverted
numerically using a Gaver-Stehfest numerical inversion, such as
that described in Villinger, H., "Solving Cylindrical Geothermal
Problems Using Gaver-Stehfest Inverse Laplace Transform,"
Geophysics, (1985).
[0026] a=Distance from origin, ft
[0027] B=Formation volume factor, RB/STB
[0028] C=Wellbore storage, bbls/psi
[0029] c.sub.f Formation compressibility, psi.sup.-1
[0030] c.sub.t=Total compressibility, psi.sup.-1
[0031] d.sub.F=Distance to fault, ft
[0032] F.sub.CDf=Dimensionless fracture conductivity
[0033] F.sub.CF=Dimensional fracture conductivity, md-ft
[0034] F.sub.CDF=Dimensionless fault conductivity
[0035] F.sub.CF=Dimensional fault conductivity, md-ft
[0036] k=Matrix permeability, md
[0037] k.sub.f=Fracture permeability, md
[0038] k.sub.F=Fault permeability, md
[0039] k.sub.d=Dimensionless matrix permeability, md
[0040] k.sub.df=Dimensionless fracture permeability, md
[0041] k.sub.fw.sub.f=Fracture conductivity, md-ft
[0042] f.sub.r=Reference permeability, and
[0043] k.sub.n=(n) reservoir permeability, md
[0044] P.sub.i=Initial formation pressure, psi
[0045] P.sub.1=Region-1 pressure, psi
[0046] P.sub.2=Region-2 pressure, psi
[0047] P.sub.f=Fracture pressure, psi
[0048] P.sub.wf=Flowing BHP, psi
[0049] P.sub.d=dimensionless pressure
[0050] P.sub.d1=Dimensionless Region-1 pressure
[0051] P.sub.d2=Dimensionless Region-2 pressure
[0052] P.sub.df=Dimensionless fracture pressure
[0053] P.sub.dwf=Dimensionless well flowing pressure
[0054] p=Pressure in Laplace domain
[0055] p=Pressure in Fourier domain
[0056] q=Flow rate at surface, STB/D
[0057] r.sub.w=Wellbore radius, ft
[0058] r=Distance from the center of wellbore, ft
[0059] s=Laplace parameter
[0060] t.sub.D=Dimensionless time
[0061] t.sub.Df=Fracture dimensionless time
[0062] w.sub.f=Fracture width, ft
[0063] x.sub.f=Fracture half-length, ft
[0064] x.sub.d=Dimensionless x-coordinates
[0065] y.sub.d=Dimensionless y-coordinates
[0066] .DELTA.p=Pressure change since start of transient test,
psi
[0067] .DELTA.t=Time elapsed since start of test, hours
[0068] .eta.=0.0002637 k/.phi..mu.ct, hydraulic diffusivity,
ft.sup.2/hr
[0069] .eta..sub.DF=Fault hydraulic diffusivity, dimensionless
[0070] .eta..sub.Df=Fracture hydraulic diffusivity,
dimensionless
[0071] .eta..sub.D=Matrix hydraulic diffusivity, dimensionless
[0072] .mu.=Viscosity, cp
[0073] .phi.=Porosity, fraction
[0074] .rho.=Fourier parameter
[0075] Subscripts
[0076] C=Conductivity
[0077] D=Dimensionless
[0078] F=Fault
[0079] f=Fracture
[0080] w=Wellbore
[0081] The formation two dimensional flow illustrated in FIGS. 1
and 2 in the regions of the well bore 10, fracture 14 and fault 18
can be characterized according to the following Equations:
Region 1 : .differential. 2 p _ _ D 1 .differential. y D 2 = (
.rho. 2 + s .eta. D ) p _ _ D 1 ( 1 a ) Fracture : - .rho. 2 p _ _
Df + k D F CDf [ .differential. p _ _ D 2 .differential. y D y D =
0 - .differential. p _ _ D 1 .differential. y D y D = 0 ] + 2 .pi.
F CDf s = ( s p _ _ Df .eta. Df ) ( 1 b ) Region 2 : .differential.
2 p _ _ D 2 .differential. y D 2 = ( .rho. 2 + s .eta. D ) p _ _ D
2 ( 1 c ) Fault : - .rho. 2 p _ _ DF + k D F CD F [ .differential.
p _ _ D 3 .differential. y D - .differential. p _ _ D 2
.differential. y D ] y D = d F = ( s p _ _ DF .eta. DF ) ( 1 d )
Region 3 : .differential. 2 p _ _ D 3 .differential. y D 2 = (
.rho. 2 + s .eta. D ) p _ _ D 3 ( 1 e ) ##EQU00001##
Where the qualities of Region 1, 2 & 3 are identical.
[0082] As has been described above, Laplace and Fourier
transformations are applied to the five equations above governing
the two dimensional flow in these three regions, fracture and
fault. These mathematical transformations were with respect to
dimensionless time (t.sub.D), in terms of transformed parameter (s)
and a space variable (x.sub.d), in terms of the transformed
parameter (.phi., respectively. The equations (with the associated
boundary conditions) were solved in the Laplace space and inverted
numerically. The final equation for the wellbore pressure in
Laplace domain is set forth in Equation (2) below:
p _ wD = 2 s .intg. 0 .infin. 1 - [ e - 2 m d F [ 1 - k D ( .rho. 2
+ s .eta. D ) F CD F ( .rho. 2 + s .eta. DF ) + k D ( .rho. 2 + s
.eta. D ) 1 + k D ( .rho. 2 + s .eta. D ) F CD F ( .rho. 2 + s
.eta. DF ) + k D ( .rho. 2 + s .eta. D ) ] ] [ F CD f ( .rho. 2 + s
.eta. Df ) + 2 k D ( .rho. 2 + s .eta. D ) ] + [ e - 2 m d F [ 1 -
k D ( .rho. 2 + s .eta. D ) F CD F ( .rho. 2 + s .eta. DF ) + k D (
.rho. 2 + s .eta. D ) 1 + k D ( .rho. 2 + s .eta. D ) F CD F (
.rho. 2 + s .eta. DF ) + k D ( .rho. 2 + s .eta. D ) ] ] [ F CD f (
.rho. 2 + s .eta. Df ) ] d .rho. ( 2 ) ##EQU00002##
where: .eta..sub.D, .eta..sub.Df and .eta..sub.DF are the
dimensionless hydraulic diffusivity of matrices, fracture and
fault, respectively, as defined:
.eta. Dn = 0.000264 ( ( .PHI. c t .mu. ) n k f k rn ( .PHI. c t
.mu. ) ) = 0.000264 ( .eta. .eta. n ) ##EQU00003##
where:
n=1,2,3,f&F
F.sub.CDf is the dimensionless fracture conductivity described
by
F CDf = k f w f k r w and F CDF = k F w F k r w , ##EQU00004##
the region's reference permeability is: k.sub.r=1.0 md, and
k D = k k r ##EQU00005##
is the matrix dimensionless permeability, and the dimensionless
pressure is:
p Df = k rf h [ p i - p f ] 141.2 q .beta..mu. , ##EQU00006##
the dimensionless coordinates written as:
x D = x r w and y D = y r w ##EQU00007##
with the dimensionless time being expressed as:
t D f = 0.000264 k r t .PHI..mu. c t r w 2 . ##EQU00008##
Processing Methodology
[0083] A comprehensive computer implemented methodology of modeling
to characterize fractures network in homogeneous petroleum
reservoirs according to the present invention is illustrated
schematically in FIGS. 3 and 4. FIG. 3 illustrates a flow chart T
setting forth the methodology of the present invention for
developing type-curves of pressure and pressure derivatives as
functions of time for different fracture and fault conductivities.
FIG. 4 illustrates a flow chart F setting forth the methodology of
the present invention for modeling to characterize fractures
networks.
[0084] The flow chart T (FIG. 3) and the flow chart F (FIG. 4)
illustrate the structure of the logic of the present invention as
embodied in computer program software. Those skilled in this art
will appreciate that the flow charts illustrate the structures of
computer program code elements including logic circuits on an
integrated circuit that function according to this invention.
Manifestly, the invention is practiced in its essential embodiment
by a machine component that renders the program code elements in a
form that instructs a digital processing apparatus (that is, a
computer) to perform a sequence of data transformation or
processing steps corresponding to those shown.
[0085] The flow chart T of FIG. 3 illustrates schematically a
preferred sequence of steps of a computer implemented process for
developing type-curves of pressure and pressure derivatives as
functions of dimensionless time for different fracture and fault
conductivities for a subsurface formation or layer of interest.
[0086] As shown at step 40, processing according to the present
invention begins with data regarding the formation rock, fluid and
geometric properties of the layer R and well 10 being stored in
memory of a data processing system D (FIG. 5). The data regarding
formation rock, fluid and geometric properties are obtained from
well logs, core samples, fluid analysis reports, pressure transient
tests and other conventional sources of such data. During step 42,
a starting value for each of dimensional fracture conductivity
F.sub.Cf and dimensional fault conductivity F.sub.CF are
initialized.
[0087] During step 44, model values of the pressure derivative are
obtained by the data processing system D based on a specified input
value of dimensional fracture conductivity F.sub.Cf and dimensional
fault conductivity F.sub.CF and the pressure transient test data
obtained for the region of interest. The derivative is calculated
using a computer code that multiplies the dimensionless time
(t.sub.D), in terms of Laplace transform parameter (s), by the
change in well pressure with respect to time to produce the well
test derivative and plot it in a log-log scale. In step 46, the
model values of the pressure derivative for the specified input
value of dimensional fracture conductivity F.sub.Cf and dimensional
fault conductivity F.sub.CF during step 44 are stored in memory of
the data processing system D, together with the input value of
dimensional fracture conductivity F.sub.Cf and dimensional fault
conductivity F.sub.CF.
[0088] As indicated schematically at step 48, the values of
fracture conductivity and fault conductivity are adjusted as
required for a range of postulated values deemed likely to be
present based on the pressure transient test data, and additional
model values of pressure derivative obtained as described above in
step 44 and stored in memory of the data processing system D. In
this way a set of model values for type-curves are stored in the
data processing system D and are available as indicated at step 50
for presentation as output displays from the data processing system
D for analysis by reservoir engineers and analysts.
[0089] The flow chart F of FIG. 4 illustrates schematically a
preferred sequence of steps of a computer implemented process for
modeling to characterize fractures networks. As indicated at step
60, a time range is selected from the pressure and time data
obtained during pressure transient test of layer R. The model and
its structure have been described above in terms of Equation 1 in
the Laplace domain. During step 62, model values of present
pressure and pressure derivative with time are obtained according
to the methodology of flowchart T of FIG. 3 and formatted in a form
display in log-log plots, and made available for comparison with
actual test data and for output display as diagnostic plots by data
processing system D (FIG. 5) in such format. During step 64, the
petrophysical and reservoir data of both the well 10, fracture 14
and fault 18 are read in from storage memory for processing in the
data processing system D.
[0090] During step 66, actual values for well pressure and pressure
derivative are obtained according to actual measured well pressure
transient tests data according to Equation (1) above in the data
processing system D. During step 68, model pressure and derivative
plots based on actual pressure transient testing are generated and
then made ready to compare with the model pressure and derivative
of the data obtained during step 62. The well pressure and pressure
derivative values determined during step 68 are also formatted in a
form for storage and subsequent display in log-log plots, and are
available in that format for output display by data processing
system D.
[0091] During step 70, the values for well pressure and pressure
derivative determined from actual pressure transient test data
results during step 66 are compared with the model values of well
pressure and pressure derivative in the log-plot format resulting
from step 62. This comparison is done by super-imposing of pressure
data from the actual pressure transient test data results on the
proposed type curve or reservoir model.
[0092] Step 72 involves an evaluation of the results of comparison
step 72. If the well pressure and pressure derivative values
obtained during step 68, which are compared with model values
during step 70 indicate that the generated actual values being
compared do correspond within a specified acceptable degree to the
model data, an acceptable value of well pressure and pressure
derivative is indicated.
[0093] It is a common practice to leave the criteria of determining
the closeness between the generated values form actual pressure
transient tests and the model values up to the experience and
judgment of the user analyst or engineer. Such a process involves
minimizing the standard deviation between the measured pressure and
pressure derivatives based on postulated fracture and fault
conductivity values and the model pressure and pressure and
pressure derivative values to a preset criterion value (for
example, 0.1). Once such a preset criterion value is satisfied in
step 72, the user is thus satisfied to call the model as the
reasonably well matched one for the fracture and fault conductivity
values
[0094] Then, as indicated at step 74 the fracture and fault
parameters indicated by the model are reported as those for the
layer being analyzed. During step 76, the fracture and fault
parameters are displayed as results from the data processing system
D.
[0095] If the results of step 72 indicate an unacceptable match
between pressure or pressure derivative, or both of them, in the
measured data and that of the model values being compared, the
value of either or both of the dimensional fracture conductivity
F.sub.Cf and dimensional fault conductivity F.sub.CF are adjusted
during step 78. The distance to fault d.sub.F and matrix
permeability k may also be adjusted during step 78. Processing
returns to step 66 for processing of the actual well data based on
the adjusted values of fracture and/or fault conductivity.
Processing continues for further iterations until during step 72 an
acceptable agreement is achieved between the measured data and the
model data. This indicates, as noted, that the dimensional fracture
conductivity and dimensional fault conductivity values of the
current iteration are proper indications of the complex flow
geometry.
Data Processing System
[0096] As illustrated in FIG. 5, the data processing system D
includes a computer 100 having a processor 102 and memory 104
coupled to the processor 102 to store operating instructions,
control information and database records therein. The data
processing system D may be a multicore processor with nodes such as
those from Intel Corporation or Advanced Micro Devices (AMD), an
HPC Linux cluster computer or a mainframe computer of any
conventional type of suitable processing capacity such as those
available from International Business Machines (IBM) of Armonk,
N.Y. or other source. The data processing system D may also be a
computer of any conventional type of suitable processing capacity,
such as a personal computer, laptop computer, or any other suitable
processing apparatus. It should thus be understood that a number of
commercially available data processing systems and types of
computers may be used for this purpose.
[0097] The processor 102 is, however, typically in the form of a
personal computer having a user interface 106 and an output display
108 for displaying output data or records of processing of force
measurements performed according to the present invention. The
output display 108 includes components such as a printer and an
output display screen capable of providing printed output
information or visible displays in the form of graphs, data sheets,
graphical images, data plots and the like as output records or
images.
[0098] The user interface 106 of computer 100 also includes a
suitable user input device or input/output control unit 110 to
provide a user access to control or access information and database
records and operate the computer 100.
[0099] Data processing system D further includes a database 114
stored in memory, which may be internal memory 114, or an external,
networked, or non-networked memory as indicated at 116 in an
associated database server 118. The database 114 also contains
various data including the time and pressure data obtained during
pressure transient testing of the layer under analysis, as well as
the rock, fluid and geometric properties of layer R and well 10,
and other formation properties, physical constants, parameters,
data measurements identified above with respect to FIGS. 1 and 2
and the Nomenclature table.
[0100] The data processing system D includes program code 120
stored in a data storage device, such as memory 104 of the computer
100. The program code 120, according to the present invention is in
the form of computer operable instructions causing the data
processor 102 to perform the methodology of modeling to
characterize fractures network in homogeneous petroleum reservoirs
as shown in FIGS. 3 and 4.
[0101] It should be noted that program code 120 may be in the form
of microcode, programs, routines, or symbolic computer operable
languages that provide a specific set of ordered operations that
control the functioning of the data processing system D and direct
its operation. The instructions of program code 120 may be stored
in non-transitory memory 104 of the computer 100, or on computer
diskette, magnetic tape, conventional hard disk drive, electronic
read-only memory, optical storage device, or other appropriate data
storage device having a computer usable medium stored thereon.
Program code 120 may also be contained on a data storage device
such as server 118 as a non-transitory computer readable medium, as
shown.
[0102] The processor 102 of the computer 100 accesses the pressure
transient testing data and other input data measurements as
described above to perform the logic of the present invention,
which may be executed by the processor 102 as a series of
computer-executable instructions. The stored computer operable
instructions cause the data processor computer 100 to develop
type-curves of pressure and pressure derivatives as functions of
time for different fracture and fault conductivities according to
the methodology of FIG. 3 and to develop models to characterize
fractures networks according to FIG. 4. Results of such processing
are then available on output display 108. FIGS. 6 through 9 are
example displays of such results.
Model Behavior
[0103] FIG. 6 is a display of a model type-curve set of
dimensionless time versus dimensionless pressure and its
log-derivative for a selected set of different fracture and fault
conductivities which have been determined in a data processing
system according to the process of FIG. 3 described above. FIG. 6
shows determined model pressure at 200 from well data and the
determined model pressure derivative is shown at 202. Radial flow
is indicated at 204 in FIG. 6. Model pressure type-curves for a set
of selected values of dimensional fracture conductivity F.sub.Cf
values of 0.1e1, 1.5e2 and 1.5e4 are shown at 210, 212, and 214,
respectively, in FIG. 6. Model pressure derivative type curves for
a set of selected values of dimensional fault conductivity F.sub.CF
values of 1e8, 1e9 and 1e10 are shown at 216, 218, and 220,
respectively.
[0104] The type-curves displayed in FIG. 6 shows some distinctive
features of flow conditions of subsurface wells where complex
fracture networks may be occurring. First, fractured well pressure
behavior at early times such as at 222, where the type-curve
indicates a 1/4 slope is of interest. This segment of the
type-curves is indicative of a bilinear flow well behavior
reflecting two linear flow regimes along and into a fracture such
as shown schematically at 14 in FIGS. 1 and 2.
[0105] The type-curves of FIG. 6 indicate at 224 well behavior of a
radial flow demonstrating transient flow in the matrix around a
fracture, such as that shown schematically at 22 in FIGS. 1 and 2.
Thirdly, a "down-turn" or dip in the type-curves of FIG. 6, such as
that shown at 226 with a negative slope of unit value, which is
indicative of the beginning of a conductive fault such as that
shown schematically at in FIGS. 1 and 2 with enhancement of rock
quality. Further, as shown at 228 in the type-curves of FIG. 6, the
subsequent increase or up-turn in FIG. 6 indicates a bilinear flow
regime and also indicating the finite nature of fault 18. The
type-curves of FIG. 6 further indicate at 204 for subsequent time a
radial flow regime of the bounding blocks of Regions 1 and Region
2.
[0106] FIG. 7 is a display of a model type-curve set of
dimensionless time versus dimensionless pressure log-derivative for
a different selected set of different dimensional fracture
conductivities F.sub.Cf and dimensional fault conductivities
F.sub.CF which have also been determined in a data processing
system according to the process of FIG. 3 described above.
[0107] The pressure derivative type-curves of FIG. 7 are for
dimensional fracture conductivity F.sub.d of 1e3, 1e4, 1e5, and 1e6
as indicated and for dimensional fault conductivity F.sub.CF of
1e8, 1e9, and 1e10, as indicated. It is noted that the pressure
derivative type-curves of FIG. 7 exhibit at 230 a distinctive
feature of an early fracture linear flow regime at very early times
until such a fracture linear flow ends as shown schematically at
232, with bilinear flow starting at 234 in the manner also
indicated in the type-curves of FIG. 6. The early fracture linear
flow feature shown in the type-curves of FIG. 7 reflects the first
fluid flow into a well from a fracture alone as shown schematically
at 10 and 14, and confirms the stability of the solution even at a
very early time. The pressure derivative type-curves of FIG. 7 also
indicate at 236 beginning of a conductive fault and at 238, a
bilinear flow regime of the type described in FIG. 6.
Synthetic Flow Geometry Network Model
[0108] A synthetic numerically-built model of simulated flow
geometry with a well intersecting a fracture network, was
constructed and the pressure data were generated by a backward
modelling of the given well rate, fluid, reservoir, fracture and
fault parameters and properties. The pressure data for the
simulated flow geometry of the model were then analyzed in a
commercial well-test package (i. e. ECRIN of KAPPA Associates). The
results obtained for the numerical model are shown at 250 in FIG. 8
for pressure and at 252 for pressure derivative. Processing results
obtained according to the methods of FIGS. 3 and 4 indicated a
dimensional fracture conductivity F.sub.Cf value of 1e5 and a
dimensional fault conductivity F.sub.CF value of 1e8 as indicated
in FIG. 8. The results are plotted in a log-log plot format as
shown at 262 for pressure and 264 for pressure derivative in FIG.
8, along with the type-curves as indicated at 250 and 252 from the
model data. Initial bi-linear flow is indicated in FIG. 8 at 266 in
both the model data and the results according to the present
invention, followed by beginning of a conductive fault as shown at
268, with a subsequent increase or up-turn shown at 270 indicating
bilinear flow, and followed by radial flow as indicated at 272.
[0109] Heavy lines 280 and 282 have been added in FIG. 8 in those
portions of the data plots, where substantial conformity exists
between the type-curves 250 and 260 and the pressure derivative
type-curves 252 and 264 for the fracture conductivity of 1e5, and
for a fault conductivity of 1e8. As is evident from FIG. 8, a good
agreement between the curves plotted is noted in those areas. Table
1 contains a comparison of the fracture conductivities and other
parameter values both for the synthetic flow geometry network model
and according to the present invention. The value of the
permeability is determined by dividing the flow capacity (kh) by
the layer thickness. The flow capacity is an output of the model
selected. Again, good agreement between the values is also
indicated.
TABLE-US-00001 TABLE 1 Comparison Between the Results of a
Numerically Based Model and the Present Invention Numerical Model
Present Invention x.sub.f d.sub.F F.sub.Cf-F.sub.CF k x.sub.f
d.sub.F F.sub.Cf-F.sub.CF k (ft) (ft) (md ft) (md) (ft) (ft) (md
ft) (md) 2.0e5 5.0e3 1.0e5-1.0e8 33 Not 5.0e3 1.0e5-1.0e8 33 Esti-
mated
Field Data Well Model
[0110] A well model case example form an actual well in a producing
field provided a data set for comparison with processing results
according to the present invention. The well model corresponds to a
vertical well intersecting a fracture network in a tight homogenous
reservoir. The case example was to evaluate results according to
the present invention in comparison with an existing example of
data from an actual well. Pressure transient testing of the actual
well has determined the well to exhibit a flow which is dominated
by a fracture bi-linear flow regime for both pressure type-curve at
298 and pressure derivative type-curve at 256 in FIG. 9, followed
by beginning of a conductive fault in pressure derivative
type-curve with a negative half-slope as indicated at 290, followed
by an increase at 292 indicating a bi-linear flow regime.
[0111] Heavy lines 296 and 298 have been added in FIG. 9 in those
portions of the data plots where substantial conformity exists
between the type-curves according to the present invention for the
determined conductivities and the flow geometry model data curves.
As is evident from FIG. 9, a good agreement is noted, indicating
the dimensional fracture conductivity of 1e5, and for the
dimensional fault conductivity of 4.35e4. Table 2 contains an
indication of the fracture conductivities and permeability
parameter values obtained according to the present invention both
for the flow geometry network and the flow measures model. The
calculated parameters are resulting from the model match. As a
result of the match these parameters are obtained.
TABLE-US-00002 TABLE 2 Results Obtained for the Field Data Set by
the Approach of the Present Invention Results x.sub.f d.sub.F
F.sub.Cf-F.sub.CF k (ft) (ft) (md-ft) (md) Not Estimated 105
1.8e3-4.35e4 1.6
Reservoir Permeability, k.sub.r
[0112] Dimensional Fracture Conductivity,
F Cf = kf wf ##EQU00009##
[0113] Dimensionless Fracture Conductivity,
F CDf = k f w f k r r w ##EQU00010##
[0114] Distance to. Fault, d.sub.F
[0115] Dimensional Fault Conductivity, F.sub.Cf=k.sub.Fk.sub.wf
[0116] Dimensionless Fault Conductivity,
F CDF = k F w F k r r w ##EQU00011##
[0117] From the foregoing, it can be seen that the present
invention provides a new methodology where pressure transient data
is processed so that a complex flowing geometry with flow from
fractures and faults is rigorously described based on values of
fracture conductivities and fault conductivities which are
determined. Thus, the present invention provides models of the
complex flow geometry which conforms to both numerical models and
actual field data. The present invention provides reliable
reservoir models based on the pressure transient testing of a
reservoir.
[0118] Type-curves such as those shown in FIG. 6 indicate how a
complex network of fractures appears when recording pressure
transient data from oil and gas wells in a reservoir. Accordingly,
data that show similar behavior can be matched using such
type-curves. Once the match is obtained, the values of the fracture
nature and dimensions can be determined with a high degree of
accuracy.
[0119] The present invention thus provides accurate semi-analytical
solutions for a well intersecting fractures network in homogenous
reservoir(s). This is of considerable value in view of increasing
activities in production from naturally faulted geological settings
and unconventional reservoirs. The developed present invention
offers more flexible schemes to easily carry out modelling with
increasing certainty and larger positive impact on the management
decisions of such reservoirs.
[0120] The invention has been sufficiently described so that a
person with average knowledge in the field of reservoir modeling
and simulation may reproduce and obtain the results mentioned in
the invention herein. Nonetheless, any skilled person in the field
of technique, subject of the invention herein, may carry out
modifications not described in the request herein, to apply these
modifications to a determined structure and methodology, or in the
use and practice thereof, requires the claimed matter in the
following claims; such structures and processes shall be covered
within the scope of the invention.
[0121] It should be noted and understood that there can be
improvements and modifications made of the present invention
described in detail above without departing from the spirit or
scope of the invention as set forth in the accompanying claims.
* * * * *