A method for quickly calculating the response of anisotropic induction logging in an inclined shaft in a invaded formation

Abstract

The application discloses a kind of inclined shaft anisotropy has the fast calculation method of invasion stratum induction logging response, it is related to the technical field of electrical logging in oil exploration and development, comprising: constructing three-dimensional heterogeneous stratum model containing inclined shaft anisotropy invasion;Extracting invasion zone longitudinal model and original stratum longitudinal model;Considering induction logging instrument parameters, using semi-analytical algorithm and 0-dimensional inversion, obtain equivalent stratum model;Point by point construction radial heterogeneous model;In turn calculate the response of induction logging instrument different source distance and frequency operating mode, each mode response combination obtains induction logging synthetic apparent resistivity curve;Through all measurement depth points point by point cycle calculation, finally obtain the logging response of whole well section.The inclined shaft anisotropy has the hierarchical superposition of stratum decomposition for invasion, by combining semi-analytical solution and neural network algorithm, induction logging response calculation speed is improved more than three orders of magnitude.

Description

Technical Field

[0001] This invention relates to the field of electrical logging technology in petroleum exploration and development, and belongs to the category of forward modeling methods for electrical logging. In particular, it relates to a rapid calculation method for the response of anisotropic intrusive formation induction logging in deviated wells. Background Technology

[0002] Induction logging is an essential method for resistivity measurement in complex oil and gas exploration and development, offering advantages such as a large detection range, high resolution, and sensitivity to intrusion. Compared to the measurement environment of vertical wells, the anisotropic effects are aggravated in deviated wells, with the influences of intrusion, layer thickness, and well inclination coupling together, leading to a more complex induction logging response. Forward modeling is the foundation for the qualitative interpretation and quantitative evaluation of this type of logging response. However, deviated well 3D forward modeling suffers from high dimensionality, large memory consumption, and low efficiency. In particular, induction logging forward modeling involves the calculation of array source distance and frequency, resulting in excessive computational load, which severely restricts the processing and inversion of this type of logging data. In recent years, domestic and international research has also attempted to introduce deep learning and other methods to accelerate the forward modeling of deviated well induction logging responses. However, the excessive number of 3D model parameters, the difficulty in generating databases, and the weak generalization ability mean that intelligent and rapid 3D forward modeling of induction logging remains unrealistic.

[0003] Therefore, there is an urgent need to develop a rapid calculation method for the three-dimensional formation induction logging response of inclined wells. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention discloses a rapid calculation method for induction logging response in anisotropic invasive formations in deviated wells. This method changes the concept of strict numerical forward modeling of three-dimensional formations, and improves the calculation efficiency by more than a thousand times by decomposing longitudinal and transverse influencing factors and combining rapid calculation methods for longitudinal and radial stratification logging responses.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A rapid calculation method for induction logging response in anisotropic formations of deviated wells includes the following steps:

[0007] s1. Considering complex formations and wellbore environments, and taking into account vertical influencing factors such as well inclination, layer thickness, and uniaxial resistivity anisotropy, as well as radial influencing factors such as instrument structure, wellbore, and symmetrical mud invasion, a three-dimensional heterogeneous formation model M with anisotropic invasion and deviated wells is constructed. It is assumed that the formation consists of N layers, with each vertical formation interface being parallel to the others. Model M is described by 6N+3 parameters, including: the original formation resistivity R of each layer. th,i R tv,i Intrusion resistivity R xoh,i R xov,i , Intrusion depth DI i Layer thickness H i A total of 6N formation parameters; mud filtrate resistivity Rmf , wellbore radius r and wellbore inclination angle φ.

[0008] s2. Extract the invaded zone longitudinal model M xo and the virgin formation longitudinal model M t from the model M xo , M t , respectively, by considering only the longitudinal formation heterogeneity, where M t is a layered uniaxial anisotropic formation, and the resistivity of each layer is taken as the corresponding invaded zone / virgin formation value in M th,i . Take M tv,i as an example, which is described by 3N+1 parameters: the virgin formation resistivity R i of each layer, layer thickness H xo , a total of 3N formation parameters, and one global parameter, wellbore inclination angle φ.

[0009] s3. Calculate the apparent resistivity and of M t and M t , respectively, by considering the induction logging instrument frequency and source spacing parameters, using a semi-analytical algorithm, and combining 0D inversion to obtain the equivalent invaded zone model M , the equivalent virgin formation model M , the equivalent invaded zone resistivity R , and the equivalent virgin formation resistivity R , which take into account the wellbore inclination and longitudinal formation heterogeneity;

[0010] s4. Use the equivalent model obtained in step s3 to construct a calculation model that takes into account the radial heterogeneity distribution at the current sampling point, and combine the radial layered medium response calculation method to approximate the induction logging response of three-dimensional heterogeneous formations;

[0011] s5. Set the source spacing and frequency parameters under different instrument operating modes in turn, execute steps s3 and s4, combine the responses of each mode, and obtain the induction logging synthetic apparent resistivity response;

[0012] s6. Finally, obtain the induction logging synthetic apparent resistivity response of the anisotropic invaded formation of the entire wellbore section of the deviated well by cyclically executing steps s3 to s5 for all measured depth points.

[0013] Optionally, the step s3 is specifically:

[0014] s3.1 Set the induction logging instrument frequency and source spacing parameters, and ignore the coil size effect by regarding the transmitting and receiving coils as point transmitting and point receiving;

[0015] s3.2 Calculate the apparent resistivity and of M t , respectively, by considering the induction logging instrument frequency and source spacing parameters, using a semi-analytical algorithm, and combining 0D inversion to obtain the equivalent invaded zone model M , the equivalent virgin formation model M , the equivalent invaded zone resistivity R , and the equivalent virgin formation resistivity R , which take into account the wellbore inclination and longitudinal formation heterogeneity;, considering the relative dip angle between the instrument and the formation, the apparent resistivity of the original formation at the current logging point is calculated by using a one-dimensional semi-analytical forward method ;

[0016] s3.3 A homogeneous isotropic medium is constructed, a 0-dimensional medium analytical formula and a gradient optimization algorithm are combined, the resistivity of the isotropic medium is continuously updated, the forward result is consistent with the measured apparent resistivity , and the resistivity of the homogeneous medium is determined , is the equivalent resistivity at the current point, which covers the influence of the resistivity of the original formation, the layer thickness and the dip angle;

[0017] s3.4 A longitudinal model M xo of the invaded zone is obtained by one-dimensional forward calculation to obtain the apparent resistivity of the invaded zone , step s3.3 is executed, and the equivalent resistivity of the invaded zone at the current logging point is obtained by inversion , which covers the influence of the resistivity of the invaded zone, the layer thickness and the dip angle.

[0018] Optionally, the step s4 is specifically:

[0019] s4.1 A cylindrical layered radial heterogeneous calculation model M r is constructed, which includes a borehole, an instrument and a stepped invasion, wherein the hole diameter and the invasion depth take the corresponding parameter values at the current logging point, and the resistivity of the original formation and the resistivity of the invaded zone are set as obtained in step s3 ;

[0020] s4.2 Five radial heterogeneous formation control parameters are sequentially cycled to obtain a series of input calculation models T, wherein the hole diameter and the invasion depth are linearly discrete, the mud resistivity, the resistivity of the invaded zone and the resistivity of the original formation are logarithmically discrete, and the mode matching algorithm is combined with the instrument frequency and the source distance parameters to obtain the apparent conductivity of the induction logging corresponding to each calculation model ;

[0021] s4.3 Based on the theory of Doll geometric factor, the radial integral contribution analytical formula of single-transmit-single-receive coil system is obtained, , g r represents the radial differential geometric factor, represents the conductivity at r, and the apparent conductivity without frequency influence is determined by combining the model parameters shown in step s4.2 ;

[0022] s4.4 Taking the input calculation model T as input, - ​For output, the neural network is trained to establish a mapping relationship between the radial heterogeneous model and the apparent conductivity residual, and the weight coefficients of each layer of neurons are obtained;

[0023] s4.5 input and The apparent conductivity without frequency influence is calculated by using step s4.3, the neural network weight coefficients obtained by step s4.4 are combined to calculate the apparent conductivity residual; the apparent conductivity without frequency influence and the apparent conductivity residual are added to obtain the induction logging apparent resistivity, which further considers the influence of radial heterogeneity, and realizes the approximate calculation of the induction logging response of the three-dimensional heterogeneous formation.

[0024] The beneficial effects of the present application are that the present application establishes a three-dimensional heterogeneous formation model containing well deviation, layer thickness, resistivity anisotropy, borehole and axisymmetric mud invasion; two sets of longitudinal heterogeneous formation models are extracted from the three-dimensional formation model for the original formation and the invaded zone; considering the induction logging instrument parameters, the semi-analytical algorithm and 0D inversion are used to obtain an equivalent formation model considering the influence of well deviation and formation longitudinal heterogeneity; for any sampling point, a calculation model considering radial heterogeneity is constructed point by point to efficiently approximate the induction logging response of the three-dimensional heterogeneous formation; the responses of the induction logging instrument in different source distance and frequency modes are calculated in turn, and the combined responses of each mode obtain the induction logging synthetic apparent resistivity curve; through the point-by-point cyclic calculation of all measurement depth points, the logging response of the whole well section is finally obtained. The present application breaks through the framework of traditional three-dimensional numerical forward modeling, decomposes the anisotropic invaded formation of the inclined well into hierarchical superposition of longitudinal heterogeneity and radial heterogeneity, and improves the calculation speed of the induction logging response by more than three orders of magnitude by combining semi-analytical solution and neural network algorithms, thereby providing technical support for three-dimensional real-time inversion processing of data. BRIEF DESCRIPTION OF DRAWINGS

[0025] Figure 1 The flow chart of the present application is shown in the figure.

[0026] Figure 2 The schematic diagram of the present application is shown in the figure.

[0027] Figure 3 The schematic diagram of the present application is shown in the figure.

[0028] Figure 4 The anisotropic invaded formation of the inclined well is shown in the figure.

[0029] Figure 5 The equivalent invaded zone resistivity and the equivalent original formation resistivity value are shown in the figure.

[0030] Figure 6 The apparent resistivity values of each sub-array in different well deviation angles for an embodiment of the present application are shown in the table below.

[0031] Figure 7 The anisotropic Oklahoma model for an embodiment of the present application is shown in the table below.

[0032] Figure 8 The anisotropic Oklahoma model for an embodiment of the present application is shown in the table below. DETAILED DESCRIPTION

[0033] In order to make the objectives, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of the present application. Therefore, the following detailed description of the embodiments of the present application provided in the accompanying drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of the present application.

[0034] A fast calculation method of anisotropic invaded formation induction logging response in deviated well, as shown in FIG. 1, comprises the following steps: Figure 1

[0035] s1. Constructing a deviated well anisotropic invaded formation model M containing well deviation, layer thickness, uniaxial anisotropy of resistivity, borehole and symmetrical mud invasion. The following will be further described by taking the formation model and HDIL instrument shown in FIG. 2 as an example. Figure 4

[0036] Figure 4 The three-layer deviated well anisotropic invaded formation calculation model M shown in FIG. 3, each layer has a thickness of 5 m, the model M is described by 21 parameters, two formation interfaces Z1, Z2; the invasion zone resistivity is assigned as R xoh,1 = 3 Ω·m, R xov,1 = 12 Ω·m, R xoh,2 = 8 Ω·m, R xov,2 = 32 Ω·m, R xoh,3 = 3 Ω·m, R xov,2 = 12 Ω·m; the original formation resistivity is assigned as R th,1 = 5 Ω·m, R tv,1 = 20 Ω·m, R th,2 = 10 Ω·m, R​​tv,2 =40Ω·m, R th,3 =5Ω·m, R tv,3 =20Ω·m; the penetration depth of all three layers is 0.5m; the mud resistivity is assigned as R. mf =3Ω·m, well diameter 8 inches, well inclination angle 60°.

[0037] s2. Targeting Figure 4 The stratigraphic model shown uses, for example Figure 2 The decomposition and extraction process shown extracts the longitudinal model M of the intrusion zone. xo And the original vertical stratigraphic model M t .

[0038] s3. Considering the HDIL induction logging instrument, when the source distance is 1.524m and the frequency is 30kHz, calculate M using a layered semi-analytical algorithm. xo and M t Corresponding apparent resistivity and By combining 0-dimensional inversion, the equivalent resistivity of the intrusion zone, considering the effects of well deviation and vertical formation heterogeneity, is obtained. and equivalent original formation resistivity .

[0039] Step s4 will be described in further detail below:

[0040] s3.1 When the source distance is 1.524m, the frequency is 30kHz, and the coil radius is 0.0445m, the influence of coil size is ignored, and the transmitting and receiving coils are regarded as point transmission and point reception.

[0041] s3.2 Vertical model M of the undisturbed strata t Using a one-dimensional semi-analytical forward modeling method, the apparent resistivity of the original formation at the current logging point was calculated. Taking the apparent resistivity of the untouched formation at some well logging points as an example: when the vertical depth is 2.5m, =8.887Ω·m, when the vertical depth is 7.5m, =15.748Ω·m, when the vertical depth is 12.5m, =8.887Ω·m;

[0042] s3.3 Constructs a homogeneous isotropic medium, and combines the analytical expression of the 0-dimensional medium with a gradient optimization algorithm to continuously update the resistivity of the isotropic medium, so that the forward modeling results are consistent with the measured apparent resistivity. Consistent, determining the resistivity of a homogeneous medium Taking the equivalent original formation resistivity at some well logging points as an example: when the vertical depth is 2.5m, = 7.772 Ω·m, when the vertical depth is 7.5m, = 14.282 Ω·m, when the vertical depth is 12.5m, = 7.772 Ω·m;

[0043] s3.4 on the longitudinal model M of the invasion zone xo , the apparent resistivity of the invasion zone is obtained by one-dimensional forward , select the apparent resistivity of the invasion zone at some logging points as an example: when the vertical depth is 2.5m, = 5.565 Ω·m, when the vertical depth is 7.5m, = 12.553 Ω·m, when the vertical depth is 12.5m, = 5.565 Ω·m; execute step s3.3, and the equivalent invasion zone resistivity at the current logging point is obtained by inversion , select the equivalent invasion zone resistivity at some logging points as an example: when the vertical depth is 2.5m, = 4.770 Ω·m, when the vertical depth is 7.5m, = 11.240 Ω·m, when the vertical depth is 12.5m, = 4.770 Ω·m.

[0044] s4. Using the equivalent model obtained in step s3, using the equivalent invasion zone resistivity and the equivalent original formation resistivity , a calculation model considering the radial heterogeneous distribution of the current sampling point is constructed, combined with the response calculation method of radial layered medium, to efficiently approximate the response of three-dimensional heterogeneous formation induction logging.

[0045] s5. Set the source distance and frequency parameters under different working modes of the instrument in turn, execute steps s3 and s4, and combine the responses of each mode, as shown in Figure 6 , to obtain the synthetic apparent resistivity response of induction logging.

[0046] s6. By cyclically executing steps s3 to s5 on all measured depth points, the synthetic apparent resistivity response of induction logging of the anisotropic invaded formation of the whole well section of the deviated well is finally obtained, as shown in Figure 6 , from left to right, the apparent resistivity values of each subarray when the well deviation angles are 0°, 60°, and 89°, respectively. Figure 7 and Figure 8respectively represent the anisotropic Oklahoma model and the model subarray response at different hole angles, it can be seen that the greater the hole angle, the greater the influence of anisotropy on the subarray response, the subarray curve appears to be lifted and the curve separation degree is larger. The calculation method of the present application is highly consistent with the simulation results of the three-dimensional finite element algorithm, the maximum relative error is not more than 3.1%, and the average error is 1.4%, which verifies the accuracy and applicability of the method of the present application. For the anisotropic complex three-dimensional heterogeneous formation model, the three-dimensional finite element algorithm forward time is 84 hours, and the calculation method of the present application takes about 100s, and the speed is improved by about 3000 times.

[0047] Of course, the above description is not a limitation on the present application, and the present application is not limited to the above examples, and the changes, modifications, additions or replacements made by the skilled in the art within the essential scope of the present application should also belong to the protection scope of the present application.

Claims

1. A method for fast calculation of deviated well anisotropic invaded formation induction logging response, characterized in that, Comprise the following steps: s1. For complex formation and borehole environment, considering longitudinal and radial factors, build a three-dimensional anisotropic invaded formation model M containing deviated wells; s2. For the invaded zone and the virgin formation, respectively, only considering the longitudinal formation heterogeneity effect, extract the invaded zone longitudinal model M xo and the virgin formation longitudinal model M t , M xo / M t are layered uniaxial anisotropic formations, and the resistivity of each layer takes the corresponding value in M for the invaded zone / virgin formation. s3. Considering the induction logging instrument frequency and source distance parameters, using a semi-analytical algorithm, M xo and M t The corresponding apparent resistivity and , combined with 0-dimensional inversion, obtain the equivalent invasion zone model considering the effects of well deviation and formation longitudinal heterogeneity , the equivalent virgin formation model , the equivalent invasion zone resistivity and the equivalent virgin formation resistivity ; s4. Using the equivalent model obtained in step s3, construct a calculation model considering the radial heterogeneous distribution of the current sampling point, combine the radial layered medium response calculation method, and approximate the three-dimensional heterogeneous formation induction logging response; s5. Set the source distance and frequency parameters under different working modes of the instrument in turn, execute steps s3 and s4, combine the responses of each mode, and obtain the synthetic apparent resistivity response of the induction logging; s6. Through the cyclic execution of steps s3 to s5 for all measurement depth points, the final induction logging synthetic apparent resistivity response of the full well section of the anisotropic invaded formation of the deviated well is obtained.

2. The method for fast calculation of the response of anisotropic induction logging in deviated well in invaded formations according to claim 1, characterized in that, The step s3 is specifically: s3.1 Set the frequency and source distance parameters of the induction logging instrument, ignore the size of the coil, and consider the transmitting and receiving coils as point transmission and point reception; s3.2 to the original formation longitudinal model M t , considering the relative dip angle between the instrument and the formation, the apparent resistivity of the original formation at the current logging point is calculated by using one-dimensional semi-analytical forward modeling method ; s3.3 Construct a uniform isotropic medium, combined with 0-dimensional medium analytical formula and gradient optimization algorithm, constantly update the isotropic medium resistivity, so that the forward result is consistent with the measured apparent resistivity at the current point, determine the equivalent original formation resistivity at the current point ; s3.4 on the intrusion zone longitudinal model M xo , one-dimensional forward to get the apparent resistivity of intrusion zone , perform step s3.3, and the inversion obtains the equivalent intrusion zone resistivity of the current logging point .

3. The method for fast calculation of the response of anisotropic induction logging in deviated well in invaded formations according to claim 1, characterized in that, The step s4 is specifically: s4.1 Constructing a columnar layered radial heterogeneous calculation model M r , containing a borehole, an instrument and a stepped invasion, wherein the hole diameter and the invasion depth take the corresponding parameter values at the current logging point, and the original formation resistivity and the invaded zone resistivity are set as the results obtained in step s3 and ; s4.2 sequentially loop five radial anisotropic formation control parameters to obtain a series of input calculation models T, wherein the well diameter and the invasion depth are linearly discretized, the mud resistivity, the invasion zone resistivity and the original formation resistivity are logarithmically discretized, the pattern matching algorithm is used, and the corresponding induction logging apparent conductivity of each calculation model is obtained in combination with the instrument frequency and the source distance parameters ; s4.3 Based on the theory of Doll geometric factor, the analytical expression of the radial integral contribution of the single-shot single-receiver coil system is obtained, and the apparent conductivity without frequency influence is determined by combining the model parameters shown in step s4.2 ; s4.4 taking the input calculation model T as input, - as output, training the neural network, establishing the mapping relationship between the radial heterogeneous model and the apparent conductivity residual, and obtaining the weight coefficients of each layer of neurons; s4.5 input and , using the step s4.3 to calculate the apparent conductivity without frequency influence, combining the neural network weight coefficient obtained in the step s4.4 to calculate the apparent conductivity residual; adding the apparent conductivity without frequency influence and the apparent conductivity residual to obtain the induction logging apparent resistivity, and realizing the approximation calculation of the induction logging response of the three-dimensional heterogeneous formation.

Images