Quantitative evaluation of fracture porosity from dual laterlog based on deep learning method

Fracture porosity is one of the key parameters for characterizing fractured reservoirs.However,fracture porosity calculation is difficult with conventional logging data due to severe anisotropy of the reservoirs.To deal with the problem,the equivalent macroscopic anisotropic formation model based on dual laterolog(DLL)data is adopted to cyclically assign such parameters as bedrock resistivity(RB),fluid resistivity in fractures(RFL),fracture dip angle(FDA)and fracture thickness as well as fracture spacing,and to produce massive data for formation modeling.A large number of training data obtained through three dimensional finite element forward modeling and the functional relationship between DLL responses and fracture parameters that are trained and summarized by deep neural network,are combined to establish a new fast forward model for calculating DLL responses in fractured formations.A new fracture porosity inversion model for fractured reservoirs based on gradient optimization inversion algorithm combined with multi-initial inversion strategy is then proposed.While running the model,formation is divided into eight intervals according to bedrock resistivity and fracture dip angle from 0°to 90°is divided every 0.5°to improve the operation speed and efficiency.The results of numerical verification show that when bedrock resistivity is greater than 1000Ωm,the mean absolute error(MAE)of fracture porosity inversion is 0.001658%for horizontal fractures,0.00413%for intermediate fractures and 0.0027%for quasi-vertical fractures.When bedrock resistivity is between 100Ωm and 1000Ωm,MAE of fracture porosity inversion is 0.003%for horizontal fractures,0.0034%for intermediate fractures and 0.00348%for quasi-vertical fractures.Fracture parameters determined by the fracture porosity inversion model with actual data are in good agreement with the results of micro resistivity imaging logging.

Analysis and application of the response characteristics of DLL and LWD resistivity in horizontal well

There exist different response characteristics in the resistivity measurements of dual laterolog （DLL） and logging while drilling （LWD） electromagnetic wave propagation logging in highly deviated and horizontal wells due to the difference in their measuring principles. In this study, we first use the integral equation method simulated the response characteristics of LWD resistivity and use the three dimensional finite element method （3D-FEM） simulated the response characteristics of DLL resistivity in horizontal wells, and then analyzed the response differences between the DLL and LWD resistivity. The comparative analysis indicated that the response differences may be caused by different factors such as differences in the angle of instrument inclination, anisotropy, formation interface, and mud intrusion. In the interface, the curves of the LWD resistivity become sharp with increases in the deviation while those of the DLL resistivity gradually become smooth. Both curves are affected by the anisotropy although the effect on DLL resistivity is lower than the LWD resistivity. These differences aid in providing a reasonable explanation in the horizontal well. However, this can also simultaneously lead to false results. At the end of the study, we explain the effects of the differences in the interpretation of the horizontal well based on the results and actual data analysis.

3D laterolog array sonde design and response simulation

A new three-dimensional laterolog array sonde（3D-LS） is presented. The 3DLS is based on existing high-resolution laterolog array and azimuthal resistivity imaging sondes with radial, longitudinal, and circumferential detection abilities. Six investigation modes are designed using the 3D finite-element method and different investigation depths are simulated based on the pseudo-geometrical factor of the six modes. The invasion profile is described using multi-array radial logs. From the analysis of the pseudo-geometrical factor, the investigation depth of the 3D-LS is about 1.5 m for conductive invasion, which is close to that of the dual laterolog tool but greater than that of the highly integrated azimuthal laterolog sonde. The vertical and azimuthal resolution is also analyzed with the same method. The 3DLS can detect low-resistivity anomalies of 0.5 m thickness and 15？ around the borehole for infinitely thick formations. This study lays the foundation for more work on 3D laterolog array sonde for evaluating low-resistivity anomalies.

Dual laterolog borehole correction based on dynamic tool constants

The positive and negative difference of deep and shallow resisitivity in formation without invasion is caused mainly by the fixed two tool constants from numerical simulations. A dynamic calibration method for tool constants is proposed based on the effects of the mud and formation resisitivity ratio on the two constants calculated using the finite element method （FEM）. Finally, four specific examples are given to validate the dynamic calibration method. It is an automatic borehole correction method and can give more accurate formation resistivity. The method is useful for dual laterolog logging.

Numerical simulation of the dual laterolog for carbonate cave reservoirs and response characteristics

Cave carbonate formations are characterized by heterogeneity, which makes electrical log prediction difficult. It is currently important to know how to use the dual laterolog to accurately identify and quantitatively evaluate caves. Using numerical simulation to calculate electrical log responses can provide a theoretical basis for cave identification and evaluation. In this paper, based on the dual laterolog principles, we first study different size spherical cave models using the finite element method （FEM）, determine a relation between resistivity and cave filling after comprehensively studying the log responses of cave models with different filling material, and finally study the dual laterolog responses on caves filled with shale, limestone, conglomerate, and thin laminated formation of sand and shale. The numerical results provide a theoretical basis for identification and evaluation of carbonate cave reservoirs.

Response characteristics of array lateral logs and their primary inversion in reservoirs with fracture-induced anisotropy

In order to identify fractured reservoirs and determine their fracture parameters with a high definition array laterolog,we built a fracture-induced anisotropic formation model with a parallel fracture group.The three-dimensional finite element method is used to simulate the responses of the array laterolog,and then the primary inversion method is utilized.Numerical simulation shows that when the fracture spacing is small,the array laterolog response of the fracture group is the same as that of a formation with macroscopic electrical anisotropy.The apparent resistivity of the array laterolog is approximately inversely proportional to fracture porosity.The anisotropy depends on the fracture porosity in the fractured formation,which accordingly results in response variation of the array laterolog.The higher the fracture dip,the larger the apparent resistivity.When the fracture dip is low the difference between the deep and shallow apparent resistivities is small,and when the dip is high the difference turns out to be positive.The fracture parameters were inverted using the Marquardt non-linear least squares method.The results,both fracture porosity and dip show a good match with parameters in the actual formation model.This will promote the application of the array laterolog in evaluating fractured reservoirs.

Interpreting Dual Laterolog Fracture Data in Fractured Carbonate Formation

The estimation of fractures is key to evaluating fractured carbonate reservoirs. It is difficult to evaluate this kind of reservoir because of its heterogeneously distributed fractures and anisotropy, A three-dimensional numerical model was used to simulate the responses of the dual laterolog （DLL） in a fractured formation based on a macro-isotropic anisotropic model, Accordingly, a fast fracture computing method was developed. First, the apparent conductivity of the DLL is linearly related to the porosity of the fracture and the conductivity of pore fluid. Second, the amplitude difference of the deep and shallow apparent resistivity logs is mainly dependent on the dip angle of the fracture. Then the response of the DLL to a formation with dip angle fractures is approximately depicted as a function of the bulk resistivity of the rock, the porosity of the fractures and the conductivity of fracture fluid. This function can be used to compute the porosity of fracture quickly. The actual data show that the fracture parameters determined by the DLL closely coincide with the formation micro imager log.

Numerical and physical simulations of array laterolog in deviated anisotropic formation

Due to the tremendous amount of high-resolution measurement information,array laterolog is widely used in evaluations of deviated anisotropic reservoirs.However,the precision of a complementary numerical simulation should be improved as high as the core of fine-scale reservoir evaluation.Therefore,the 3D finite element method(3D-FEM)is presented to simulate the array laterolog responses.Notably,a downscaled physical simulation system is introduced to validate and calibrate the precision of the 3D-FEM.First,the size of the downscaled system is determined by COMSOL.Then,the surrounding and investigated beds are represented by a sodium chloride solution and planks soaked in solution,respectively.Finally,a half-space measurement scheme is presented to improve the experimental efficiency.Moreover,the corresponding sensitivity function and separation factor are established to analyze the effects of the formation anisotro py and dipping angle on the array laterolog responses.The numerical and experimental results indicate that the half-space method is practical,and the mean relative error between the numerical and experimental results is less than 5%,which indicates that the numerical simulation is accurate.With the proposed approach,the reversal angle of array laterolog response curves in anisotropic formations can be observed,and this range is determined to be 50°-62°.

Fast inversion of array laterolog measurements in an axisymmetric medium

The array laterolog is an important tool for complex formation logging evaluation due to its high resolution and large detection depth.However,its logging responses are seriously affected by leakage events due to the surrounding rock and by mud invasion.These factors must be considered when inverting array lateral logging data,so that the inversion results reflect the true formation conditions as much as possible.The difficulties encountered in the inversion of array lateral logging data are:too many inversion parameters cause the calculation of the Jacobian matrix to be difficult and the time required to select the initial inversion values due to the slow forward-modeling speed.In this paper,we develop a fast processing method for array laterolog data.First,it is important to clearly define the main controlling factors for the array laterolog response,such as thickness,the surrounding rock,and invasion.Second,based on a depth-window technique,processing the array laterolog data for the entire well is transformed into multiple 2 D inversions of the layers using a series of continuous depth windows.For each formation in a depth window,combined with the1 D equivalent fast-forward algorithm,rapid extraction of the radial resistivity profile of the formation is achieved.Finally,the 1 D inversion result is used as the initial state to further eliminate the influence of surrounding rocks and layer thicknesses on the apparent resistivity response.Numerical simulation results show that the factors affecting the response of the array laterolog are the invasion properties,the layer thicknesses,and the surrounding rocks;the windowing technique greatly reduces the number of inversion parameters needed and improves the inversion speed.A real application of the method shows that 2 D inversion can rapidly reconstruct the actual resistivity distribution and improve the accuracy of reservoir saturation calculations.

Forward simulation of array laterolog resistivity in anisotropic formation and its application

A scaling-down experiment system of array laterolog resistivity was developed, and a corresponding formation model was built by 3 D finite element numerical method to study the effect of different factors on the logging response quantitatively. The error between the experimental and numerical results was less than 5%, validating the reliability of the numerical simulation method. The single factor analysis of the formation relative dip, resistivity anisotropy and drilling fluid invasion was carried out by numerical simulation method, and the results show that:(1) The increase of relative dip can lead to the increase of formation resistivity, but the increasing value is relatively small, and the values of five array resistivity curves will reverse when the relative dip angle reaches a certain degree.(2) The increase of anisotropy coefficient λ can also cause the formation resistivity to rise, and the resistivity will increase by about 10% when λ increases from 1.0 to 1.5 in vertical wells.(3) Drilling fluid invasion has a more significant effect on the logging response than the former two factors. The order of the five curves will change due to drilling fluid invasion in anisotropic formation and the change rule is contrary to resistivity anisotropy. Taking the logging data of the Yingxi oilfield in the Qaidam Basin as an example, an anisotropic formation model considering drilling fluid invasion was built, and the numerical simulation results from the above methods were basically consistent with the logging data, which verified the accuracy of the method again. The results of this study lay a theoretical foundation for multiple-parameter inversion in anisotropic formation under complex well conditions.

Anisotropy interpretation and the coherence research between resistivity and acoustic anisotropy in tight sands

Aiming at the problem of anisotropy inversion of tight sands, a new method for extracting resistivity anisotropy from array laterolog and micro-resistivity scanning imaging logging is proposed, and also the consistency of electric and acoustic anisotropy is discussed. Array laterolog includes resistivity anisotropy information, but numerical simulation shows that drilling fluid invasion has the greatest influence on the response, followed by the relative dip angle θ and electrical anisotropy coefficient λ. A new inversion method to determine ri, Rxo, Rt and λ is developed with the given θ and initial values of invasion radius ri, flushed zone resistivity Rxo, in-situ formation resistivity Rt. Micro-resistivity image can also be used for describing the resistivity distribution information in different directions, and the electrical characteristics from micro-resistivity log in different azimuths, lateral and vertical, can be compared to extract electric anisotropy information. Directional arrangement of mineral particles in tight sands and fracture development are the intrinsic causes of anisotropy, which in turn brings about anisotropy in resistivity and acoustic velocity, so the resistivity anisotropy and acoustic velocity anisotropy are consistent in trends. Analysis of log data of several wells show that the electrical anisotropy and acoustic anisotropy extracted from array laterolog, micro-resistivity imaging and cross-dipole acoustic logs respectively are consistent in trend and magnitude, proving the inversion method is accurate and the anisotropies of different formation physical parameters caused by the intrinsic structure of tight sand reservoir are consistent. This research provides a new idea for evaluating anisotropy of tight sands.

Investigation on influence factors of dual laterologs curve form

In order to investigate the influences of caliper, formation thickness and invaded zone on the form of dual laterologs, forward modeling technique were applied to calculate the dual laterologs for different cases. The result shows that the resistivity logs become smoother and lower as the borehole diameter increases, the increase of the contrast between mud resistivity and formation resistivity induce the logs to be more pointed. When the formation thickness is less than lm, the two-peak on the logs for resistive invasion vanished, and for thickness between 1 m and 4 m, the form of logs does not vary significantly. If the formation thickness is greater than 4 m, a platform appears on the logs at the middle of the formation. The thinner the invaded zone is, the more obvious the invasion feature on the laterologs is. For thick invaded zone the form of logs tend to be that of an uninvaded resistive formation. The form and amplitude of logs depend on the resistivity contrast between invaded zone, uninvaded formation and adjacentlayers.