CN112859197A - Digital wellbore resistivity simulation method based on homogenized formation electromagnetic field theory - Google Patents
Digital wellbore resistivity simulation method based on homogenized formation electromagnetic field theory Download PDFInfo
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Abstract
The invention provides a digital wellbore resistivity simulation method based on a homogenized formation electromagnetic field theory, and belongs to the technical field of well logging interpretation and evaluation. Constructing a digital shaft based on the combination of the multi-scale digital core and the electrical imaging logging data and the formation element logging data; for each voxel in the obtained digital shaft, firstly calculating the mixed conductivity of clay bound water and free water in each voxel, then calculating the mixed resistivity of apparent formation water and a skeleton in each voxel, determining the conductivity of the voxel, and finally calculating the mixed conductivity of each voxel layer by layer according to the depth to obtain the conductivity of the digital shaft; and realizing a digital wellbore resistivity simulation method based on a homogenized formation electromagnetic field theory. The invention effectively solves the problem that the existing digital core is only limited to micro-scale research, provides a brand new thought for resistivity upscale simulation, expands the application range of the digital core and has strong practicability.
Description
Technical Field
The invention belongs to the technical field of well logging interpretation and evaluation, and relates to a digital wellbore resistivity simulation method based on a homogenized formation electromagnetic field theory.
Background
The electrical logging is still a necessary item for oil and gas exploration, the resistivity is particularly important in the aspects of oil and gas saturation calculation, oil and gas reservoir identification and reserve calculation, and the research on the electrical characteristics of rocks is still a hot spot. The existing digital core technology mainly focuses on the research on the physical characteristics at the microscale, neglects the scale effect of the digital core on the heterogeneous stratum, establishes a large-scale digital shaft model, and can better reflect the actual characteristics of the stratum. At present, the numerical simulation method of the resistivity of the digital rock core mainly comprises a finite element method, a kirchhoff circuit node method, a random walk method and a lattice Boltzmann method. The lattice Boltzmann method and the random walk method are both simulated based on the movement of microscopic ions and can only be used on a microscopic model with voxels as specific components; the finite element method and the kirchhoff circuit node method can simulate the resistivity of a digital shaft, but the equivalent resistivity of voxels in a model is difficult to determine, so that the error is large and the precision is not satisfactory. At present, no more perfect upscaling simulation method for digital wellbore resistivity exists.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a digital wellbore resistivity simulation method based on a homogenized formation electromagnetic field theory, solves the technical problem of digital wellbore resistivity upscaling simulation, and provides a brand new thought for resistivity upscaling simulation.
In order to achieve the purpose, the invention adopts the following technical scheme to realize the purpose:
the invention discloses a digital wellbore resistivity simulation method based on a homogenized formation electromagnetic field theory, which is characterized in that a digital wellbore is constructed based on a multi-scale digital core and combined with electrical imaging logging data and formation element logging data; for each voxel in the obtained digital shaft, firstly calculating the mixed conductivity of clay bound water and free water in each voxel, then calculating the mixed resistivity of apparent formation water and a skeleton in each voxel, determining the conductivity of the voxel, and finally calculating the mixed conductivity of each voxel layer by layer according to the depth to obtain the conductivity of the digital shaft; and realizing a digital wellbore resistivity simulation method based on a homogenized formation electromagnetic field theory.
Preferably, the method comprises the following steps:
step one, constructing a multi-scale digital core by adopting digital core data with different resolutions and different scales;
combining the multi-scale digital rock core obtained in the step one with electrical imaging logging data and formation element logging data to construct a digital shaft;
step three, calculating the mixed conductivity of clay bound water and free water in each voxel according to the digital shaft obtained in the step two aiming at each voxel in the obtained digital shaft to obtain the conductivity of visible formation water;
step four, calculating the mixed conductivity of the apparent formation water and the skeleton in each voxel according to the digital shaft obtained in the step two and the apparent formation water conductivity obtained in the step three to obtain the voxel conductivity of each voxel in each voxel;
and step five, according to the voxel conductivity of each voxel obtained in the step five, calculating the conductivity of the mixture of each voxel layer by layer according to the depth to obtain the conductivity of the digital shaft.
Preferably, the multi-scale digital core is realized by the following steps:
preparing a large-size rock core sample, and performing CT scanning; drilling a medium-size core sample from the large-size core sample, and improving the resolution to perform CT scanning; drilling a small-size core sample from the medium-size core sample, and improving the resolution again to perform CT or electron microscope scanning; obtaining digital core images with different resolutions and different scales; establishing a proportional relation curve of the gray value of the low-resolution image and the components through registration of digital core images with different resolutions and different scales and associated segmentation of the gray image, and mapping the relation curve to all the low-resolution images to obtain the multi-scale digital core.
Further preferably, in the second step, the constructing a digital wellbore by combining the multi-scale digital core obtained in the first step with the electrical imaging logging data and the formation element logging data includes the following steps:
s2.1, the grid size is consistent with the sampling interval of the electrical imaging logging data, and a pore and mineral data set is used as each voxel in each voxel;
s2.2, converting the dynamic resistivity distribution of the electric imaging logging into a porosity distribution image, and rolling the porosity distribution into a cylindrical surface by combining a well diameter curve;
s2.3, constructing a digital shaft porosity model by using a multi-point geostatistical algorithm by using the multi-scale digital rock core as a training image, the porosity distribution image obtained in the S2.2 as hard data and the logging porosity as soft data;
and S2.4, determining various mineral contents by utilizing various mineral contents obtained from the stratum element logging data and combining the digital shaft porosity model obtained in the step S2.3 to obtain a digital shaft mineral model, namely realizing the construction of the digital shaft.
Further preferably, the calculation formula of the apparent stratum water conductivity in the step three is as follows:
in the formula, σweConsidering the conductivity of formation water, S/m; sfwIs the free water saturation, decimal; scwClay irreducible water saturation, decimal; sigmafwIs free water conductivity, S/m; sigmacwIs the clay bound water conductivity, S/m.
Wherein preferably the free water saturation and the clay irreducible water saturation are measured by nuclear magnetic resonance logging T2And obtaining a spectrum, wherein the free water conductivity is obtained from water analysis data of the well or an adjacent well.
Preferably, the clay-bound water conductivity is obtained by inverse calculation of nuclear magnetic resonance and resistivity logging data of adjacent mudstone sections by an Archie formula, or is obtained by calculation of a regional empirical formula.
Further preferably, the calculation formula of the voxel conductivity in step four is:
in the formula, σMvoxelIs the conductivity of one voxel, S/m; lambda [ alpha ]MvoxelIs the dielectric constant of one voxel, F/m; lambda [ alpha ]weF/m, which is the dielectric constant of formation water; viIs the content, decimal fraction, of the ith component; lambda [ alpha ]iIs the dielectric constant of the ith component, F/m; phi is the formation porosity, decimal; sigmaweThe S/m is determined by the formation water conductivity.
Further preferably, the calculation formula of the digital wellbore conductivity in the fifth step is as follows:
in the formula, σtConductivity of the digital wellbore, S/m; k is 1, 2, 3, …, N is the total number of voxels of a digital well bore with a certain depth; sigmakIs the conductivity, S/m, of the kth voxel.
Compared with the prior art, the invention has the following beneficial effects:
the invention discloses a digital wellbore resistivity simulation method based on a homogenized formation electromagnetic field theory, wherein a digital wellbore is constructed through a multi-scale digital core and logging information, the scale effect caused by formation heterogeneity can be reduced, and a model can better reflect the actual formation characteristics; the electrical conductivity of a digital shaft voxel can be well determined by simulating the electrical resistivity through the homogenized formation electromagnetic field theory, and upscale simulation is carried out on the electrical resistivity of the digital shaft, so that the digital shaft electrical resistivity simulation method based on the homogenized formation electromagnetic field theory provides a digital shaft electrical resistivity construction method and an electrical resistivity simulation method, the requirement that the size and resolution of a sample are difficult to be considered by the conventional digital core is improved, and the problems that the scale effect is obvious in the heterogeneous formation and the difference between the simulation result and the actual characteristics of the formation is large are solved. The method can be used for forward modeling and inversion research of resistivity, provides a stratum model as real as possible for logging instrument simulation, verifies and simulates a logging curve by the real logging curve, and can guide the improvement of the existing logging instrument and the research and development of a new logging instrument. The method solves the problem that the conventional digital rock core is only limited to the research of micro scale, expands the application range of the digital rock core and has strong practicability.
Furthermore, a multi-scale digital core with the largest size and the highest resolution can be constructed by using core samples with different sizes, such as large, medium and small, and corresponding scanning resolutions, and the representativeness of the multi-scale digital core is better than that of a traditional digital core with a single resolution.
Furthermore, a digital shaft is constructed through the multi-scale digital core and the logging data, so that the macroscopic heterogeneity of the reservoir can be better reflected, and a stratum model is provided for subsequent physical attribute simulation, logging instrument simulation, interpretation evaluation and engineering application.
Furthermore, the conductivity of the mixed clay-bound water and free water in each voxel is calculated by adopting a nonlinear series-parallel theory of a homogenized formation electromagnetic theory, and the theoretical basis is firmer than that of a traditional double-water model.
Furthermore, the conductivity of each voxel after being mixed is calculated by adopting a homogenized formation electromagnetic theory, the calculation amount is less than that of the conventional finite element method and kirchhoff circuit node method, the calculation efficiency is high, and a brand new thought is provided for resistivity upscaling simulation.
Drawings
FIG. 1 is a core imaging slice diagram of tight sandstone with different resolutions according to an embodiment of the invention; wherein (a) is a resolution of 14 μm, (b) is a resolution of 3 μm, and (c) is a resolution of 50 nm.
Fig. 2 is a diagram of an electrophotographic image-to-porosity distribution result according to an embodiment of the present invention.
FIG. 3 is a graph of porosity and mineral models of a digital wellbore according to an embodiment of the present invention; wherein, (a) is porosity, (b) is clay, (c) is quartz, (d) is feldspar, and (e) is heavy mineral.
FIG. 4 is an XX well digital wellbore porosity and mineral modeling accuracy analysis diagram according to an embodiment of the invention.
FIG. 5 is a comparison of the effects of a simulation of complete water resistivity for a XX well according to embodiments of the invention.
FIG. 6 is a flow chart of a method for simulating the resistivity of a digital wellbore based on the homogenized formation electromagnetic field theory according to the present invention.
Detailed Description
In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious 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 derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the terms "first," "second," and the like in the description and claims of the present invention and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are capable of operation in sequences other than those illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
The invention discloses a digital wellbore resistivity simulation method based on a homogenized formation electromagnetic field theory, which comprises the following steps of:
step one, constructing a multi-scale digital core by adopting digital core data with different resolutions and different scales;
step two, constructing a digital shaft by combining the multi-scale digital core with electrical imaging logging data and formation element logging data;
step three, according to the digital shaft, aiming at each voxel in the obtained digital shaft, calculating the mixed conductivity of clay bound water and free water in each voxel, namely the apparent formation water conductivity;
step four, calculating the mixed conductivity of the apparent formation water and the skeleton in each voxel according to the conductivity of the digital shaft and the apparent formation water, and obtaining the voxel conductivity of each voxel in each voxel;
and step five, according to the voxel conductivity, calculating the conductivity of each voxel mixture layer by layer according to the depth, thereby obtaining the conductivity of the digital shaft.
Specifically, the method for constructing the multi-scale digital core in the first step is realized by the following steps:
preparing a large-size rock core sample, and performing CT scanning; drilling a medium-size core sample from the large-size core sample, and improving the resolution to perform CT scanning; drilling a small-size core sample from the medium-size core sample, improving the resolution again to perform CT or electron microscope scanning, and obtaining digital cores with different resolutions and different scales by utilizing the characteristic that the size of the sample is in inverse proportion to the resolution; establishing a proportional relation curve of the gray value of the low-resolution image and the components through registration of the digital core images with different resolutions and associated segmentation of the gray image, and mapping the relation curve to all the low-resolution images to obtain the multi-scale digital core.
Specifically, the size range of a large-size core sample is 25-100 mm, the size range of a medium-size core sample is 5-10 mm, and the size range of a small-size core sample is 1-5 mm. Wherein, the corresponding scanning resolution is 14-60 microns, 3-10 microns and 50-100 nanometers respectively.
Specifically, based on the fact that the rock under the stratum is composed of a pore space and a skeleton (namely various minerals), the digital shaft is composed of a porosity model and a mineral model, and the method for constructing the digital shaft in the second step comprises the following steps:
s2.1 defines the data framework of a digital wellbore as: the grid size is consistent with the sampling interval of the electrical imaging logging data, and each voxel is a pore and mineral data set;
s2.2, converting the dynamic resistivity distribution of the electric imaging logging into a porosity distribution image, and rolling the porosity distribution into a cylindrical surface by combining a well diameter curve;
and S2.3, constructing a digital shaft porosity model by using a multi-scale digital core as a training image, the porosity distribution image obtained in the S2.2 as hard data, the logging porosity as soft data and a multi-point geostatistics algorithm.
And S2.4, determining various mineral contents by utilizing various mineral contents obtained from the stratum element logging data and combining the digital shaft porosity model to obtain a digital shaft mineral model, namely realizing the construction of the digital shaft.
Preferably, in S2.1, the grid size and the sampling interval of the electrical imaging logging data are consistent to be 1-5 mm. Specifically, the calculation formula of apparent formation water conductivity in the third step is as follows:
in the formula, σweConsidering the conductivity of formation water, S/m; sfwIs the free water saturation, decimal; scwClay irreducible water saturation, decimal; sigmafwIs free water conductivity, S/m; sigmacwIs the clay bound water conductivity, S/m. Wherein, the saturation is percentage content, sometimes the unit of industry is%, the value is between 0-100, sometimes the decimal, the value is between 0-1.
Specifically, the free water saturation and the clay irreducible water saturation are measured by a nuclear magnetic resonance logging T2Obtaining a spectrum, wherein the free water conductivity is obtained from water analysis data of the well or an adjacent well; the conductivity of the clay bound water is obtained by inverse calculation of nuclear magnetic resonance and resistivity logging data of adjacent mudstone sections by an Archie formula, and can also be obtained by calculation of a regional empirical formula.
Specifically, the voxel conductivity calculation formula in step four is as follows:
in the formula, σMvoxelIs the conductivity of one voxel, S/m; lambda [ alpha ]MvoxelIs the dielectric constant of one voxel, F/m; lambda [ alpha ]weF/m, which is the dielectric constant of formation water; viIs the content, decimal fraction, of the ith component; lambda [ alpha ]iIs the dielectric constant of the ith component, F/m; phi is the formation porosity, decimal; sigmaweThe S/m is determined by the formation water conductivity.
Specifically, in the fifth step, the calculation formula of the conductivity of the digital wellbore is as follows:
in the formula, σtConductivity of the digital wellbore, S/m; k is 1, 2, 3, …N, N is the total number of voxels of a digital shaft with a certain depth; sigmakIs the conductivity, S/m, of the kth voxel.
The present invention will now be described in further detail with reference to the following figures and specific examples, which are intended to be illustrative, but not limiting, of the invention.
In this embodiment, a standard column sample with a diameter of 2.5 cm is taken to perform low-resolution (14 micron) CT scanning, and a small sample with a diameter of 5mm is drilled from the standard sample to perform high-resolution (3 micron) CT scanning, so as to obtain 2 CT image data with different dimensions and different resolutions. For the low-permeability tight sandstone reservoir in this embodiment, the 3-micron CT cannot identify the micropores and the throats, and further improves the resolution, and performs wide-ion-beam scanning electron microscope (BIB-SEM) imaging with the resolution of 50nm on a small sample (the BIB-SEM electron microscope has a large scanning field of view, and does not need to reduce the size of the rock sample), so as to obtain 3 kinds of sample data with different resolutions (see fig. 1).
And (3) homing the core images with different resolutions by using an image registration algorithm, and coordinating the small-size images to the large-size images to realize the one-to-one correspondence of the spatial positions of the images and establish the relevance between the images. And then carrying out multi-scale image segmentation on the 3-resolution image. And sequentially carrying out image segmentation on the images with different resolutions according to the resolution from high to low, and establishing a quantitative relation between the image gray value and the porosity and the mineral content according to the image registration relation to obtain the digital core model of the rock sample with each scale. And finally, combining image registration, fusing pores with different scales and minerals with different components by using multi-scale association segmentation, and constructing a multi-scale digital core model.
Based on a multipoint geostatistics Filtersmi algorithm, the resistivity dynamic graph data of the electric imaging logging is used as a training object, and the blank strips are filled to form a complete borehole wall resistivity image. The shallow lateral resistivity curve is used for scaling the electrical imaging data, the electrical imaging data are converted into a flushing zone resistivity image, and the resistivity is converted into the apparent porosity by using an Archie's formula. And (3) linearly scaling the apparent porosity by taking the total porosity as constraint, calculating to obtain the real porosity value of each point, converting the resistivity distribution into a porosity distribution image, and finally combining a well diameter curve to roll the porosity distribution into a three-dimensional cylinder (see figure 2).
And determining the transverse scale of the built well bore on the basis of finely dividing the stratum, and establishing a geometric model of the whole well bore. The built digital shaft model is a regular voxel model, grid division is consistent with voxel resolution, and the voxel resolution is consistent with electrical imaging resolution. Because the grid is large in size, one grid may contain a plurality of pores and a plurality of minerals, and each voxel is a pore and mineral data set, and the pores and the distribution proportion of each mineral component replace a single component represented by the original digital core grid.
And (3) combining the multi-scale digital rock core and the electrical imaging logging data, and constructing a digital wellbore porosity model of each layer by using a Filtersmin algorithm in multipoint geostatistics. The training image is from a multi-scale digital core model, the hard data is a porosity two-dimensional image rolled into a cylindrical surface, and the soft data is a logging porosity curve and used for constraining the porosity distribution of each layer. And determining various mineral contents by using various mineral contents obtained from the formation element logging data and combining the established digital shaft porosity model by using an optimization method to obtain a mineral model of the digital shaft, namely the digital shaft model. Wherein the optimization method comprises: determining various mineral contents by an optimization method by minimizing the error between the average mineral content of each voxel and various mineral contents obtained from the logging data of the formation elements; this is because each voxel data consists of porosity and various minerals, porosity + total mineral content being 1; by knowing the porosity model, the total mineral content of each voxel is determined, and the various mineral contents are determined by using the formation element logging data.
A digital wellbore model for the XX well was constructed using the method described above, with a diameter of 0.5m, a length of 11m, and a voxel resolution of 5mm (see FIG. 3). FIG. 4 is a graph showing the comparative effect of each component of a digital wellbore model in an XX well 1614-1625m interval, wherein the relative error between the porosity of the model and the logging porosity is 3.16% (see Table 1), and the relative error between the porosity of the model and the porosity of helium in a laboratory is 8.00%.
TABLE 1XX well digital wellbore modeling error analysis
Each voxel in the conventional digital core grid model is a specific component, and a corresponding initial resistivity value can be assigned according to the specific component. The digital well bore model mesh established by the invention is coarse, one voxel comprises a plurality of pores and a plurality of minerals, so that each voxel is defined as a pore and mineral data set, and the resistivity of each voxel cannot be directly determined. The conductivity calculation method based on the mixture is combined with a sand shale stratum model, firstly, the conductivity of the mixture of clay bound water and free water in each voxel is calculated to serve as the conductivity of apparent stratum water, then the conductivity of the mixture of dielectric media and the apparent stratum water in each voxel is calculated to serve as the conductivity of the voxel, and finally the conductivity of the mixture of each voxel in the digital shaft is calculated layer by layer according to the depth, namely the conductivity of the digital shaft.
According to the electromagnetic field theory of the homogenized stratum, the electric conduction mode of the actual stratum cannot be simply seen as that all mixtures are in parallel or in series connection, the stratum is simplified into a mode that a series of thin sheets are superposed, the interior of each thin sheet is in parallel connection, and then each thin sheet is in series connection and conducts to form a nonlinear series-parallel connection structure. Referring to a double-water model, clay bound water and free water are only used for conducting electricity in the sand shale stratum and are a mixture of a conductor and a conductor, and the conductivity of the mixed two kinds of water is calculated to be used as the apparent stratum water conductivity. For a fully hydrated formation, we obtain:
in the formula, σweConsidering the conductivity of formation water, S/m; sfwIs the free water saturation, decimal; scwClay irreducible water saturation, decimal; sigmafwIs free water conductivity, S/m; sigmacwIs the clay bound water conductivity, S/m.
The free water saturation and the clay bound water saturation are measured by nuclear magnetic resonance well logging T2Obtaining a spectrum, wherein the free water conductivity is obtained from water analysis data of the well or an adjacent well; the conductivity of the clay bound water is obtained by inverse calculation of nuclear magnetic resonance and resistivity logging data of adjacent mudstone sections by an Archie formula, and can also be obtained by calculation of a regional empirical formula.
Each voxel in the digital well bore can be used as a unit of the stratum, namely a stratum water and skeleton mixture, namely a conductor and insulator mixture, each voxel is considered to be an isotropic mixture, and when the rock is completely hydrated, the calculation formula of the conductivity of the voxel can be obtained as follows:
in the formula, σMvoxelIs the conductivity of one voxel, S/m; lambda [ alpha ]MvoxelIs the dielectric constant of one voxel, F/m; lambda [ alpha ]weF/m, which is the dielectric constant of formation water; viIs the content, decimal fraction, of the ith component; lambda [ alpha ]iIs the dielectric constant of the ith component, F/m; phi is the formation porosity, decimal.
The conductivity of free water and clay bound water of the same sand body in the stratum is unchanged, but the proportion of the two kinds of water is changed, and the conductivity of stratum water is changed according to different voxels. In addition, the proportions of the components of different voxels are different, so that the conductivities of the voxels are different, the digital wellbore can be formed by mixing the digital wellbore as a series of voxels with different conductivities, and the conductivity calculation formula of the digital wellbore is as follows:
in the formula, σtConductivity of the digital wellbore, S/m; k is 1, 2, 3, …, N is the total number of voxels of a digital well bore with a certain depth; sigmakIs the conductivity, S/m, of the kth voxel.
The method is used for simulating the XX well resistivity, the free water resistivity of the well section is 0.21 omega-m, and the clay bound water resistivity is 0.083 omega-m. FIG. 4 is a comparison of the XX well simulation effect, and the 7 th trace is the clay-bound water and free water porosity calculated by NMR logging; the 8 th path is the comparison of the porosity of the digital shaft model with the results of well logging and laboratory analysis; and the 9 th channel is the comparison of the simulated complete water-bearing resistivity and the logging data inversion complete water-bearing resistivity, the consistency of the change rules of the simulated complete water-bearing resistivity and the logging data inversion complete water-bearing resistivity is good, and the average relative error is 7.81 percent.
As shown in FIG. 6, a flow chart of a method for simulating the resistivity of a digital wellbore based on the theory of homogenized formation electromagnetic fields is provided for an embodiment.
Finally, it should be noted that the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, and although the present invention has been described in detail with reference to examples, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, which should be covered by the claims of the present invention.
The above-mentioned contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modification made on the basis of the technical idea of the present invention falls within the protection scope of the claims of the present invention.
Claims (9)
1. A digital wellbore resistivity simulation method based on a homogenized formation electromagnetic field theory is characterized in that a digital wellbore is constructed based on a multi-scale digital core and combined with electrical imaging logging data and formation element logging data; for each voxel in the obtained digital shaft, firstly calculating the mixed conductivity of clay bound water and free water in each voxel, then calculating the mixed resistivity of apparent formation water and a skeleton in each voxel, determining the conductivity of the voxel, and finally calculating the mixed conductivity of each voxel layer by layer according to the depth to obtain the conductivity of the digital shaft; and realizing a digital wellbore resistivity simulation method based on a homogenized formation electromagnetic field theory.
2. The method of claim 1 for simulating the resistivity of a digital wellbore based on the theory of homogenized formation electromagnetic fields, comprising the steps of:
step one, constructing a multi-scale digital core by adopting digital core data with different resolutions and different scales;
combining the multi-scale digital rock core obtained in the step one with electrical imaging logging data and formation element logging data to construct a digital shaft;
step three, calculating the mixed conductivity of clay bound water and free water in each voxel according to the digital shaft obtained in the step two aiming at each voxel in the obtained digital shaft to obtain the conductivity of visible formation water;
step four, calculating the mixed conductivity of the apparent formation water and the skeleton in each voxel according to the digital shaft obtained in the step two and the apparent formation water conductivity obtained in the step three to obtain the voxel conductivity of each voxel in each voxel;
and step five, according to the voxel conductivity of each voxel obtained in the step five, calculating the conductivity of the mixture of each voxel layer by layer according to the depth to obtain the conductivity of the digital shaft.
3. The method for simulating the resistivity of the digital wellbore based on the homogenized formation electromagnetic field theory is characterized in that the multi-scale digital core is realized by the following steps:
preparing a large-size rock core sample, and performing CT scanning; drilling a medium-size core sample from the large-size core sample, and improving the resolution to perform CT scanning; drilling a small-size core sample from the medium-size core sample, and improving the resolution again to perform CT or electron microscope scanning; obtaining digital core images with different resolutions and different scales;
establishing a proportional relation curve of the gray value of the low-resolution image and the components through registration of digital core images with different resolutions and different scales and associated segmentation of the gray image, and mapping the relation curve to all the low-resolution images to obtain the multi-scale digital core.
4. The method for simulating the resistivity of the digital wellbore based on the homogenized formation electromagnetic field theory as claimed in claim 2, wherein in the second step, the multi-scale digital core obtained in the first step is combined with the electrical imaging logging data and the formation element logging data to construct the digital wellbore, and the method comprises the following steps:
s2.1, the grid size is consistent with the sampling interval of the electrical imaging logging data, and a pore and mineral data set is used as each voxel in each voxel;
s2.2, converting the dynamic resistivity distribution of the electric imaging logging into a porosity distribution image, and rolling the porosity distribution into a cylindrical surface by combining a well diameter curve;
s2.3, constructing a digital shaft porosity model by using a multi-point geostatistical algorithm by using the multi-scale digital rock core as a training image, the porosity distribution image obtained in the S2.2 as hard data and the logging porosity as soft data;
and S2.4, determining various mineral contents by utilizing various mineral contents obtained from the stratum element logging data and combining the digital shaft porosity model obtained in the step S2.3 to obtain a digital shaft mineral model, namely realizing the construction of the digital shaft.
5. The method for simulating the resistivity of the digital wellbore based on the homogenized formation electromagnetic field theory as claimed in claim 2, wherein the calculation formula of the conductivity of the formation water in the step three is as follows:
in the formula, σweConsidering the conductivity of formation water, S/m; sfwIs the free water saturation, decimal; scwClay irreducible water saturation, decimal; sigmafwIs free water conductivity, S/m; sigmacwIs the clay bound water conductivity, S/m.
6. The method of claim 5, wherein the free water saturation and the clay irreducible water saturation are measured by NMR logging (T) for the homogenized formation electromagnetic field theory2And obtaining a spectrum, wherein the free water conductivity is obtained from water analysis data of the well or an adjacent well.
7. The method of claim 5, wherein the clay-bound water conductivity is obtained by inverse calculation of NMR and resistivity well logging data of adjacent mudstone sections by an Archie's formula or by a regional empirical formula.
8. The method for simulating the resistivity of the digital wellbore based on the electromagnetic field theory of the homogenized formation according to claim 2, wherein the calculation formula of the voxel conductivity in the fourth step is as follows:
in the formula, σMvoxelIs the conductivity of one voxel, S/m; lambda [ alpha ]MvoxelIs the dielectric constant of one voxel, F/m; lambda [ alpha ]weF/m, which is the dielectric constant of formation water; viIs the content, decimal fraction, of the ith component; lambda [ alpha ]iIs the dielectric constant of the ith component, F/m; phi is the formation porosity, decimal; sigmaweThe S/m is determined by the formation water conductivity.
9. The method of claim 2, wherein the equation for calculating the conductivity of the digital wellbore in step five is as follows:
in the formula, σtConductivity of the digital wellbore, S/m; k is 1, 2, 3, …, N is the total number of voxels of a digital well bore with a certain depth; sigmakIs the conductivity, S/m, of the kth voxel.
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