A method for improving the longitudinal resolution accuracy of through-casing density measurement

Abstract

The present invention belongs to the technical field of well logging, and particularly relates to a method for improving the longitudinal resolution accuracy of through-casing density measurement. Starting from the nuclear well logging physical principle, this method analyzes and derives the functional relationship between the nuclear well logging measurement curve and the true formation physical parameters, and based on this relationship, a method for improving the resolution of density and neutron porosity logging data for through-casing logging based on the nuclear physics principle is proposed, which is an improvement method that is neither instrument-based nor repetitive measurement. By using the sliding window method to establish the corresponding optimization problem, and introducing neutron-density cross-constraints to reduce the uncertainty of the logging data after improving the resolution. It effectively improves the resolution of density and neutron porosity logging data, providing guidance for the exploration of actual thin-layer oil reservoirs.

Description

Technical Field

[0001] The present invention belongs to the technical field of logging, and particularly relates to a method for improving the longitudinal resolution accuracy for through-casing density measurement. Background Art

[0002] In nuclear logging tools, due to hardware limitations, the logging tool can only perform weighted averaging on the lithology of the measured area. If the layer thickness is lower than the resolution of the logging tool, it will cause errors in logging data, that is, it is difficult to distinguish thin layers between layers, resulting in the neglect of thin layers, and further causing economic losses. In relatively uniform, thick and clean formations, logging interpretation is relatively simple, but due to the complexity of the reservoir, the uncertainty of logging interpretation also increases. One of the sources of complexity is thin layers, whose thickness is much smaller than the existing instrument resolution, and many thin layers cannot be detected, thus unable to be reasonably evaluated. Although there are currently some logging tools with a resolution of 0.2 m, not every well can meet the corresponding logging requirements, and the measurement cost of such tools is relatively high.

[0003] In addition, in order to reinforce the wellbore, ensure safe drilling continuation, isolate oil, gas and water layers, and ensure separate zone testing and reasonable exploitation of oil and gas, it is necessary to run casing into the well and fill cement between the well and the casing. Compared with open-hole wells, the casing and cement in cased wells replace part of the mud in the original wellbore space, making logging more difficult.

[0004] Therefore, studying a method for improving the resolution of logging data for non-repetitive measurement of formation density in a through-casing environment, without instrument improvement and with low cost, has positive significance for reducing costs and increasing efficiency in oil and gas exploitation. Summary of the Invention

[0005] In view of this, the present invention provides a method for improving the longitudinal resolution accuracy for through-casing density measurement to solve the problems existing in existing logging, especially through-casing logging, such as inaccurate logging, difficult interpretation and high cost.

[0006] To solve the above problems, the present invention adopts the following technical solutions:

[0007] A method for improving the longitudinal resolution accuracy for through-casing density measurement includes the following steps:

[0008] Step 1: According to the nuclear logging principle, deduce the functional relationship between the true formation physical parameters and the instrument measurement values in the casing environment, where the true formation physical parameters include density and porosity;

[0009] Step 2: Based on the functional relationship obtained in S1, construct a sliding window matrix equation set based on depth information;

[0010] Step 3: Solve the sliding window matrix equations, and introduce the cross-constraint method of neutrons and density under casing measurement to limit the dynamic range of the logging curves obtained by solving, so as to obtain the logging curves with constraints as the final logging data.

[0011] Further, the derivation process of the functional relationship between the true formation density, porosity and the measured values of the instrument under the casing environment in Step 1 is as follows:

[0012] Assume that the multiple-scattered gamma rays detected by the detector are the contributions of the virtual source. Then the gamma ray intensity S s contributed by the casing homogeneous geological formation to the detector is:

[0013] S s = I v dTG(d, r 0 , μ 0 , μ)

[0014] In the formula, S s is the gamma ray intensity contributed by the casing and the homogeneous geological formation to the detector; I v is the source strength of the virtual source, and the virtual source consists of a gamma ray with source energy and no scattering; dT is the thickness of the volume element; G(d, r 0 , μ 0 , μ) represents an integral term, that is, the casing thickness, geometric position and physical parameters of the casing and the medium.

[0015] When G(d, r 0 , μ 0 , μ) remains unchanged, the magnitude of S s is proportional to the volume and the unscattered source strength I v at a distance r from the source after passing through the casing. Therefore, according to the ray intensity in multiple formations, the total formation density ρ s can be calculated by using the inversion algorithm;

[0016] ρ s = ρ 1 dT 1 G(d, r 0 , μ 0 , μ) + ρ 2 dT 2 G(d, r 0 , μ 0 , μ) + ρ 3 dT 3 G(d, r 0 , μ 0 , μ)

[0017] In the formula, ρ 1 , ρ 2 , ρ 3are the density values of different strata;

[0018] Then the density at the m-depth point can be expressed as:

[0019]

[0020] In the formula, ρ m is the measured value of the logging curve; w i is the weight coefficient of each geological layer; ρ i are the physical parameters of the casing and each stratum; ρ m varies with the depth point;

[0021] Assume that the vertical detection range of the detection instrument is VR, then the functional relationship reflecting the casing, the true formation density, porosity and the measured value of the instrument is expressed as:

[0022]

[0023] In the formula, m(i) is the logging value at the i-th measurement point, and ρ(z) represents the true physical parameters of the casing and each stratum within a detection range.

[0024] Furthermore, the establishment process of the neutron-density cross-constraint method introduced in step 3 includes the steps:

[0025] 2.1. According to the balance principle, establish a volume model in the formation:

[0026] V ma +V sh +V oil +V gas +V water = 1

[0027] In the formula, V ma is the relative volume of the rock skeleton; V sh is the relative volume of the mudstone; V oil , V gas , V water represent the relative volumes of oil, gas, and water in the rock pores respectively, and the sum of their relative volumes is equal to the porosity φ;

[0028] 2.2. According to the inverse relationship between density and porosity in log interpretation and the volume model established in 2.1, calculate the lower limit ρ lb and upper limit ρ ub of the formation density, the lower limit φ lb and upper limit φ ub of the porosity respectively;

[0029] 2.3. Based on the functional relationship obtained in step 1, introduce the lower limit ρ lband the upper limit of formation density ρ ub and the lower limit of porosity φ lb and the upper limit φ ub to determine the dynamic constraint range of the logging curve.

[0030] Furthermore, in the step S2, before constructing the sliding window matrix equation set based on the depth information, weight compensation is performed on the formation farthest from the central depth point within the detection volume.

[0031] Furthermore, in the step 3, the least squares method is used to solve the sliding window matrix equation set.

[0032] Even further, in the process of using the least squares method to solve in the step 3, the square of the error between the true measurement curve and the calculated logging curve is used as the loss function.

[0033] The method for improving the vertical resolution accuracy provided by the present invention starts from the nuclear logging physical principle, analyzes and derives the functional relationship between the nuclear logging measurement curve and the true formation physical parameters. Based on this functional relationship, through a depth-based sliding window matrix and introducing neutron and density cross-constraints, the uncertainty of the logging data after improving the resolution is reduced.

[0034] Compared with the prior art, the present invention proposes a method for improving the resolution of density and neutron porosity logging data for through-casing non-instrument improvement and non-repetitive measurement based on the nuclear physics principle. It effectively improves the resolution of density and neutron porosity logging data and provides guidance for the exploration of actual thin-layer oil reservoirs. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a schematic diagram of the relative positions of the volume element dV, the detector, and the radiation source in the formation;

[0036] Figure 2 It is the relative position of the geological layer with a thickness of dT, the detector, and the radioactive source;

[0037] Figure 3 The contribution of a single geological layer to the detector;

[0038] Figure 4 The depth-based sliding window and its corresponding formation;

[0039] Figure 5 The result of improving the resolution of through-casing logging data. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0040] The following describes the present invention in detail with reference to the drawings and embodiments.

[0041] A method for improving the vertical resolution accuracy for through-casing density measurement provided by this embodiment includes the following steps:

[0042] Step 1: According to the nuclear logging principle, the functional relationship between the true formation physical parameters and the instrument measurement values in the casing environment is derived. The true formation physical parameters include density and porosity.

[0043] In this embodiment, the density logging is taken as an example for derivation. Most of the particles detected by the density instrument detector are the particles scattered in the formation near the detector. These multiple-scattered gamma rays detected by the detector can be regarded as a virtual source I composed of a gamma ray with the source energy and no scattering. v Contributed. In a homogeneous medium, assume the intensity of the instrument source is I 0 , the casing thickness is d, then the point source intensity I v of the unscattered ray at a distance r from the source after passing through the casing, that is, the virtual source strength is:

[0044]

[0045] In the formula, I v is the source strength of the virtual point source; I 0 is the source strength of the instrument radiation source; μ is the formation mass attenuation coefficient; μ 0 is the casing mass attenuation coefficient; ρ is the formation density; ρ 0 is the casing density; d is the casing thickness; r is the distance between the virtual point source and the instrument source after passing through the casing.

[0046] Assume that the unit volume element at a distance x from the detector after passing through the casing is dV, as Figure 1 shown, the ray intensity dI p contributed by the unit volume element detected by the detector, then dI p is:

[0047]

[0048] In the formula, dI p is the ray intensity contributed by the volume element dV detected by the detector; x is the distance between the unit volume element and the detector after passing through the casing.

[0049] Also, because dV = rdrdθdT and x 2 ≈r 2 +z 2 then dI p is converted to:

[0050]

[0051] In the formula, z is the distance between the radioactive source and the detector of the instrument; dr is the side length of the volume element; dθ is the angle between the volume element and the horizontal plane; dT is the thickness of the volume element.

[0052] If integrated in the Z-axis direction, as Figure 2 shown, that is, to calculate the ray intensity contributed by a formation with an infinite thickness of dT, the calculation formula is:

[0053]

[0054] That is: I p = I v dTf(d, r 0 , z, μ 0 , μ)

[0055] For the convenience of writing, the integral term is represented by f(d, r 0 , z, μ 0 , μ), where r 0 represents the position of the wellbore wall.

[0056] Therefore, in a finite homogeneous formation, the gamma ray intensity S s contributed to the detector can be represented by the area under the curve, as Figure 3 shown, and its expression is:

[0057]

[0058] In the formula, S s is the gamma ray intensity contributed by the casing and the homogeneous formation to the detector; G(d, r 0 , μ 0 , μ) represents an integral term, that is, the casing thickness, geometric position, and physical parameters of the casing and the medium.

[0059] When G(d, r 0 , μ 0 , μ) remains unchanged, the magnitude of S s is proportional to the volume and the unscattered source strength I v at a distance r from the source. Therefore, in multiple formations, the total formation density ρ s can be calculated using the inversion algorithm based on the ray intensity;

[0060] ρ s = ρ 1 dT 1 G(d, r 0 , μ 0 , μ)+ρ 2 dT 2 G(d, r 0 , μ 0 , μ)+ρ 3 dT 3 G(d, r 0 , μ 0 , μ)

[0061] Where ρ 1 , ρ 2 , ρ 3 are the density values of different strata;

[0062] Then the density at the m-depth point can be expressed as:

[0063]

[0064] Where ρ m is the measured value of the logging curve; w i is the weight coefficient of each geological layer; ρ i are the physical parameters of the casing and each stratum; ρ m varies with the depth point;

[0065] Assume the vertical detection range of the detection instrument is VR, then the functional relationship reflecting the casing, the true formation density, porosity and the measured value of the instrument is expressed as:

[0066]

[0067] Where m(i) is the logging value at the i-th measurement point, and ρ(z) represents the true physical parameters of the casing and each stratum within a detection range.

[0068] Step 2: Based on the functional relationship obtained in Step 1, construct a sliding window matrix equation set based on depth information.

[0069] During the acquisition of logging information, the detection volume range of nuclear logging is described as a sphere, and the calculation formula for each layer w′ i within the detection volume range is as follows:

[0070]

[0071] Where v i is the volume of the i-th stratum; V is the instrument detection volume.

[0072] Since the stratum farthest from the central depth point within the detection volume range captures the least, in the method of obtaining the true density and porosity of the formation and obtaining high-resolution neutron porosity and density logging data, a greater weight needs to be assigned to the stratum farthest from the central depth point. Therefore, the weight w i is equal to the weight after taking the reciprocal of w′ i and normalizing each stratum.

[0073] In this embodiment, a sliding window matrix equation set based on depth information is constructed, based on the weighted weights. As can be seen from the functional relationship between the true formation physical parameters and the instrument measurement values in Step 1, the value of the geophysical parameter at a certain depth point of the logging curve is equal to the weighted average of all formation geophysical parameters within the instrument detection range. Assuming there are 5 formations within the entire detection range, in order to obtain sufficient equations, the range containing several adjacent data is defined as a window, that is, in the sliding window, the data is grouped in a window. The sliding window slides in the data stream according to the specified interval. When new data is acquired, the old data is removed by sliding the sliding window and the new data is incorporated.

[0074] During nuclear logging, within a single sliding window, the tool samples each formation within the detection volume. As the sliding window moves with depth, the sampling interval is shifted until all depth measurements of the entire well are completed. There is partial overlap in the formations sampled by the sliding window each time.

[0075] Figure 4 The schematic diagram of the depth-based sliding window and its corresponding formations is shown. The dashed area in the figure represents the nth detection volume, and the solid area represents the (n + 1)th detection volume. The displacement between the two is the sampling interval when the tool measures the formation parameters. Within the entire depth range, the formation parameters within each investigation volume and the logging values form an equation in the matrix equation set. The matrix equation set can be obtained by this depth-based sliding window method:

[0076]

[0077] where w in is the weight coefficient of the ith formation in the nth detection volume; where m(1) and m(2) are ignored because the corresponding depths cannot be used to establish a complete equation.

[0078] Step 3: Solve the sliding window matrix equation set, and introduce the cross-constraint method of the downhole measurement of neutrons and density to limit the dynamic range of the logging curve obtained by the solution, so as to obtain a logging curve with constraints as the final logging curve.

[0079] In this embodiment, the least squares method is used to solve the sliding window matrix equation set, that is, it is solved using the following formula:

[0080]

[0081] s.t. constraints

[0082] where p hi *are the high-resolution formation density and formation porosity; sim(i) is the i-th value of the newly measured logging curve, which is obtained by weighted averaging the newly acquired high-resolution logging curve, in order to match the resolution of this value with the original measured value for facilitating relevant calculations.

[0083] During the solution process, the square of the error between the true measured value and the calculated high-resolution logging curve, that is, after weighted averaging and having the same resolution as the true measured value, is used as the loss function; when the loss function reaches below the set threshold, the iteration ends to obtain the final high-resolution density and neutron logging curves.

[0084] During the implementation process, to reduce the uncertainty of the logging data after the resolution improvement. In this embodiment, the neutron-density cross-constraint method is introduced to constrain the logging curve. And the process of introducing the neutron-density cross-constraint includes the following steps:

[0085] 2.1. According to the detection characteristics of the logging method and the differences in physical properties of various substances in the rock, the actual rock is transformed into several homogeneous parts by volume, and then the contribution of each part is studied separately. The sum of the contributions of each part constitutes the macroscopic physical quantity. That is, two principles should be included in establishing the volume model in the formation:

[0086] (1) According to the principle of material balance, the sum of the volumes V i of each part is equal to the rock volume V:

[0087]

[0088] (2) The macroscopic physical quantity M of the rock, such as density porosity, etc., is equal to the sum of the macroscopic physical quantities M i of each part:

[0089]

[0090] The volume model established in the formation is:

[0091] V ma +V sh +V oil +V gas +V water =1

[0092] In the formula, V ma is the relative volume of the rock skeleton; V sh is the relative volume of the mudstone; V oil , V gas , V water respectively represent the relative volumes of oil, gas, and water in the rock pores, and the sum of their relative volumes is equal to the porosity φ.

[0093] 2.2. According to the definitions of density and porosity in well logging interpretation, it can be known that the density of the formation is inversely proportional to the porosity, that is, the larger the porosity, the smaller the density. That is to say, the neutron and density can be calculated from each other. Therefore, using the volume model established in 2.1, calculate the lower and upper limits of the formation density and the lower and upper limits of the porosity.

[0094] When the porosity is larger and the density is smaller, obtain the lower limit ρ of the formation density lb , and vice versa to obtain the upper limit ρ of the formation density ub

[0095] ρ lb =(1 - φ - V sh )ρ ma + V sh ρ sh + φρ mix

[0096] ρ ub = V ma ρ ma + V sh ρ sh =(1 - V sh )ρ ma + V sh ρ sh

[0097] In the formula, ρ ma , ρ sh , ρ mix respectively represent the density of the rock skeleton, the density of the mudstone, and the density of the mixture in the pores.

[0098] Similarly, the porosity in the formation can also be obtained from the density. The lower and upper limits of the porosity are:

[0099]

[0100] In the formula, φ lb represents the lower limit of the porosity; ρ b represents the measured density value.

[0101]

[0102] In the formula, φ ub represents the upper limit of the porosity; ρ min is the minimum value of the density measurement.

[0103] 2.3. From the functional relationship obtained in step 1, based on the values on the well logging curve and the corresponding relationship of the weighted average of the formation physical properties in the range above and below a certain depth point, determine the dynamic constraint range of each well logging curve:

[0104]

[0105]

[0106] where l ub * represents the upper limit of the dynamic range constraint; l lb * represents the lower limit of the dynamic range constraint; l i is the logging value of the current i-depth point; ε is the compensation value; Δ is the number of measurement points included in one sampling range of the instrument; max l represents the maximum value among all measurement points in the sampling range; min l represents the minimum value among all measurement points in the sampling range.

[0107] The above method for improving the longitudinal resolution accuracy of through-casing density measurement can improve the longitudinal resolution accuracy of through-casing formation density measurement and enable it to effectively identify thin layers in the formation.

[0108] Figure 5 shows the original density logging data and neutron porosity logging data, as well as the high-resolution density logging data and neutron porosity logging data processed by the above method for improving the resolution accuracy. From Figure 5 it can be seen that the original density and neutron porosity logging basically have no response to thin layers, while there are obvious fluctuations in the curves processed by the method for improving the resolution accuracy of this embodiment. It can be seen that the logging data obtained by the method for improving the resolution accuracy of this embodiment has an obvious response to thin layers.

[0109] In summary, it can be seen that the density and neutron porosity logging processed by the method for improving the resolution accuracy of this embodiment have significantly improved responses to thin layers in the formation, and their resolution has also significantly improved compared with the original logging. The improved density logging data and neutron logging data can effectively identify thin layers in the formation.

[0110] The above embodiments are only used to illustrate the technical method of the present invention and not to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those of ordinary skill in the art should understand that the technical method of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical method of the present invention.

Claims

1. A method for improving the longitudinal resolution accuracy of through-casing density logging ， It is characterized in that it includes the following steps: Step 1: According to the nuclear logging principle, deduce the functional relationship between the true formation physical parameters and the instrument measurement values in the casing environment. The true formation physical parameters include density and porosity; Assume that the multiple-scattered gamma rays detected by the detector contribute to the virtual source. Then, the gamma-ray intensity S contributed by the casing in a homogeneous geological formation to the detector s is as follows: S s = I v dTG(d, r 0 , μ 0 , μ) Where S s is the gamma ray intensity contributed by the t casing and the homogeneous geological formation to the detector; I v is the source strength of the virtual source, which consists of a gamma ray with source energy and no scattering; dT is the thickness of the volume element; G(d, r 0 , μ 0 , μ) represents an integral term, i.e., the casing thickness, geometric position, and physical parameters of the casing and the medium, where r 0 represents the position of the wellbore wall, and μ is the mass attenuation coefficient; When G(d, r 0 , μ 0 , μ) remains unchanged, the magnitude of S s is proportional to the volume and the unscattered source intensity I v at a distance r from the source after passing through the casing. Therefore, in multiple formations, the total formation density ρ s can be calculated using an inversion algorithm based on the ray intensity; ρ s = ρ 1 dT 1 G(d, r 0 , μ 0 , μ) + ρ 2 dT 2 G(d, r 0 , μ 0 , μ) + ρ 3 dT 3 G(d, r 0 , μ 0 , μ) where ρ 1 , ρ 2 , ρ 3 are the density values of different strata; Then the density at the m depth point can be expressed as: where ρ m is the measured value of the logging curve; w i is the weight coefficient of each geological layer; ρ i is the physical parameter of the casing and each formation; ρ m varies with the change of the depth point; Assume the vertical detection range of the detection instrument is VR, then the functional relationship between the casing, true formation density, porosity and the instrument measurement value is expressed as: In the formula, m(i) is the logging value at the i-th measurement point, and ρ(z) represents the true physical parameters of the casing and each formation within a detection range; Step 2: Based on the functional relationship obtained in Step 1, construct a sliding window matrix equation set based on depth information; Step 3: Solve the sliding window matrix equation set, and introduce the cross-constraint method of neutrons and density in post-casing measurement to limit the dynamic range of the solved logging curve, so as to obtain a constrained logging curve as the final logging data. The process includes: 3.1: According to the balance principle, establish a volume model in the formation: V ma +V sh +V oil +V gas +V water = 1 Where, V ma is the relative volume of the rock skeleton; V sh is the relative volume of the mudstone; V oil , V gas , V water respectively represent the relative volumes of oil, gas, and water in the rock pores, and the sum of their relative volumes is equal to the porosity φ; 3.

2. Calculate the lower limit ρ of the formation density and the upper limit ρ of the formation density, as well as the lower limit φ and the upper limit φ of the porosity, respectively, based on the inverse relationship between density and porosity in well logging interpretation and the volume model established in 2.

1. lb and the upper limit ρ of the formation density ub , the lower limit φ of the porosity lb and the upper limit φ ub ; 3.

3. Based on the functional relationship obtained in Step 1, introduce the lower limit ρ of the formation density obtained in 2.2 lb and the upper limit ρ of the formation density ub , the lower limit φ of the porosity lb and the upper limit φ ub , and determine the dynamic constraint range of the logging curve.

2. According to a method for improving the longitudinal resolution accuracy of through-casing density logging as described in claim 1 It is characterized in that in Step 2, before constructing the sliding window matrix equation set based on depth information, weight compensation is performed on the formation farthest from the center depth point within the detection volume.

3. According to a method for improving the longitudinal resolution accuracy of through-casing density logging as described in claim 1 It is characterized in that in Step 3, the least squares method is used to solve the sliding window matrix equation set.

4. According to a method for improving the longitudinal resolution accuracy of through-casing density logging as described in claim 1 It is characterized in that in the process of using the least squares method to solve in Step 3, the square of the error between the true measurement curve and the calculated logging curve is used as the loss function.

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