CN112302607A - Method for explaining artificial fracture parameters of tight gas reservoir fractured horizontal well - Google Patents
Method for explaining artificial fracture parameters of tight gas reservoir fractured horizontal well Download PDFInfo
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Abstract
The invention discloses a method for explaining parameters of artificial fractures of a compact gas reservoir fractured horizontal well, which comprises the following steps of: initially assigning an artificial fracture parameter vector, setting the initial iteration step number to be k as 0, and setting the initial damping factor to be xi00.001; calculating a wellbore temperature profile for a current iteration step
Inversion error of wellbore temperature profile of k-th inversion iteration
temperature-Accord matrix of k-th inversion iteration
Temperature diagonal matrix omegakCurrent iterative step
Increment of (2)
Calculating an inversion fracture parameter vector for the k +1 th iteration step
Inversion error of wellbore temperature profile of k +1 th inversion iteration
Judgment of
Whether one of inversion iteration termination conditions is met, if so, stopping iteration; otherwise, let k be k +1, continue iteration until meeting the inversion iteration termination condition, output the present one
And (5) explaining the result of the artificial fracture parameter inversion. According to the invention, the parameters of all levels of artificial fractures of the compact gas reservoir fractured horizontal well can be quantitatively explained by carrying out inversion on actually measured wellbore temperature profile data.
Description
Technical Field
The invention relates to a method for explaining parameters of artificial fractures of a compact gas reservoir fractured horizontal well, and belongs to the field of oil and gas exploitation.
Background
As an important natural gas resource, the dense gas reservoir has very rich reserves in China. However, the dense gas reservoir has low permeability and compactness and a complex pore structure, so that the yield of dense gas in China is generally low. In order to improve the yield and the development benefit of the compact gas reservoir, the compact gas reservoir is mainly exploited by fracturing a horizontal well at present, so that the artificial fracture formed by hydraulic fracturing is of great importance to the effectiveness of fracturing modification, and the capacity of the compact gas reservoir fractured horizontal well is also directly determined. In order to ensure the effectiveness of fracturing modification of a compact gas reservoir horizontal well, the fracturing modification effect must be accurately evaluated, so that quantitative diagnosis of artificial fracture parameters (such as half length of fracture, flow conductivity and the like) is very important.
The conventional fractured horizontal well artificial fracture diagnosis and test technology mainly comprises a near-well monitoring technology (such as a tracer, a warm production logging technology and the like) and a remote monitoring technology (such as a microseism technology and the like), wherein the near-well monitoring technology is mainly used for identifying the type of an artificial fracture inflow fluid, can provide part of near-well zone fracture information, and cannot acquire the specific geometric dimension parameters of the artificial fracture; the remote monitoring technology has the main advantages that the overall range of hydraulic fracturing pressure response is monitored, the overall range of hydraulic fracturing modification is visually judged, but the defect that characteristic parameters of effective supporting cracks are difficult to obtain is overcome, the crack extension range of remote monitoring is far larger than the actual effective artificial crack control range, and therefore the specific parameters of each artificial crack of a fractured horizontal well are difficult to directly measure by the conventional testing technology.
In recent years, with continuous popularization and application of a horizontal well shaft Temperature profile testing technology, particularly rapid development of a Distributed optical fiber Temperature measuring (DTS) technology, a Temperature profile of a whole well section of a fractured horizontal well can be monitored in real time at present, and real-time continuous fractured horizontal well shaft Temperature profile data is provided. The method has the advantages that effective artificial fractures formed by fracturing transformation can be visually identified and positioned on an actually measured shaft temperature profile, research shows that the temperature profile of the gas reservoir fractured horizontal well shaft has obvious temperature drop at the position of the effective artificial fractures, and certain positive correlation exists between the temperature drop at the position of the artificial fractures and fracture flow and artificial fracture parameters, so that an inversion model is established through a mathematical algorithm, the actually measured shaft temperature profile data is translated, the corresponding relation between the artificial fracture parameters and the shaft temperature profile is found, quantitative evaluation is realized, and each artificial fracture parameter can be quantitatively explained. However, at present, the research for quantitatively explaining the artificial fracture parameters of the compact gas reservoir fractured horizontal well according to actually measured wellbore temperature profile data is basically blank in China.
Therefore, a set of compact gas reservoir fractured horizontal well artificial fracture parameter explanation model and method are very necessary to be established for quantitatively explaining all levels of artificial fracture parameters of the compact gas reservoir fractured horizontal well, and a new method is provided for quantitatively diagnosing the compact gas reservoir fractured horizontal well artificial fracture parameters and quantitatively evaluating the fracturing modification effect, so that the efficient and economic development of the compact gas reservoir in China is promoted.
Disclosure of Invention
The invention mainly overcomes the defects in the prior art and provides a method for explaining parameters of artificial fractures of a compact gas reservoir fractured horizontal well.
The technical scheme provided by the invention for solving the technical problems is as follows: a method for explaining artificial fracture parameters of a tight gas reservoir fractured horizontal well comprises the following steps:
s1, according to the measured shaft temperature profile of the target fractured horizontal well
Determining a temperature drop profile of a wellbore temperature profile at each fracture location
According to
Initial assignment of artificial fracture parameter vector as
Setting the initial iteration step number to k as 0 and the initial damping factor as xi0＝0.001；
S2, during the k-th inversion iteration, the current inverted artificial fracture parameter vector is used
Inputting a shaft temperature profile prediction model to calculate the shaft temperature profile of the current iteration step
S3, calculating the inversion error of the well temperature profile of the k-th inversion iteration through an error function equation
S4, calculating the temperature-Accord ratio matrix of the k-th inversion iteration
S5, Accord matrix according to temperature
Calculating the temperature diagonal matrix omegak；
S6 diagonal matrix omega according to temperaturekCalculating the current iteration step
Increment of (2)
S7, according to the current iteration step
Increment of (2)
Calculating an inversion fracture parameter vector for the k +1 th iteration step
S8, carrying out inversion on the fracture parameter vector of the (k + 1) th iteration step
Inputting the wellbore temperature profile prediction model to calculate the wellbore temperature profile of the (k + 1) th iteration step
And calculating the inversion error of the wellbore temperature profile of the k +1 th inversion iteration by using the error function equation
S9, and inverting the borehole temperature profile inversion error of the k-th inversion iteration in the step S3
Wellbore temperature profile inversion error iterated with the k +1 th inversion in step S8
Comparing; if it is
Xi (xi)k+1＝10ξkOtherwise, let xik+1＝0.1ξkThen continuing the next step;
s10, judgment
Whether one of inversion iteration termination conditions is met, if so, stopping iteration; otherwise, k is set to k +1, and then the step S2 is performed until the inversion iteration termination condition is met, the inversion task is completed, and the current output is output
And (4) carrying out inversion interpretation on the artificial fracture parameters of the target fractured horizontal well.
The further technical solution is that the error equations in the steps S3 and S8 are as follows:
in the formula (I), the compound is shown in the specification,
for the inversion error of the wellbore temperature profile at the k step,
for a measured temperature profile of the wellbore,
for the predicted wellbore temperature profile in the k-th inversion iteration, superscript' represents the vector transpose.
The further technical solution is that, in the step S4, the following equation is used for calculation:
in the formula (I), the compound is shown in the specification,
representing the temperature Accord matrix, T is the calculated value of the temperature profile of the wellbore, ejAnd the j component in the unit vector, N is the number of effective artificial fractures of the target fractured horizontal well, δ represents a minor fluctuation variable, i is 1,2 … N, j is 1, and 2 … N.
The further technical solution is that, in the step S5, the following equation is used for calculation:
in the formula, omegakRepresenting the temperature diagonal matrix, diag representing the diagonal matrix operation of the matrix,
representing a temperature-Attic ratio matrix.
The further technical solution is that, in the step S6, the following equation is used for calculation:
in the formula (I), the compound is shown in the specification,
for the current iteration step
The increment of (a) is increased by (b),
is an error term, xikDenotes the damping factor, ΩkA temperature diagonal matrix is represented that represents the temperature,
representing a temperature-Attic ratio matrix.
The further technical solution is that, in the step S7, the following equation is used for calculation:
in the formula (I), the compound is shown in the specification,
for the current iteration step
The increment of (a) is increased by (b),
the inverted fracture parameter vector for the (k + 1) th iteration step,
is the current iteration step.
Further, the inversion iteration termination condition in step S10 includes:
(1)
indicating that the inversion error of the shaft temperature profile meets the temperature error precision epsilonT；
(2)
The difference between the artificial fracture parameter vectors obtained by two adjacent inversion iterations is small enough, and the accuracy epsilon of the artificial fracture parameter iteration error is high when the artificial fracture parameter vectors are fullFrac。
The invention has the following beneficial effects:
1) according to the invention, by carrying out inversion on actually measured wellbore temperature profile data, quantitative explanation can be carried out on all levels of artificial fracture parameters of the compact gas reservoir fractured horizontal well;
2) the invention provides an explanation model and a method for quantitatively explaining parameters of each artificial crack of a fractured horizontal well of a compact gas reservoir, which can help technicians in the field to accurately evaluate the fracturing improvement effect and ensure the effectiveness of fracturing improvement, thereby promoting the high efficiency and economy of the compact gas reservoir in China.
Drawings
FIG. 1 is a schematic diagram of an inversion explanation process of manual fracture parameters of a tight gas reservoir fractured horizontal well;
FIG. 2 is a schematic diagram of a temperature profile of a tight gas reservoir fractured horizontal well measured wellbore;
FIG. 3 is a schematic diagram of the temperature drop distribution of the measured wellbore temperature profile at each stage of artificial fracture location;
FIG. 4 is a schematic diagram of an initialized artificial fracture half-length distribution;
FIG. 5 is a schematic diagram of a fit between an inverted simulated wellbore temperature profile and an actual wellbore temperature profile;
FIG. 6 is a schematic diagram of the inverted artificial crack half-length distribution.
Detailed Description
The technical solution of the present invention will be described in detail and fully with reference to the following embodiments, and it should be understood that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without inventive effort based on the embodiments of the present invention, are within the scope of the present invention.
As shown in fig. 1, the method for explaining the artificial fracture parameters of the tight gas reservoir fractured horizontal well, provided by the invention, comprises the following specific steps of taking the tight gas reservoir fractured horizontal well as a target fractured horizontal well, taking the half length of an artificial fracture as an example of the artificial fracture parameter to be explained, and carrying out quantitative explanation on the artificial parameters of the tight gas reservoir fractured horizontal well by adopting the method:
(1) based on the measured wellbore temperature profile of the target fractured horizontal well as shown in FIG. 2
Determining a temperature drop profile of a wellbore temperature profile at each fracture location
As in FIG. 3, according to
Initial assignment of artificial fracture parameter vector as
The corresponding artificial crack half-length distribution is shown in fig. 4, where k is 0 for the initial iteration step number and ξ is the initial damping factor0＝0.001；
(2) At the k-th inversion iterationThe current inverted artificial fracture parameter vector is used
Inputting a shaft temperature profile prediction model to calculate the shaft temperature profile of the current iteration step
(3) Calculating the inversion error of the borehole temperature profile of the k-th inversion iteration by the following error function equation
In the formula (I), the compound is shown in the specification,
for the inversion error of the wellbore temperature profile at the k step,
for a measured temperature profile of the wellbore,
for the predicted shaft temperature profile in the k-th inversion iteration, superscript' represents vector transposition;
(4) calculating a temperature-Accord ratio matrix of the k-th inversion iteration through the following equation
In the formula (I), the compound is shown in the specification,
representing the temperature Accord matrix, T is the calculated value of the temperature profile of the wellbore, ejThe j component in the unit vector is, N is the effective artificial fracture number of the target fractured horizontal well, δ represents a minor fluctuation variable, i is 1,2 … N, j is 1,2 … N;
(5) according to the temperature Accord matrix
And the following equation calculates the temperature diagonal matrix omegak；
In the formula, omegakRepresenting the temperature diagonal matrix, diag representing the diagonal matrix operation of the matrix,
representing a temperature-Accord matrix;
(6) diagonal matrix omega according to temperaturekAnd calculating the current iteration step by the following equation
Increment of (2)
In the formula (I), the compound is shown in the specification,
for the current iteration step
The increment of (a) is increased by (b),
is an error term, xikDenotes the damping factor, ΩkA temperature diagonal matrix is represented that represents the temperature,
representing a temperature-Accord matrix;
(7) according to the current iteration step
Increment of (2)
And calculating the inverted fracture parameter vector of the k +1 iteration step by the following equation
In the formula (I), the compound is shown in the specification,
for the current iteration step
The increment of (a) is increased by (b),
the inverted fracture parameter vector for the (k + 1) th iteration step,
the current iteration step;
(8) the inversion crack parameter vector of the k +1 iteration step
Inputting the wellbore temperature profile prediction model to calculate the wellbore temperature profile of the (k + 1) th iteration step
And calculating the inversion error of the wellbore temperature profile of the k +1 th inversion iteration by using the error function equation
(9) Then the inversion error of the wellbore temperature profile of the kth inversion iteration in the step (3) is calculated
Wellbore temperature profile inversion error iterated with the k +1 th inversion in step S8
Comparing; if it is
Xi (xi)k+1＝10ξkOtherwise, let xik+1＝0.1ξkThen continuing the next step;
(10) judgment of
Whether one of the inversion iteration termination conditions is satisfied, and if so, indicating a basis
Fitting the simulated wellbore temperature profile to the measured wellbore temperature profile, and stopping iteration as shown in fig. 5; otherwise, k is set to be k +1, then the step (2) is carried out until the inversion iteration termination condition is met, the inversion task is completed, and the current output is output
The results of the interpretation of the artificial fracture parameters for the target fractured horizontal well, as shown in FIG. 6Shown in the specification;
wherein the inversion iteration termination condition comprises:
1)
indicating that the inversion error of the shaft temperature profile meets the temperature error precision epsilonT；
2)
The difference between the artificial fracture parameter vectors obtained by two adjacent inversion iterations is small enough, and the accuracy epsilon of the artificial fracture parameter iteration error is high when the artificial fracture parameter vectors are fullFrac。
The wellbore temperature profile data of the present invention may be acquired, but is not limited to, by distributed fiber optic, drag-type production logging tools.
The wellbore temperature profile prediction model is a comprehensive temperature model comprising:
tight reservoir seepage model:
tight reservoir thermal model:
artificial fracture seepage model:
artificial fracture thermal model:
horizontal wellbore flow model:
horizontal wellbore thermal model:
in the formula: cgIs a gas compression coefficient, MPa-1；CpHeat capacity, J/(kg. K); f is the coefficient of friction of the well wall, decimal; kJTIs the Joule Thompson coefficient, K/MPa; kTThe rock thermal conductivity is J/(m.s.K); k is a radical ofxPermeability in the x-direction of the reservoir, mD; k is a radical ofyPermeability in the y-direction of the reservoir, mD; k is a radical ofzPermeability in the z-direction of the reservoir, mD; p is reservoir pressure, MPa; q. q.sFIs the fluid flow velocity in the fracture, m/s; q. q.swbThe rate of heat transfer to the wellbore for a unit volume of rock in the well cementation zone, J/(m)3·s)；RinwIs the wellbore inner diameter, m; t represents the production time, days; t represents temperature, K; t isIFluid inflow temperature, K; v. ofIM/s, the flow velocity of the incoming fluid; v is the flow velocity of the fluid, m/s;
porosity, decimal; mu.sgIs the gas viscosity, mPas; psi is pseudo pressure, MPa2mP.s; beta is the thermal expansion coefficient, 1/K; gamma is the degree of opening of the shaft, decimal; rho is the fluid density, kg/m3；ρIIn terms of density of the influent, kg/m3(ii) a Theta is the horizontal wellbore inclination angle, °; subscript F is an artificial crack, subscript x is indicated in the x-direction, subscript y is indicated in the y-direction, and subscript z is indicated in the z-direction.
The artificial fracture parameters include, but are not limited to, artificial fracture half-length, artificial fracture conductivity, and artificial fracture permeability.
Although the present invention has been described with reference to the above embodiments, it should be understood that the present invention is not limited to the above embodiments, and those skilled in the art can make various changes and modifications without departing from the scope of the present invention.
Claims (7)
1. A method for explaining parameters of artificial fractures of a compact gas reservoir fractured horizontal well is characterized by comprising the following steps of:
s1, according to the measured shaft temperature profile of the target fractured horizontal well
Determining a temperature drop profile of a wellbore temperature profile at each fracture location
According to
Initial assignment of artificial fracture parameter vector as
Setting the initial iteration step number to k as 0 and the initial damping factor as xi0＝0.001；
S2, during the k-th inversion iteration, the current inverted artificial fracture parameter vector is used
Inputting a shaft temperature profile prediction model to calculate the shaft temperature profile of the current iteration step
S3, calculating the k step inverse through an error function equationIterative wellbore temperature profile inversion error
S4, calculating the temperature-Accord ratio matrix of the k-th inversion iteration
S5, Accord matrix according to temperature
Calculating the temperature diagonal matrix omegak；
S6 diagonal matrix omega according to temperaturekCalculating the current iteration step
Increment of (2)
S7, according to the current iteration step
Increment of (2)
Calculating an inversion fracture parameter vector for the k +1 th iteration step
S8, carrying out inversion on the fracture parameter vector of the (k + 1) th iteration step
Inputting the wellbore temperature profile prediction model to calculate the wellbore temperature profile of the (k + 1) th iteration step
And calculating the inversion error of the wellbore temperature profile of the k +1 th inversion iteration by using the error function equation
S9, and inverting the borehole temperature profile inversion error of the k-th inversion iteration in the step S3
Wellbore temperature profile inversion error iterated with the k +1 th inversion in step S8
Comparing; if it is
Xi (xi)k+1＝10ξkOtherwise, let xik+1＝0.1ξkThen continuing the next step;
s10, judgment
Whether one of inversion iteration termination conditions is met, if so, stopping iteration; otherwise, k is set to k +1, and then the step S2 is performed until the inversion iteration termination condition is met, the inversion task is completed, and the current output is output
And (4) carrying out inversion interpretation on the artificial fracture parameters of the target fractured horizontal well.
2. The method for interpreting the parameters of the artificial fractures of the tight gas reservoir fractured horizontal well, according to the claim 1, is characterized in that the error equations in the steps S3 and S8 are as follows:
in the formula (I), the compound is shown in the specification,
for the inversion error of the wellbore temperature profile at the k step,
for a measured temperature profile of the wellbore,
for the predicted wellbore temperature profile in the k-th inversion iteration, superscript' represents the vector transpose.
3. The method for interpreting the parameters of the artificial fractures of the tight gas reservoir fractured horizontal well according to the claim 1, wherein the step S4 is implemented by the following equation:
in the formula (I), the compound is shown in the specification,
representing the temperature Accord matrix, T is the calculated value of the temperature profile of the wellbore, ejAnd the j component in the unit vector, N is the number of effective artificial fractures of the target fractured horizontal well, δ represents a minor fluctuation variable, i is 1,2 … N, j is 1, and 2 … N.
4. The method for interpreting the parameters of the artificial fractures of the tight gas reservoir fractured horizontal well according to the claim 3, wherein the step S5 is implemented by the following equation:
in the formula, omegakRepresenting the temperature diagonal matrix, diag representing the diagonal matrix operation of the matrix,
representing a temperature-Attic ratio matrix.
5. The method for interpreting the parameters of the artificial fractures of the tight gas reservoir fractured horizontal well, according to the claim 4, is characterized in that the step S6 is implemented by the following equation:
in the formula (I), the compound is shown in the specification,
for the current iteration step
The increment of (a) is increased by (b),
is an error term, xikDenotes the damping factor, ΩkA temperature diagonal matrix is represented that represents the temperature,
representing a temperature-Attic ratio matrix.
6. The method for interpreting the parameters of the artificial fractures of the tight gas reservoir fractured horizontal well, according to the claim 5, is characterized in that the step S7 is implemented by the following equation:
in the formula (I), the compound is shown in the specification,
for the current iteration step
The increment of (a) is increased by (b),
the inverted fracture parameter vector for the (k + 1) th iteration step,
is the current iteration step.
7. The method for interpreting the parameters of the artificial fracture of the tight gas reservoir fractured horizontal well according to the claim 1, wherein the inversion iteration termination condition in the step S10 comprises the following steps:
(1)
indicating that the inversion error of the shaft temperature profile meets the temperature error precision epsilonT；
(2)
The difference between the artificial fracture parameter vectors obtained by two adjacent inversion iterations is small enough, and the accuracy epsilon of the artificial fracture parameter iteration error is high when the artificial fracture parameter vectors are fullFrac。
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| 朱世琰: "基于分布式光纤温度测试的水平井产出剖面解释理论研究", 《中国优秀博士学位论文全文数据库（电子期刊）工程科技Ⅰ辑》 * |
| 罗红文等: "基于DTS数据反演的低渗气藏压裂水平井产出剖面解释新方法", 《天然气地球科学》 * |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114282387A (en) * | 2021-12-29 | 2022-04-05 | 西南石油大学 | DTS-based comprehensive evaluation method for steam injection horizontal well of heavy oil reservoir |
| CN114562254A (en) * | 2022-01-24 | 2022-05-31 | 中油奥博(成都)科技有限公司 | Micro-structure optical fiber-based underground well fluid pressure measurement system and measurement method |
| CN114595504A (en) * | 2022-03-09 | 2022-06-07 | 西南石油大学 | Shale gas reservoir fractured horizontal well output profile inversion interpretation method |
| CN114595504B (en) * | 2022-03-09 | 2023-03-10 | 西南石油大学 | Inversion interpretation method for output profile of shale gas reservoir fractured horizontal well |
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