CN116122794B - Complex stratum environment array resistivity logging decoupling dimension-reducing forward modeling method - Google Patents

Abstract

The invention discloses a forward modeling method for array resistivity logging decoupling and dimension reduction in complex formation environment, including establishing a three-dimensional heterogeneous anisotropic electrical logging model M; generating a three-dimensional heterogeneous isotropic formation model M1 _j after decoupling of anisotropic parameters; looping p detection modes of array resistivity logging to generate models M1 ₁ ~ M1 _p ; constructing a columnar layered vertical well model M2 _j ⁱ layer by layer for model M1 _j , and then generating a horizontal layered formation inclined well model M3 _j ; looping p detection modes of array resistivity logging to generate a one-dimensional horizontal layered isotropic calculation model M3 ₁ ~ M3 _p ; using a one-dimensional model, calculating the apparent resistivity response corresponding to the jth detection mode point by point; looping all detection models to obtain a complex formation environment array resistivity logging response curve. The invention can degrade the three-dimensional calculation of array resistivity logging in complex environment to one dimension, greatly improve the forward modeling efficiency, and provide strong support for real-time inversion and quantitative interpretation of array resistivity data.

Description

A decoupling and dimension reduction forward modeling method for array resistivity logging in complex formation environment

Technical Field

The invention relates to the technical field of electrical logging in petroleum exploration and development, belongs to the category of electrical logging forward modeling calculation methods, and in particular to a decoupling and dimensionality reduction forward modeling method for array resistivity logging in a complex formation environment.

Background technique

With the continuous progress of oil exploration and development, the geological environment has become increasingly complex, the underground rock formations have become more special, and the anisotropy of the formations can no longer be ignored. In addition, the angle changes caused by factors such as the formations not being perpendicular to the drilling and the instrument tilt, and the different invasion depths of different formations have made the three-dimensional forward simulation calculation of the logging response more and more accurate and slow, and it is impossible to accurately generate the forward apparent resistivity curve, reflect the actual underground situation, and quickly provide a large amount of data for inversion.

Therefore, it is urgent to study a decoupling and dimensionality reduction forward modeling method for array resistivity logging in complex formation environments to improve the speed and accuracy of forward modeling calculations, obtain a large amount of data for inversion, and better train the inversion model.

Summary of the invention

In order to solve the above technical problems, the present invention discloses a decoupling and dimensionality reduction forward modeling method for array resistivity logging in a complex formation environment, in order to improve the forward modeling efficiency, provide strong support for the real-time inversion and quantitative interpretation of array resistivity data, and obtain a large amount of data information for the inversion process.

To achieve the above object, the present invention adopts the following technical solutions:

A decoupling and dimension reduction forward modeling method for array resistivity logging in a complex formation environment comprises the following steps:

s1. Aiming at the complex formation structure and drilling environment, the three-dimensional heterogeneous anisotropic electrical logging calculation model M is established after borehole correction, considering the factors of layer thickness, surrounding rock, well inclination, invasion state, borehole environment, electrical anisotropy, instrument structure and relative position. Assuming that the formation is N layers, the model M is described by 6N+2 parameters, including: (1) N-1 formation interfaces, which constitute N-1 parameters; (2) the original formation resistivity R _th,i and R _tv,i of each formation, the invasion zone resistivity R _xoh,i and R _xov,i and the invasion depth DI _i , a total of 5N parameters; (3) the mud filtrate resistivity R _mf , the wellbore diameter r, the formation dip Consists of 3 separate parameters;

s2. For the jth detection mode of array resistivity logging, combined with the relative dip information, the equivalent isotropic resistivity value of each region is calculated to generate a three-dimensional heterogeneous isotropic formation calculation model M1 _j after anisotropic parameter decoupling; for the model corresponding to each array resistivity logging detection mode after anisotropic decoupling, M1 _j is described by 4N+2 parameters, including: (1) N-1 formation interfaces, which constitute N-1 parameters; (2) equivalent original formation resistivity Intrusion zone resistivity/> and penetration depth DI _i , a total of 3N parameters; (3) R _mf , r, /> Consists of 3 separate parameters;

s3. For p detection modes of array resistivity logging, execute step s2 in sequence to generate p groups of new calculation models M1 ₁ -M1 _p . After anisotropic decoupling, there are p*(4N+2) parameters for p different detection modes;

s4. For the three-dimensional isotropic model M1 _j in step s3, a columnar layered vertical well model M2 _j ⁱ is constructed layer by layer, the macro resistivity value of the layer is calculated, and then a horizontal layered formation inclined well calculation model M3 _j is generated to achieve decoupling of radial heterogeneity parameters and convert the three-dimensional forward modeling into a reduced-dimensional nested one-dimensional forward modeling;

s5. For the array resistivity logging p detection modes, execute step s4 in sequence to generate p groups of new horizontal layered formation inclined well one-dimensional calculation models M3 ₁ ~M3 _p ;

s6. Using the one-dimensional model obtained in step s5, taking into account the relative dip angle and layer thickness parameters, and combining with a one-dimensional fast pseudo-analytical algorithm, calculate the apparent resistivity response corresponding to the i-th detection mode point by point;

s7. Cycle all detection models to obtain the array resistivity logging response curve in complex formation environment.

Optionally, in step s2, the anisotropic decoupling method is:

s2.1. Consider the dip angle and anisotropy calculation to decouple the anisotropic effect, calculate the equivalent isotropic resistivity of each area respectively, and obtain an isotropic three-dimensional formation model; divide the N formations into original formations and intrusion zones respectively, and process the N original formations and intrusion zones in turn in a cycle;

s2.2. For the invasion zone of the i-th stratum, determine whether the horizontal and vertical resistivities (R _xoh,i , R _xov,i ) of the invasion zone are consistent. If they are consistent, take the horizontal resistivity as the equivalent resistivity of the layer. If the two are inconsistent, execute step s2.3;

s2.3. Establish an infinitely thick homogeneous anisotropic medium model. The horizontal resistivity and vertical resistivity of the model are R _xoh,i and R _xov,i respectively. Under the condition, calculate the apparent resistivity value of the jth detection mode, and regard the resistivity as the equivalent resistivity of the layer/>

s2.4. For the original stratum of the i-th stratum, determine whether the horizontal and vertical resistivities (Rth _,i , Rtv _,i ) of the original stratum are consistent. If they are consistent, take the horizontal resistivity as the equivalent resistivity of the stratum. If the two are inconsistent, execute step s2.5;

s2.5. Establish an infinitely thick homogeneous anisotropic medium model. The horizontal resistivity and vertical resistivity of the model are R _th,i and R _tv,i respectively. Under the condition, calculate the apparent resistivity value of the jth detection mode, and regard the resistivity as the equivalent resistivity of the layer/>

S2.6. Comprehensive all the formation interfaces, invasion zone radius and wellbore environment in step S1, combined with the results of step S2.3 and step S2.5 and/> A three-dimensional isotropic model M1 _j for the j-th detection mode is formed, which contains 4N+4 parameters.

Optionally, the step s4 is specifically:

s4.1. Perform radial parameter decoupling on the new three-dimensional formation model M1 _j after anisotropic decoupling, and build a columnar layered vertical well model M2 _j ⁱ (i=1, ..., N) layer by layer;

s4.2. For the i-th layer, the model parameters are the original formation resistivity Intrusion zone resistivity/> Invasion radius DI _i , mud resistivity R _mf and wellbore r are expressed;

s4.3. For the columnar layered vertical well model established in the i-th layer, the apparent resistivity value of the j-th detection mode is calculated using a pseudo-analytical algorithm, and the apparent resistivity value is equivalent to the macroscopic formation resistivity of the layer;

s4.4. Cycle through N layers to obtain the equivalent resistivity of each layer;

s4.5. For the jth detection mode, the various parameters formed in step s4.3 are used in combination with the formation dip angle to establish a horizontal layered inclined well formation model M3 _j . The model parameters are composed of the formation interface _Zi , the dip angle and equivalent formation resistivity/> express;

s4.6. Cycle the p detection modes in sequence to obtain a horizontal layered inclined well formation model after the cycle.

The beneficial effect of the present invention is that the present invention provides a method for decoupling and reducing the dimension of array resistivity logging in a complex formation environment, converting the anisotropic three-dimensional forward modeling into two one-dimensional model hierarchical forward modeling by reducing the dimension and decoupling, and extracting the macro resistivity information of the three-dimensional anisotropic formation by combining a one-dimensional fast pseudo-analytic algorithm, which greatly improves the forward calculation speed and provides multiple sets of initial values for inversion. The method proposed by the present invention can effectively degrade the three-dimensional calculation of array resistivity logging in a complex environment to one dimension, greatly improve the forward modeling efficiency, and provide strong support for the real-time inversion and quantitative interpretation of array resistivity data.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart of anisotropic decoupling and dimensionality reduction decoupling of a three-dimensional formation model in the present invention;

FIG2 is a schematic diagram showing that an anisotropic formation is equivalent to an isotropic formation in the present invention;

FIG3 is a schematic diagram of dimensionality reduction and decoupling of a three-dimensional formation model in the present invention;

FIG4 is a specific implementation example of the anisotropic formation model in the present invention;

FIG5 is anisotropic equivalent isotropic apparent resistivity values under different detection modes in the present invention;

FIG6 shows the equivalent resistivity values of horizontal layered formations under different detection modes in the present invention;

FIG7 is a forward modeling response under different detection modes in the present invention;

FIG8 is a graph showing the change in apparent resistivity of each of the three strata listed in the present invention in different detection modes versus invasion depth.

Detailed ways

The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

A decoupling and dimension reduction forward modeling method for array resistivity logging in a complex formation environment, as shown in FIG1 , comprises the following steps:

s1. For complex formation structure and drilling environment, considering layer thickness, surrounding rock, well deviation, invasion state, borehole environment, electrical anisotropy, instrument structure and relative position factors, a three-dimensional heterogeneous anisotropic electrical logging calculation model M is established after borehole correction. The formation model and HDIL array shown in Figure 4 are used as an example for further explanation:

The three-dimensional heterogeneous anisotropic electrical logging calculation model shown in Figure 4 includes three layers of invaded anisotropic formations, with the upper and lower layers being 5 m thick and the middle layer being 10 m thick. The model M is described by 20 parameters, and the two formation interfaces are Z ₁ and Z ₂ ; the resistivity of the invaded zone is assigned as R _xoh,3 = 5Ω·m, R _xov,3 = 10Ω·m, R _xoh,2 = 7Ω·m, R xov _,2 = 21Ω·m, R _xov,1 = 10Ω·m, and R _xoh,1 = 18Ω·m; the resistivity of the original formation is assigned as R _th,3 = 15Ω·m, R _tv,3 = 20Ω·m, R _th,2 = 10Ω·m, R _tv,2 = 15Ω·m, R _tv,1 = 13Ω·m, and R _th,1 = 7Ω·m; the invasion depths of the three layers are assigned as DI ₁ and DI 2 , respectively. =1m, DI ₃ =0.7m, DI ₂ =1.5m; well inclination Well diameter: 8 inches; mud resistivity: R _mf = 0.1Ω·m.

s2. For the formation model shown in FIG. 4 , the equivalent isotropic process shown in FIG. 2 is used to cycle the j-th detection mode of the array resistivity logging, calculate the equivalent isotropic resistivity value of each region, and generate a three-dimensional heterogeneous isotropic formation calculation model M1 _j after decoupling of anisotropic parameters;

S3. Cycle the 7 modes of array resistivity logging, execute step s2 in sequence, generate the three-dimensional heterogeneous isotropic formation calculation model M1 ₁ ~ M1 ₇ after anisotropic parameter decoupling, and the equivalent resistivity parameters after anisotropic decoupling are shown in Figure 5, where the left figure is the isotropic invasion zone resistivity and the right figure is the isotropic original formation resistivity; it can be seen that the isotropic resistivity of each anisotropic formation module and each detection mode after equivalent is slightly different, but the separation is small. The difference reflects the influence of anisotropy, and the small separation indicates that the sensitivity of each sub-array to anisotropy is weak. The specific parameter values are: each detection mode contains 14 parameters, and each detection mode contains the following parameters: two formation interfaces are Z ₁ and Z ₂ ; the three-layer invasion depths are assigned DI ₁ = 1m, DI ₃ = 0.7m, DI ₂ = 1.5m respectively; the well deviation Well diameter: 8 inches; Mud resistivity: R _mf = 0.1Ω·m;

Detection mode 1: The equivalent isotropic intrusion zone resistivity is The equivalent isotropic original formation resistivity is / >

Detection mode 2: The equivalent isotropic intrusion zone resistivity is The equivalent isotropic original formation resistivity is / >

Detection mode 3: The equivalent isotropic intrusion zone resistivity value is The equivalent isotropic original formation resistivity is / >

Detection mode 4: The equivalent isotropic intrusion zone resistivity is The equivalent isotropic original formation resistivity is / >

Detection mode 5: The equivalent isotropic intrusion zone resistivity value is The equivalent isotropic original formation resistivity is / >

Detection mode 6: The equivalent isotropic intrusion zone resistivity value is The equivalent isotropic original formation resistivity is / >

Detection mode 7: The equivalent isotropic intrusion zone resistivity value is The equivalent isotropic original formation resistivity is / >

S4. Decoupling radial heterogeneity parameters using the method shown in FIG3: for the three-dimensional isotropic model _M1j in step s2, construct a columnar layered vertical well model _M2j ^layer by layer, calculate the macro resistivity value of the layer, and the calculated result is shown in FIG6, and then generate a horizontal layered formation inclined well calculation model _M3j ; it can be seen that the macro resistivity values of each detection model are quite different, reflecting the radial detection capabilities of different detection modes and the influence of mud invasion; after anisotropic decoupling, there are 98 parameters for 7 different detection modes;

s5. Cycle the array resistivity logging 7 detection modes and execute step s4 in sequence to generate 7 groups of horizontal layered formation inclined well one-dimensional calculation models M3 ₁ to M3 ₇ . The equivalent macro resistivity values of each layer are shown in FIG6 ;

s6. Using the one-dimensional model obtained in step s5, taking into account the relative dip and layer thickness parameters, combined with the one-dimensional fast pseudo-analytic algorithm, the apparent resistivity response corresponding to the jth detection mode is calculated point by point, and the response results shown in Figure 7 are obtained by cycling through 7 detection modes. The response results are roughly the same as the model calculation results. The calculation speed after decoupling is about 400 logging points/second, while the normal three-dimensional calculation speed without decoupling is about 10 seconds to 1 minute per logging point.

s7. All detection models are looped to obtain the array resistivity logging response in the radial direction of the formation model, as shown in Figure 8. The three figures respectively show the changes in the apparent resistivity response values of the three formations with the radial invasion depth. The overall change is that the apparent resistivity value changes from the invasion zone resistivity being greatly affected to the original formation being greatly affected with the invasion depth. When the invasion depth is consistent with the invasion depth set by the model, the apparent resistivity results obtained by the seven detection modes are consistent.

Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the protection scope of the present invention.

Claims (1)

1. The decoupling dimension-reducing forward modeling method for array resistivity logging in the complex stratum environment is characterized by comprising the following steps of:

s1. aiming at complex stratum structures and drilling environments, taking layer thickness, surrounding rock, well deviation, invasion state, well hole environment, electrical anisotropy, instrument structure and relative position factors into consideration, and establishing a three-dimensional heterogeneous anisotropic electrical logging calculation model M after well hole correction;

s2, calculating equivalent isotropic resistivity values of all areas according to a jth detection mode of array resistivity logging and relative inclination angle information, and generating a three-dimensional heterogeneous isotropic stratum calculation model M1 _j with decoupled anisotropic parameters;

s3. performing p detection mode cycles on the array resistivity well, sequentially executing step s2, and generating p groups of new calculation models M1 ₁～M1_p;

s4. constructing a columnar layering vertical well model M2 _j ⁱ layer by layer on the three-dimensional isotropic model M1 _j in the step s3, calculating the macroscopic resistivity value of the layer, further generating a horizontal layering stratums inclined well calculation model M3 _j, realizing decoupling of radial heterogeneous parameters, and converting three-dimensional forward modeling into dimension-reducing nested one-dimensional forward modeling;

s5. carrying out p detection mode cycles on the array resistivity logging, sequentially executing step s4, and generating p groups of new horizontal lamellar inclined shaft one-dimensional calculation models M3 ₁～M3_p;

s6. calculating the apparent resistivity response corresponding to the ith detection mode point by utilizing the one-dimensional model obtained in the step s5 and combining a one-dimensional quick pseudo-analysis algorithm;

s7., circulating all the detection models to obtain a complex stratum environment array resistivity logging response curve;

In the step s2, the anisotropic decoupling method is as follows:

S2.1, decoupling the anisotropic influence by considering inclination angle and anisotropic calculation, and respectively calculating the equivalent isotropic resistivity of each region to obtain an isotropic three-dimensional stratum model; dividing the N stratum into an undisturbed stratum and an invaded zone respectively, and sequentially and circularly treating the N undisturbed stratum and the invaded zone;

s2.2. for the invaded zone of the ith stratum, judging whether the horizontal resistivity R _xoh,i and the vertical resistivity R _xov,i of the invaded zone are consistent, if so, the horizontal resistivity is the equivalent resistivity of the stratum If the two are inconsistent, executing step s2.3;

S2.3, establishing an infinitely thick uniform anisotropic medium model, wherein the horizontal resistivity and the vertical resistivity of the model are respectively R _xoh,i、R_xov,i, and the inclination angle is Under the condition, calculating the apparent resistivity value of the j detection mode, and regarding the resistivity as the equivalent resistivity/>, of the layer

S2.4. for the undisturbed stratum of the ith stratum, judging whether the horizontal resistivity R _th,i and the vertical resistivity R _tv,i of the undisturbed stratum are consistent, if so, the horizontal resistivity is the equivalent resistivity of the layerIf the two are inconsistent, executing step s2.5;

s2.5, establishing an infinitely thick uniform anisotropic medium model, wherein the horizontal resistivity and the vertical resistivity of the model are respectively R _th,i、R_tv,i, and the inclination angle is Under the condition, calculating the apparent resistivity value of the j detection mode, and regarding the resistivity as the equivalent resistivity/>, of the layer

S2.6 are combined with the results of step s2.3 and step s2.5And/>Forming a three-dimensional isotropic model M1 _j for the j-th detection mode, comprising 4n+2 parameters;

the step s4 specifically includes:

s4.1. performing radial parameter decoupling on the new three-dimensional stratum model M1 _j after anisotropic decoupling, and establishing a columnar layering vertical well model M2 _j ⁱ layer by layer, wherein i=1, N;

s4.2. for the ith layer, the model parameters are determined by the resistivity of the undisturbed formation Invaded zone resistivity/>Invasion radius DI _i, mud resistivity R _mf, and borehole diameter R;

S4.3, for the built columnar layering vertical well model of the ith layer, calculating the apparent resistivity value of the jth detection mode by using a pseudo-analytic algorithm, and equating the apparent resistivity value to the macroscopic stratum resistivity of the ith layer;

S4.4, circulating the N stratum to obtain the equivalent resistivity of each stratum;

s4.5. for the jth detection mode, using the parameters formed in step s4.3 in combination with the formation dip angle, establishing a horizontal layered inclined well formation model M3 _j, the model parameters being composed of the formation interface Z _i, the dip angle And equivalent formation resistivity/>A representation;

And S4.6, sequentially cycling the p detection modes to obtain a cycled horizontal layered inclined well stratum model.