Measuring effective fracture half-length and quantifying flux distribution in and around fractures in petroleum reservoirs
阅读说明:本技术 测量有效裂缝半长并量化石油储层中裂缝中及裂缝周围的通量分布 (Measuring effective fracture half-length and quantifying flux distribution in and around fractures in petroleum reservoirs ) 是由 费萨尔·M·阿勒塔瓦德 马哈茂德·贾迈勒艾哈迈迪 于 2018-10-30 设计创作,主要内容包括:确定了地下储层含烃地层中沿裂缝平面的通量分布,并且还确定了裂缝的有效半长。以前,沿这种裂缝平面的通量分布被认为是均匀的,这就是所谓的无限导流能力裂缝。在沿裂缝到井筒的某一距离处计算裂缝半长,其中压力变化(跨越裂缝平面)接近零。根据本发明获得的结果用于储层生产计划和管理。(Flux distributions along fracture planes in a hydrocarbon-bearing formation of a subterranean reservoir are determined, and effective half-lengths of fractures are also determined. Previously, flux distribution along such fracture planes was considered uniform, which is the so-called infinite conductivity fracture. The fracture half-length is calculated at a certain distance along the fracture to the wellbore, where the pressure variation (across the fracture plane) is close to zero. The results obtained according to the invention are used for reservoir production planning and management.)
1. A method of determining a quantitative flux distribution from a formation in a petroleum reservoir along a fracture plane intersecting a wellbore in the formation and an effective half-length of the fracture plane, comprising the steps of:
(a) performing a pressure transient test of the formation to obtain pressure transient test data;
(b) determining, by a computer process, a well pressure and a well pressure derivative of the formation from the pressure transient test data;
(c) determining, by a computer process, formation fracture parameters based on the well pressure and well pressure derivatives of the formation;
(d) determining, by a computer process, the flux distribution of the formation along the fracture based on the determined formation fracture parameters;
(e) determining, by a computer process, an effective fracture half-length of the fracture based on the determined formation fracture parameters;
(f) determining, by computer processing, a quantitative flux along a fracture plane intersecting the wellbore;
(g) storing the determined flux and flux distribution of the formation along the fracture, the quantitative flux from the fracture, and the determined effective fracture half-length of the fracture in computer memory;
(h) mapping, by a computer process, the determined flux distribution along the fracture plane and the determined effective fracture half-length of the fracture into a reservoir model.
2. The method of claim 1, wherein the determined flux distribution comprises flux of the formation in a horizontal plane at a wellbore adjacent to the fracture plane.
3. The method of claim 1, wherein the determined flux distribution comprises flux of the formation in one of two horizontal planes at a wellbore adjacent to the fracture plane.
4. The method of claim 1, wherein the determined flux distribution comprises flux of the formation in each of two horizontal planes at the wellbore adjacent to the fracture plane.
5. The method of claim 1, wherein the determined flux distribution comprises flux in a plane selected from the group consisting of: a horizontal plane of the formation at the wellbore adjacent to the fracture plane; one of two horizontal planes of the formation at the wellbore adjacent to the fracture plane; and each of two horizontal planes of the formation at the wellbore adjacent to the fracture plane.
6. The method of claim 1, further comprising the step of determining a wellbore pressure in the wellbore at a fracture plane intersecting a wellbore in the formation.
Technical Field
The present invention relates to modeling the structure of subterranean reservoirs, and more particularly, to measuring effective fracture half-length and quantifying flux distribution in and around fractures in petroleum reservoirs.
Background
In reservoir engineering, accurate modeling of subsurface reservoirs and formations, and numerical simulation of fluid flow-related processes by computer processing, are widely used for accurate hydrocarbon reservoir management and development planning. Both direct and indirect methods are used to assess the properties of hydrocarbon fluids containing rock.
Direct methods use direct measurement tools, such as logging tools. However, the ability of such tools to acquire data from the tool as a function of depth into the reservoir is limited to shallow depths, typically on the order of a few inches. For indirect measurements, pressure changes due to changes in well speed are recorded using a tool such as a manometer. I.e. indirectly measuring the flow in relation to the well and recording the pressure change over time. The obtained pressure data is then processed in a number of different ways to describe the reservoir and model the fluid flow process.
Reservoir modeling is largely an art and has its advantages and limitations. There are two main reservoir modeling approaches, namely: numerical values and analyses. Numerical modeling is flexible, but due to computer processing instability, it is difficult to accurately solve a plurality of multivariate nonlinear differential equations expressing physical relationships of reservoir rock and fluid phenomena and properties. Furthermore, as reservoirs of interest are very large and the need for precision is growing, the numerical model of the reservoir is organized into a large number of individual cells. For a typical reservoir, the number of cells may range from tens of millions to hundreds of millions. Instability and grid effects in the modeling often make numerical modeling unsuitable for solving more general/complex cases.
In contrast, pressure type curve based analysis methods are accurate, precise and stable solutions and provide a platform to address more general/complex situations. The use of semi-analytical solutions for homogeneous reservoir fractures is in line with current industry requirements, and natural fault geology and production activities for unconventional reservoirs are also increasing. Therefore, modeling of such flow curves becomes increasingly important. However, as is currently known, it is not currently possible to measure and quantify flux distribution in and around fractures in petroleum reservoirs. Numerical simulations of flow in such complex geometries are therefore currently available techniques, although in many cases such techniques are considered cumbersome and impractical.
Disclosure of Invention
Briefly, the present invention provides a new and improved method of determining quantitative flux distribution and effective half-length of fracture planes from a formation in a petroleum reservoir along fracture planes intersecting a wellbore in the formation. A pressure transient test of the formation is performed to obtain a pressure transient test measurement. The well pressure and well pressure derivatives of the formation are determined from the pressure transient test measurements by a computer process. Formation fracture parameters are determined by a computer process based on the well pressure and well pressure derivatives of the formation. Based on the determined formation fracture parameters, a flux distribution of the formation along the fracture is determined by a computer process. Based on the determined formation fracture parameters, an effective fracture half-length of the fracture is determined by a computer process. Quantification of flux along a fracture plane intersecting the wellbore is determined by a computer process. The determined flux and flux distribution of the formation along the fracture, the quantitative flux from the fracture, and the determined effective fracture half-length of the fracture are stored in a computer memory. The determined flux distribution along the fracture plane and the determined effective fracture half-length of the fracture are then mapped into a reservoir model by a computer process.
Drawings
FIG. 1A is a schematic illustration of a horizontal cross-sectional view of a producing fracture well in a reservoir in the subsurface.
FIG. 1A is another schematic illustration of a horizontal cross-section of the well of FIG. 1.
FIG. 2 is a schematic diagram showing three dimensions of the producing fracture well of FIG. 1A in isometric view.
FIG. 3 is a graph of pressure derivatives over time for a number of different fracture conductivity of a well intersecting a fracture.
FIG. 4 is a functional block diagram of a flow chart of data processing steps for modeling to determine an effective fracture half-length and quantify flux distribution in and around fractures in a petroleum reservoir in accordance with the present invention.
FIG. 5 is a schematic diagram of a data processing system for modeling to measure effective fracture half-length and quantify flux distribution in and around fractures in a petroleum reservoir in accordance with the present invention.
FIG. 6 is a graph of linear matrix flux distribution along a fracture in a single plane as a function of fracture half-length for a model obtained using synthetic data and in accordance with the present invention.
FIG. 7 is a graph of diagonal matrix flux distribution along a fracture in two planes as a function of fracture half-length for a model obtained using synthetic data and in accordance with the present invention.
FIG. 8 is a graph of diagonal and linear matrix flux distribution along a fracture in two planes as a function of fracture half-length for a model obtained using synthetic data and in accordance with the present invention.
FIG. 9 is a graph of flux accumulation as a function of time for different matrix permeabilities for a model obtained using synthetic data and in accordance with the present invention.
FIG. 10 is a graph of flux accumulation as a function of time for different fracture conductivity for a model obtained according to the present invention using synthetic data.
FIG. 11 is a plot of fracture pressure at the fracture as a function of fracture half-length and fracture half-length estimates for different fracture conductivity for a model obtained in accordance with the present invention using synthetic data.
FIG. 12 is a plot of fracture flux at the fracture as a function of fracture half-length and fracture half-length estimates for different fracture conductivity for a model obtained in accordance with the present invention using synthetic data.
FIG. 13 is a plot of flux distribution at a fracture as a function of fracture half-length for different fracture conductivity for models obtained using synthetic data and in accordance with the present invention.
FIG. 14 is a graph of pressure distribution at a fracture as a function of fracture half-length and fracture half-length estimates for different matrix conductivity for a model obtained using synthetic data and in accordance with the present invention.
FIG. 15 is a graph of flux distribution at a fracture as a function of fracture half-length for different matrix conductivity for models obtained using synthetic data and in accordance with the present invention.
FIG. 16 is a graph of flux distribution at a fracture as a function of fracture half-length and fracture half-length estimates for a composite reservoir model obtained in accordance with the present invention using synthetic data.
FIG. 17 is a graph of flux distribution at a fracture as a function of fracture half-length and fracture half-length estimates for a composite reservoir model obtained in accordance with the present invention using synthetic data.
FIG. 18 is a graph of flux distribution at a fracture as a function of fracture half-length for different well velocities obtained using synthetic data and in accordance with the present invention.
FIG. 19 is a graph of flux distribution at a fracture as a function of fracture half-length and fracture half-length estimates for different well speeds obtained using synthetic data and in accordance with the present invention.
FIG. 20 is a plot of dimensionless fracture pressure as a function of fracture half-length and fracture half-length estimates obtained using synthetic data and in accordance with the present invention.
FIG. 21 is a graph illustrating pressure and pressure derivative matching associated with synthetic data used in a model according to the present invention.
FIG. 22 is a graph of fracture pressure at the fracture as a function of fracture half-length and fracture half-length estimates obtained using synthetic data and in accordance with the present invention.
FIG. 23 is a graph illustrating pressure and pressure derivative matching associated with actual field data used in a model according to the present invention.
Detailed Description
In the drawings, FIGS. 1A and 2 show three dimensions, in horizontal cross-section and isometric views, respectively, a hydrocarbon producing fracture well 10 in a
Flux distribution along infinite conductivity fracture plane
In the case of fracture planes considered to be infinite conductivity, production pressure has previously been considered uniform across the fracture plane. Due to the flow to the well 10, the production pressure is considered to remain constant and equal to the initial pressure as the distance to the well 10 in the reservoir becomes much greater within its range than the pressure-disturbed drainage area 15 (fig. 1B). The drainage area is circular in horizontal cross-section with a drainage radius 17 as shown in fig. 1B. As used in connection with the present invention and as shown in fig. 1B, the infinite conductivity fracture plane is the plane of the drainage area 15 in which the
These types of fracture planes are therefore referred to as infinite fracture planes because the pressure is considered uniform across the plane regardless of the distance to the well. Thus, in the past it has been assumed that fluid enters a fracture such as 16 at a uniform flow rate per unit of fracture face area. Furthermore, due to the high conductivity of the fracture faces, it was thought that negligible pressure drop along the fracture resulted in a slight pressure gradient, resulting in an evenly distributed flux.
To date, previous fracture flux determination and modeling techniques have been based on the assumption that fractures have equal flux distributions along a finite length. No effort was made to determine the flow distribution along the actual length of the fracture. Furthermore, to date, no effort has been made to quantify the flux distribution along such cracks, whether in determining or estimating flux.
Flux distribution of limited conductivity along infinitely long fractures
Diagonal flux distribution on both sides of the crack in the x-y plane
To overcome the above difficulties, the present invention provides a computer-implemented method of measuring effective fracture half-length and quantifying flux distribution in and around fractures in a petroleum reservoir to model such features in the reservoir. The present invention provides an improvement over prior art processes for characterizing and modeling subterranean hydrocarbon reservoirs where there are complex flow geometries with fractures in order to evaluate and plan reservoir development. The present invention also potentially enables improved computer functionality in reservoir simulation by reducing the loss of processing time due to instability in simulator processing of reservoir models.
In accordance with the present invention, the flux distribution as a function of distance from the wellbore (e.g., 12) is considered to be non-uniform along the fracture (e.g., 14). Fig. 1 and 2 include a collection of
2. Term(s) for
Listed below are the terms of the analytical solution and the main operating equations which are processed by the computer according to the invention for forming the so-called model by calculating the pressure and the pressure derivatives. In this model, the well production is constant q STB/d, while the pressure and pressure derivatives and cross-flow rates of the three zones of the
a is the distance to the origin, ft
Beta-formation volume fraction, RB/STB
Wellbore storage, bbls/psi
cf ═ formation compressibility, psi-1
ct is total compression ratio, psi-1
dF is the distance to the fault, ft
d is a differential mathematical subscript
FCDfDimensionless fracture conductivity
FCf(iii) fracture conductivity in dimension, md-ft
FCDFDimensionless fault diversion capability
FCFFault diversion capability in dimension md-ft
h is the formation thickness, ft
k-matrix permeability md
kfPermeability to cracks, md
kFFault permeability, md
kdDimensionless permeability of the matrix, md
kdfDimensionless crack permeability, md
kf·wf(crack conductivity, md-ft)
krPermeability of reference, md
knReservoir Permeability ═ n, md
PiInitial formation pressure, psi
P1Area 1 pressure, psi
P2 for
PfCrack pressure, psi
PwfFlow BHP, psi
PdPressure without dimension
Pd1Dimensionless zone 1 pressure
Pd2Dimensionless zone 2 pressure
PdfDimensionless fracture pressure
PdwfDimensionless well flow pressure
Pressure in the Laplace domain
Pressure in the Fourier domain
Surface flow, STB/D
qDDimensionless flow
Dimensionless flow velocity in the Laplace domain
rwWellbore radius, ft
r is the distance to the center of the wellbore, ft
s-laplace parameter
tDDimensionless time
tDfDimensionless time of crack
wfWidth of crack ft
xfHalf crack length, ft
xfeEffective crack half length, ft
xDDimensionless x-coordinate
yDDimensionless y coordinate
Δ p-pressure change from the start of transient testing, psi
Δ t ═ time elapsed since the start of the self-test, hour
Eta 0.0002637 k/. mu.ct, hydraulic diffusion coefficient,
ηDFHydraulic force of faultDiffusion coefficient, dimensionless
ηDfDimensionless of hydraulic fracture propagation coefficient
ηDDimensionless as a coefficient of hydraulic diffusion of the substrate
μ ═ viscosity, cp
Δ ═ porosity, fraction
P-fourier parameter
Subscript
C is flow conductivity
D is dimensionless
e is effective
F ═ fault
f is a crack
i-init
i is imaginary/complex
inv-investigation
r is a reference
t is total
w ═ wellbore
x is x coordinate
y-coordinate
3. Physical phenomena involved
The present invention provides a method described in detail below. For theoretically infinite length fractures, the invention solves the problem of determining the half-length (x) of an uneven effective fracturefe) The complexity of (a). According to the invention, the flux distribution in physically practically limited conductivity fractures in the reservoir is taken into account. The flux distribution across the fracture plane is not uniform because of the fracture pressure (p) along the fracture 14f) Is relatively small near the well 10 and becomes larger toward the
The same features of non-uniform flux distribution are also valid for highly propped fracture and damaged fracture face cases. The flux distribution is a function of fracture conductivity and therefore fracture pressure. Fracture conductivity (F)CD) The lower the pressure drop across the fracture face between the reservoir rock matrix and the fracture.
For the purposes of the present invention, assume a fracture half-length (x)f) Is infinite. However, the effective fracture half length (x) that contributes to flowfe) Is limited. Therefore, the actual crack half-length cannot be determined directly from a given flux distribution solution. The invention is also based on the assumption that: when the pressure differential across the fracture face is zero (Δ p — 0), no fluid flow occurs. The present invention also determines flux volume and flux levels distributed along the plane of the fracture (as shown at 14). As mentioned above, previous methods are limited to a limited fracture length and are therefore forced to take into account end effects.
The present invention provides a method of measuring or estimating the half-length of a crack formed. According to the invention, this measurement is called: "effective crack half-length (x)fe)". This measurement is based on the following factors: as shown in fig. 1A and 2, at a distance from the well where the flux from the matrix is almost zero, the effective fracture half-length will be equal to that of a conventional fracture. At this physical location of the fracture, the pressure drop across the fracture-matrix interface continues to decrease as the distance from the well increases. In (x)f=xfe) At, the flux should be close to zero (q)D0), wherein:
as set forth in applicant's previously mentioned prior co-pending patent application serial No. 14/987,120, which is incorporated herein by reference for all purposes, formation two-dimensional flow may be represented in a subsurface region where wells, fractures and faults exist according to values of physical parameters in a set of five equations. The two-dimensional flow of the formation is governed by the values of the formation and fluid parameters and the relationships represented by equations (1a) through (1e) of patent application serial No. 14/987,120, which are incorporated herein by reference.
The dimensionless flux and fracture after transformation in laplace space from the solution of limited conductivity fractures can be represented by the following equations (1) and (2):
and
in fourier space, expressed by equation (3):
laplace and fourier transforms are applied to equations (1), (2), and (3) that control such two-dimensional flow in these three regions. The mathematical transformations are each directed to dimensionless times (t) in terms of transformation parameters(s)D) And a spatial variable (x) in terms of the transformation parameter (p)D). The equations (and their associated boundary conditions) are solved in laplace space and numerical inversion is performed.
The final equation for wellbore pressure in the Laplace domain is expressed as equation (4) below:
determining flux from data values obtained from pressure transient testing of wells at fractures and from formation rock porosity, permeability, fluid viscosity, formation thickness and fracture width based on equation (4)Values as a function of x and y coordinates.
The determined value may then be comparedAndplotting against x to show the pressure and flux distribution along (x), and determining the first value at which the flux value and/or pressure decay value ≧ 99.9% calculationfe). This criterion proved to provide a reasonable match to the results of the analysis case, but could beModified as needed.
Hereinbefore, ηDAnd ηDfDimensionless hydraulic diffusivity for matrix, fracture and fault, respectively, defined as follows:
wherein n is 1, 2, 3, f;
FCDfis formed by
The described dimensionless fracture conductivity;the reference permeability for this region is: k is a radical ofr=1.0md,
Is the dimensionless permeability of the matrix.The dimensionless pressures are:
dimensionless coordinates are written as:
and
dimensionless times are:
linear matrix flux distribution across the slit on the Y-channel
Similarly, by eliminating the matrix (x) according to the parameter (p)D) The fourier space variable in (e), the flow along the y channel only is:
linear fracture flux distribution inside the fracture on the X channel
Flux along the fracture can be expressed using the following method:
the fracture pressure profile associated with the x channel is:
it returns to laplace space. After substituting equation (2), the expression becomes:
the determined value may then be compared
Andrelative to xfPlotted to show the pressure and flux distribution along (x), and the first value calculated for flux value and/or pressure decay value ≧ 99.9% is determinedfe)。6. Model behavior-Observation and discussion
The next section describes the effect of many variables on the flux distribution and the solution for effective fracture half-length in the manner described above. For this study, conditions, parameter ranges and fluid/reservoir properties are as follows:
km1.0 to 10000(md)
h=100.0(ft)
rw=0.25(ft)
μ=0.7(cp)
ct=3.0e-6(psi-1)
FCf=1.0e1to 1.0e6(md ft)
FIG. 3 is a graph of a pressure derivative type of well intersecting a limited conductivity fracture between two different zones (e.g.,
Once a match is obtained between one of the flux profile curves, such as shown in FIG. 3, and the indicated flux observed from the well data, the determined values represented in equations (1) through (4)And
the solution can be solved with high accuracy by the computer processing according to the invention.7. Processing method
A comprehensive method performed by a computer to measure effective fracture half-length and quantify flux distribution in and around fractures in a petroleum reservoir is schematically illustrated in fig. 4. Fig. 4 shows a flow chart F illustrating the method of the invention for developing type curves of pressure and pressure derivative as a function of time for different fracture and fault conductivity.
Flow chart F (fig. 4) shows the logical structure of the present invention embodied in computer program software. Those skilled in the 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. It is apparent that the invention is implemented in its basic embodiment by a machine component that renders program code elements in the form of: instructing a digital processing device (i.e., a computer) to perform a series of data conversion or processing steps corresponding to those shown.
Figure 4 is a flow chart schematically illustrating a preferred sequence of steps for a process for measuring effective fracture half-length and quantifying flux distribution in and around fractures in a petroleum reservoir.
As shown in
In subsequent processing, during
During
Thus, according to the present invention, more accurate reservoir production condition assessment and prediction is provided for exploration and production decisions. Furthermore, the results obtained by the present invention provide improved historical matching of simulation results based on reservoir production to actual measured reservoir production. Thus, the present invention improves reservoir production operations, selection of drilling locations, well completion, and reservoir and production strategies.
8. Data processing system
As shown in FIG. 5, data processing system D includes a
However, the
The
Data processing system D also includes a database 114 stored in memory, which may be internal memory 114, or external network or non-network memory as shown at 116 in an associated database server 118. The database 114 also contains various data, including time and pressure data obtained during pressure transient testing of the analyzed layer; and the rock, fluid and geometric properties of the formation R and the well 10; and other formation properties; a physical constant; a parameter; the data measurements determined above with respect to fig. 1, 2 and 3 and the glossary.
Data processing system D includes
It should be noted that
As described above, the
9. Model case scenario
9.1 difference between matrix flux calculated in x-Y plane with respect to matrix flux of Y-channel
As will be described, the present invention contemplates substrate flow in the x-y planeThus allowing more realistic transients and flux calculations. As is currently known, earlier efforts have considered flow only in the y-plane
。To validate the model, a case scenario was performed to compare the proposed method with a method that only considers flow in the y-direction and is limited to the case of fracture matrix systems, with the results shown in fig. 6 and 7. The two curves are superimposed in fig. 8. For this case, the two methods are essentially identical, since they both have the same trend and value. The solution on the x-y plane results in scattered data as indicated by the discrete data points. This can be due to numerical problems and/or the nature of the diagonal flow and convergence into the fracture. For fluids, linear flow is easier than diagonal flow. However, it must be added that this is more realistic, since it makes it possible to observe the radial flow that should play a major role. In other words, the present invention allows reservoir or production engineers and analysts to easily mirror and measure flow around fractures with increased certainty and in production management decisions about hydrocarbon reservoirs. Furthermore, the present invention provides the ability to be a good platform to address more general/complex situations.
9.2 Effect of matrix Permeability on flux size
FIG. 9 shows the effect of matrix permeability on flux accumulation at the origin (x)D0). For (k)f1e3), three permeability matrix cases were performed: the permeabilities were 100md, 200md and 300md, respectively. Figure 9 shows that flux contribution from the matrix increases with increasing permeability of the matrix.
9.3 Effect of fracture conductivity on flux
FIG. 10 shows fracture conductivity kfAccumulated amount of flux (x) at originD0). Three fracture conductivity cases were performed at a matrix permeability of 100 md: the flow conductivity is 1000md-ft, 2000md-ft and 4000md-ft respectively. Figure 10 shows that the contribution from the matrix decreases with increasing fracture conductivity. For high conductivity values, the fracture acts as a source of fluid supply. Since the pressure drop across the fracture is very small, the fluid tends to flow from the fractureProvided per se; thus, the fluid flows along the fracture plane/fracture linear flow regime much faster than the fluid flowing out of the matrix providing the fracture/formation linear flow regime.
9.4 Effect of fracture conductivity on fluid Source and half Length of fracture
Assuming the well is the source (injector), FIG. 11 shows the fracture pressure profile along the fracture hole. For low fracture conductivity values (as shown at 150), the fracture pressure is high and difficult to inject into the fracture. The higher the conductivity, the lower the fracture pressure. Thus, the fluid tends to spread more into the matrix than would be the case with a higher fracture conductivity. Thus, at high fracture conductivity values as shown by
Figure 12 shows the profile distribution of fracture flux along the fracture hole. As fracture conductivity becomes greater, the fracture receives more fluid in the "injector" scenario. Since the pressure drop across the fracture is very small, fluid tends to be supplied through the fracture itself. Thus, the fluid flows in a linear flow regime along the fracture plane/fracture much faster than the fluid flowing out of the matrix supplying the fracture, the formation linear flow regime. It should be mentioned that the flux values are very small due to the high quality of the cracks and the relatively low implantation rate (2 π). The half-length of the crack between fig. 11 and 12 was estimated to be slightly different due to the standard values used in this study. The estimate is largely influenced by the first value used, and (x)fe) Estimated as 0.01% or less of the remainder of the calculated total flux.
Fig. 13 confirms the above observations. As fracture conductivity becomes greater, the fracture receives more fluid in the "injector" scenario and, therefore, less fluid is dissipated into the matrix, as shown at 160. In other words, more flux was calculated using the lower fracture conductivity values of
9.5 Effect of matrix Permeability on effective fracture half-Length
Change of matrix permeability to effective crack half-length (x)fe) Has a significant impact on the estimation of (c). FIG. 14 shows three
At 180 in FIG. 15 (x)fe80ft) found another interesting observation in which matrix flux at a distance along the length of the fracture tended to reverse in magnitude. This deflection may be attributed to a longer effective fracture half-length at lower substrate masses, which helps to increase flux into and out of the substrate.
9.6 Effect of two-zone composite System on fracture/matrix flux and effective fracture half-Length
The present invention provides flux distribution measurements of a two-zone composite reservoir across a fracture. Two sets of data were run simultaneously to display and validate the solution:
group-1 homogeneous (same quality reservoir); (k)1=k210md) a fracture well; fcf=5e4md ft,
Group-2 composite zones (reservoirs of different masses); (k)1100md and k210md) a fracture well; fcf=5e4 mdft。
Essentially,
Note that the lower the matrix permeability, the longer the fracture to accept more injection fluid. Also, for the higher matrix mass group-2, the matrix contributes/accepts flow in a greater proportion than for the lower mass group-1. For cracks, the opposite is true; that is, the fractures of the low-mass matrix group-1 are the primary source of contributing/accepting fluid. The results are shown in fig. 16 and 17.
The foregoing examples operate at reasonable matrix permeability (100md) and fracture conductivity over two orders of magnitude (5e4md-ft), replicating real cases at different well speeds (2 pi, 20 pi, and 200 pi). For higher rates, it is understood that the matrix and fracture contributions are greater as shown in fig. 18 and 19, confirming the precise behavior and physical properties of the invention.
The rate magnitude should not affect the effective fracture half-length; the rate of change should result in a different pressure magnitude, i.e. the greater the rate, the greater the pressure magnitude. For small rate changes, the interference is very small and may not be measurable. However, the radius of the pressure transient should be the same at different rates. This is consistent with the principles and assumptions for estimating survey radius; that is, the correlation is not a function of well velocity, but it measures the distance that the transient effect has covered to the reservoir.
FIG. 19 is a graph obtained by calculating the difference between the velocity values (x)fe650ft) is the same, confirming this understanding.
10. Integrated case
A comprehensive digitized, well-intersecting fracture model is constructed and pressure data is generated for analysis in a commercial well test package. The results were obtained by superimposing the pressure data of the numerical simulator on the proposed type curve. Excellent agreement between the two is recorded in table 1 and in fig. 20 and 21.
Table 1: comparison between numerical-based models and the solution results
11. Example case of the scene
The field case example dataset corresponds to vertical wells intersecting fractures in a homogeneous reservoir. The objective is to evaluate the reliability of the method on a practical field example where the flow is controlled by the fracture bilinear flow regime and the subsequent radial flow regime. Excellent agreement between the two is recorded in table 2 and in fig. 22 and 23.
Table 2: results of field data sets obtained by the method proposed by this study
As described above, the present invention is based on the assumption that no fluid flow occurs when the pressure difference across the fracture face is zero (Δ p ═ 0). It also calculates the flux volume and flux level distributed along the two fracture planes. Conventional methods are limited to a limited fracture length, thus accounting for end effects.
The present invention provides a more flexible method to easily mirror and measure flow around fractures with increased certainty and in production management decisions about hydrocarbon reservoirs. Furthermore, the present invention provides the ability to be a good platform to address the more general/complex case of different quality reservoir cells across the fault plane.
The effectiveness of the present invention is demonstrated in a systematic approach using both integrated cases and field cases. The pressure data behavior shows the expected decline in flux distribution away from the wellbore using a numerical model of the simulated flow geometry. Reservoir parameters estimated from type curves proved reasonable and satisfactory. Also, the method of the present invention was further confirmed by analyzing field examples of vertical wells intersecting limited conductivity fractures in carbonate reservoirs, which reflects a perfect match to most pressure data.
The present invention addresses the challenge of evaluating the flux fed into the fracture and determines the effective fracture half-length. This allows for accurate characterization, modeling and simulation. Therefore, the development plan for fractured reservoirs is more robust and cost effective.
The present invention has been described in sufficient detail to enable one having ordinary skill in the art of reservoir modeling and simulation to reproduce and obtain the results set forth herein. However, modifications not described in the present claims may be made by anyone skilled in the art of the technology, subject matter or technology to apply these modifications to certain structures and methods or in their use and practice, claimed subject matter; such structures and processes are intended to be within the scope of the present invention.
It is noted and understood that improvements and modifications can be made to the invention described in detail above without departing from the spirit or scope of the invention as set forth in the appended claims.
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