Figure 2 - uploaded by Dario Grana
Content may be subject to copyright.
Multimodal behaviour of well log data in the petro-elastic domain. On the left: P-impedance versus effective porosity, colour coded by facies classification (sand in red, silty sand in orange, silty shale in green); on the right: estimated bivariate joint probability assuming a three component Gaussian mixture model. The black curves on the left plot correspond to the probability contours of the pdf on the right.
Source publication
In this paper we present a case history of seismic reservoir characterization where we estimate the probability of facies from seismic data and simulate a set of reservoir models honouring seismically‐derived probabilistic information. In appraisal and development phases, seismic data have a key role in reservoir characterization and static reservo...
Context in source publication
Context 1
... properties are in general multimodal due to the presence of different facies. Within each facies we can assume that the properties are Gaussian, so that the overall probability is a linear combination of different Gaussian distributions (i.e., Gaussian probability density functions with different means and covariance matrices in each cluster). In Fig. 2 we show an example of a bivariate Gaussian mixture distribution with three components estimated in the petro-elastic domain using P-impedance and effective porosity curves measured at the well locations. Non-parametric distributions can be used as well to describe the multimodal behaviour; however in the non-parametric case the ...
Similar publications
Tight sandstone reservoirs have complex petrophysical properties, which introduce difficulties to rock physics modeling. Besides, weak reflection events appear with a high probability in the seismic profile for tight sandstones. By combining the soft-porosity model and the Gassmann’s relation, the weak reflection events are analyzed in detail, whic...
Petrophysical evaluation and rock physics analysis are the important tools to relate the reservoir properties like porosity, permeability, pore fluids with seismic parameters. Nevertheless, the uncertainties always exist in the quantification of elastic and seismic parameters estimated through wireline logs and rock physics analysis. A workflow bas...
We have evaluated a case study, in which a class-1 amplitude variation with offset (AVO) turbiditic system located offshore Cote d’Ivoire, West Africa, is characterized in terms of rock properties (lithology, porosity, and fluid content) and stratigraphic elements using well-log and prestack seismic data. The methodology applied involves (1) the co...
Shales can be distributed in sand through four different ways; laminated , structural, dispersed and any combination of these aforementioned styles. A careful analysis of well log data is required for the determination of shale distribution in sand affecting its reservoir quality. The objective of this study is to characterize the effect of shale d...
Nine different wells were carefully studied on "PAU" field and their results were integrated for thorough understanding of the reservoir sand bodies within the field. These studies include; stratigraphic well correlation, rock physics analysis, sequence stratigraphy, petrophysical evaluation of wells and reservoir volumetric evaluation in order to...
Citations
... Due to the wide range of reservoir types, geological complexity, and different reservoir development strategies across the UIB, customizing a single workflow for building geocellular models that accurately describe the other reservoir characteristics and behaviors is extremely difficult (Gomes et al., 2018). Reservoir modeling describes the complexity and heterogeneity of a reservoir (Grana et al., 2013). ...
Geocellular modeling has become extremely important, linking all petroleum disciplines, and being widely used in simulation and production forecasting in complex basin studies. In this study, we focused on the Minwal–Joyamair Fields in the Upper Indus Basin (UIB), Pakistan, which contains Cambrian to Eocene reservoir formations. Changes in sedimentary environments and structural activities within the UIB have resulted in reservoir heterogeneity, which has adversely affected reservoir performance, and it is still not fully understood. Geocellular modeling was used in this study to better understand the structural framework of the Cambrian to Eocene formations in the UIB. The 2D seismic and well log data from the Minwal–Joyamair Fields are the primary data for building the geocellular model for the Eocene (Chorgali, Sakesar) and Paleocene (Lockhart) reservoirs. The developed structural model is then populated with petrophysical properties such as porosity. The upscaled porosity for the Eocene carbonate rock units ranges 1–3%. On the other hand, the Cambrian and Permian (Tobra & Khewra) clastic reservoirs bear porosity of 3–10%. The upscaled porosity can be utilized to predict the lateral and vertical distribution in these reservoirs. Furthermore, the evaluated upscaled correlation for Eocene reservoirs (80–90%), whereas for Permian (Tobra) and Cambrian (Khewra) reservoirs, it lies between 60 and 70 %. Apart from data availability, a complete geocellular model of the field was produced, encompassing the petrophysical and facies model. The geocellular models created a high-resolution 3D reservoir model of this complex geology that can be applied to similar geology worldwide to identify prospective zones.
... It was originally proposed to provide a realistic and comprehensive estimate of the uncertainty in the inversion of petrophysical properties from seismic data (Grana and Della Rossa 2010;Grana 2018). Several successful case studies are described in the literature (see, e.g., Grana et al. 2013;Aleardi et al. 2016Aleardi et al. , 2018, and similar approaches have also been tested in time-lapse (4D) seismic inversion studies (Grana and Mukerji 2015) and, more recently, to jointly invert sonic and electrical well-log measurements in CO 2 sequestration applications (Ayani and Grana 2020). ...
... The reservoir consists of a good-quality sandstone represented by a fluviodeltaic channel system within a faulted anticline structure. Seismic data acquired in the area were processed for amplitude interpretation (Buia et al. 2010), and a detailed seismic characterization of the reservoir was performed by integrating seismic inversion, rock-physics, and facies classification (Grana et al. 2013). The geosteered well, used to test the proposed inversion, was drilled with the objective of gathering structural and stratigraphic information on the complex architecture of the reservoir. ...
... To account for the facies-dependent behavior of the rock properties, as described by the PDDs in Eqs. 1 through 3, a reference facies profile (F1 in Fig. 1c) was available from the seismic characterization study (Grana et al. 2013). This facies classification includes four classes: sand (in red), silty sand (in orange), silty-shale (in light green), and shale (in dark green). ...
This work describes a statistical rock-physics driven inversion of seismic acoustic impedance and Ultra Deep Azimuthal Resistivity (UDAR) log data, acquired while drilling, to estimate porosity, water saturation and litho-fluid facies classes around the wellbore. Despite their limited resolution, surface seismic data integrated with electromagnetic resistivity log measurements improve the description of rock properties by considering the coupled effect of pore space and fluid saturation in the joint acoustic and electrical domains.
The key aspect of the proposed inversion is that it does not explicitly use a forward model, rather the correlation between the petrophysical properties and the resulting geophysical responses is inferred probabilistically from a training dataset. The training-set is generated combining available borehole information with statistical rock-physics modelling approach. In the inversion process, given co-located measurements of seismic acoustic impedance and logging-while-drilling electromagnetic resistivity data, the pointwise probability distribution of rock-properties is derived directly from the training dataset by applying the kernel density estimation algorithm. A non-parametric statistical approach is employed to approximate non-symmetric volumetric distributions of petrophysical properties and to consider the characteristic non-linear relationship linking water-saturation with resistivity. Given an a-priori facies classification template for the samples in the training-set, it is possible to model the multimodal, facies-dependent, behavior of the petrophysical properties, together with their distinctive correlation patterns. A facies-dependent parameterization allows the effect of lithology on acoustic and resistivity response to be implicitly considered, even though the target properties of inversion are only porosity and saturation.
To provide a realistic uncertainty quantification of the estimated rock-properties, a plain Bayesian framework is described which accounts for rock-physics modelling error and to propagate seismic and resistivity data uncertainties to the inversion results. In this respect, the uncertainty related to the scale difference among the well-log data and seismic is addressed by adopting a scale reconciliation strategy based on probabilistic function. This allows transforming physically equivalent measures from one resolution to another and consistently estimate the corresponding changes in the probability distributions. The described rock physics-driven inversion can be performed efficiently during drilling, following the acquisition and inversion of UDAR data, as the time-consuming step of estimating a probabilistic model from the training-set, can be separated from inversion itself. This is of particular interest in geosteering, where the training-phase can be performed before drilling, during well planning operations. After training, the resulting probabilistic model can be stored as a look-up table. Hence, the prediction of rock-properties, given the co-located measurements of seismic acoustic impedance and log-while-drilling electromagnetic resistivity, reduces to a fast look-up table search.
The inversion workflow is validated on a clastic oil-bearing reservoir located offshore Norway, where geosteering was used to guide the placement of a horizontal appraisal well in a complex structural setting. A complete set of well logs from four nearby exploration wells is used to construct the training dataset. Porosity, water-saturation, and litho-fluid facies are estimated along the geosteered well path given a 2D curtain section of ultra deep azimuthal resistivity and the corresponding acoustic impedance section available from the 3D surface seismic data. Prior to running the inversion, the acoustic impedance data was properly depth-matched with the resistivity section using a non-rigid matching algorithm. The joint inversion results show that the proposed methodology provides realistic estimates of the rock-property distributions around the wellbore to depths of investigation of 50m. These results constitute useful information to support geosteering decisions and can also be used, post-drilling, to update or optimize existing reservoir models.
... It was originally proposed to provide a realistic and comprehensive estimate of the uncertainty in the inversion of petrophysical properties from seismic data (Grana and Della Rossa 2010;Grana 2018). Several successful case studies are described in the literature (see, e.g., Grana et al. 2013;Aleardi et al. 2016Aleardi et al. , 2018, and similar approaches have also been tested in time-lapse (4D) seismic inversion studies (Grana and Mukerji 2015) and, more recently, to jointly invert sonic and electrical well-log measurements in CO 2 sequestration applications (Ayani and Grana 2020). ...
... The reservoir consists of a good-quality sandstone represented by a fluviodeltaic channel system within a faulted anticline structure. Seismic data acquired in the area were processed for amplitude interpretation (Buia et al. 2010), and a detailed seismic characterization of the reservoir was performed by integrating seismic inversion, rock-physics, and facies classification (Grana et al. 2013). The geosteered well, used to test the proposed inversion, was drilled with the objective of gathering structural and stratigraphic information on the complex architecture of the reservoir. ...
... To account for the facies-dependent behavior of the rock properties, as described by the PDDs in Eqs. 1 through 3, a reference facies profile (F1 in Fig. 1c) was available from the seismic characterization study (Grana et al. 2013). This facies classification includes four classes: sand (in red), silty sand (in orange), silty-shale (in light green), and shale (in dark green). ...
This work describes a statistical rock-physics-driven inversion of seismic acoustic impedance (AI) and ultradeep azimuthal resistivity (UDAR) log data, acquired while drilling, to estimate porosity, water saturation, and facies classes around the wellbore. Despite their limited resolution, seismic data integrated with electromagnetic resistivity log measurements improve the description of rock properties by considering the coupled effects of pore space and fluid saturation in the joint acoustic and electrical domains.
The proposed inversion does not explicitly use a forward model, rather the correlation between the petrophysical properties and the resulting geophysical responses is inferred probabilistically from a training data set. The training set is generated by combining available borehole information with a statistical rock-physics modeling approach. In the inversion process, given colocated measurements of seismic AI and logging-while-drilling (LWD) electromagnetic resistivity data, the pointwise probability distribution of rock properties is derived directly from the training data set by applying the kernel density estimation (KDE) algorithm. A nonparametric statistical approach is used to approximate nonsymmetric volumetric distributions of petrophysical properties and to consider the characteristic nonlinear relationship linking water saturation with resistivity. Given an a priori facies classification template for the samples in the training set, it is possible to model the multimodal, facies-dependent behavior of the petrophysical properties, together with their distinctive correlation patterns. A facies-dependent parameterization allows the effect of lithology on acoustic and resistivity responses to be implicitly considered, even though the target properties of inversion are only porosity and saturation.
To provide a realistic uncertainty quantification of the estimated rock properties, a plain Bayesian framework is described to account for rock-physics modeling error and to propagate seismic and resistivity data uncertainties to the inversion results. In this respect, the uncertainty related to the scale difference among the well-log data and seismic is addressed by adopting a scale reconciliation strategy. The main feature of the described inversion lies in its fast implementation based on a look-up table that allows rock properties, with their associated uncertainty, to be estimated in real time following the acquisition and inversion of UDAR data. This gives a robust, straightforward, and fast approach that can be effortlessly integrated into existing workflows to support geosteering operations.
The inversion is validated on a clastic oil-bearing reservoir, where geosteering was used to guide the placement of a horizontal appraisal well in a complex structural setting. The results show that the proposed methodology provides realistic estimates of the rock-property distributions around the wellbore to depths of investigation of 50 m. These constitute useful information to drive geosteering decisions and can also be used, post-drilling, to update or optimize existing reservoir models.
... Using seismic data and limited well logs to obtain reservoir parameters, e.g., elastic/petrophysical parameters and facies, is one of the primary tasks of reservoir characterization. From a mathematical point of view, this is an inverse problem, which is ill-posed due to limited data bandwidth, data noise, and incomplete data coverage (Tarantola, 1987;Grana et al., 2013). In model-based inversion methods, additional constraints such as prior knowledge from well logs and sparse regularization are often used to improve inversion performance and thus recover a more realistic model of the subsurface (Buland and Omre, 2003;Bosch et al., 2010;She et al., 2019). ...
The essential task of reservoir characterization is to predict elastic/petrophysical parameters or facies from observed seismic data and evaluate their uncertainty. Deep-learning-based methods gain great popularity because of their powerful ability to obtain exact solutions for geophysical inverse problems. However, those deep learning methods use seismic data as the only input lead to difficult training and unstable inversion results (i.e., transverse discontinuity or geological unreliability). In such circumstances, it is beneficial if prior knowledge of the model domain can be incorporated into the deep learning framework. Therefore, we develop prior-based loss functions in the learning step of the deep learning models to ensure that the predictions show low errors on the training sets and their results are consistent with the known prior. Besides, the Monte Carlo dropout (MC-dropout) technique is introduced for the quantitative assessment of the uncertainty of the prediction results. We demonstrate the effectiveness of the proposed framework in the application of pre-stack seismic inversion, where the initial model built from well log interpolation is used to design the prior-based loss function. We first perform extensive experiments on the synthetic data and show that the proposed method can yield more stable and reliable results compared to traditional methods. Combined with the transfer learning strategy, the application to real data further demonstrates that the proposed deep learning framework obtains more reasonable inversion results with more horizontal continuity and higher geological reliability than traditional approaches.
... We make use of multiple datasets and geological scenarios to generate more inclusive static models. One method to explore uncertainty space and fully understand the implication of uncertainty is to build ensemble of models (Oliver et al., 2001;Grana et al., 2013) to include a wide range of parameters. Then the simulation models can be converted to synthetic seismogram, called Sim2Seis workflow (Amini, 2014). ...
... Additionally, Doyen (2007) used a Gaussian sequential simulation algorithm to obtain the acoustic impedance and shear impedance data volumes and calculated the Bayesian posterior distribution. In recent years, Grana et al. (2012aGrana et al. ( , 2013Grana et al. ( 2017Grana et al. ( , 2018, Connolly & Hughes (2016), and Lang & Grana (2018) conducted research on stochastic simulation probability inversion method based on the prior probability, conditional probability and posterior distribution sampling algorithms. Grana et al. (2012b) combined sequential Gaussian simulation and probabilistic perturbation method to obtain seismic lithofacies and obtained the inversion results of reservoir physical parameters using rock physical modelling. ...
The Upper Palaeozoic coal measures in the Ordos Basin are rich in unconventional natural gas resources; however, the reservoir heterogeneity is relatively strong, which majorly restricts the accuracy of lithology prediction. Stochastic seismic inversion can synthesize the geological–geophysical information and establish high-resolution reservoir models based on geostatistical theory to obtain good inversion results; moreover, it can characterize reservoir lithology and fluid-bearing properties. The present study aimed to propose a high-precision lithology classification method for coal-bearing strata in the Ordos Basin, using Bayesian classification and stochastic seismic inversion. Initially, the reservoir geological model was established on the basis of the sequential Gaussian simulation algorithm, and stochastic seismic inversion was performed in combination with rock physics analysis, thereby obtaining a high-resolution elastic parameter data volume. Thereafter, the probability density function (PDF) and the probability density confusion matrix (PDF confusion matrix) were introduced to quantitatively analyse the ability of sensitive elastic parameters to distinguish lithology. Eventually, a logging lithology-fluid classification template was established based on the Bayesian classification technology; furthermore, a 3D lithology-fluid prediction was completed in combination with the inversion results. The prediction results are in good accordance with the logging data, which verifies the feasibility and effectiveness of the method.
... However, these 16 methods demand high computational time relative to BLI. To partially overcome this 17 issue, in this paper, the efficiency of MCMC based seismic inversion is improved by 18 initializing it from the results provided by BLI. 19 In addition, traditional seismic inversion methodologies follow a trace-by-trace 20 approach, which means that the spatial coupling of model parameters is not builds on previous researches to re-derive geological structure-guided (i.e., the slope 5 attribute obtained from seismic data, images, or velocity models using PWD) MCMC 6 based post-stack inversion. ...
... the elastic contract is weak at the reflecting interface ݎ( ≪ 0.3), Eq. (2) can18 be alternatively expressed as Eq. (6)(Russell, 1988). ...
Seismic inversion is a common method for hydrocarbon reservoir characterization, as it consists of a proven and effective approach to derive elastic properties from reflectivity seismic data. Markov Chain Monte Carlo (MCMC) based seismic inversion approach is a suitable choice to numerically evaluate the posterior uncertainties associated with the inverse solution without assuming linear forward operators, Gaussian, or generalized Gaussian prior models. However, the existing MCMC based seismic inversion approaches are mostly performed trace-by-trace, which means that the spatial coupling of model parameters is not considered. When the results of trace-by-trace based inversion are combined to generate a 2D profile, the final results will be laterally discontinuous. Moreover, the large dimension of the model space causes low convergence efficiency of MCMC-based seismic inversion. To overcome these issues, a geological structure-guided hybrid MCMC and Bayesian linearized Inversion (BLI) methodology for seismic inversion is implemented. The geological structure information obtained using plane wave destruction (PWD) is incorporated to the MCMC based inversion algorithm in the form of dips yields more geologically meaningful results. The hybrid MCMC and BLI strategy, which takes advantage of BLI's high efficiency to provide initial configuration for MCMC, is used to improve the convergence of MCMC-based inversion. Additionally, the block coordinate descent (BCD) algorithm is introduced to replace the large-scale matrix solution in geological structure-guided, and consequently reduce memory consumption and time cost. This methodology is validated on a synthetic seismic dataset, as well as on a real case. It has proven to be a reliable approach to obtain acoustic impedance (AI) from post-stack seismic data in an efficient way. It also addresses the uncertainty related with the ill-posed characteristics of the inversion methodology itself.
... Subsurface reservoir can be characterized as a mixed model consisting of continuous model parameters, such as the elastic moduli, physical properties, etc., and several discrete parameters, such as lithofacies (i.e., shale, sandstone), fluid facies (i.e., gas, oil, water), etc. (Grana et al., 2012(Grana et al., , 2013Yin et al., 2015;Zong et al., 2015;Li et al., 2017a,b;Figueiredo et al., 2014Figueiredo et al., , 2017Figueiredo et al., , 2018. As a branch of the geosciences, the estimation of rock physical properties and fluid properties using the observed seismic reflection data is an important topic to geophysicists. ...
... Compared with the regularized solutions to seismic inverse problems, the probability density distribution of a stochastic model can be obtained by the probabilistic seismic inversion based on the geophysical mapping relationship between the observed data and the model parameters to be inverted, the results of which aid in estimating the uncertainty and reliability of the estimated model parameters. Statistical learning is the basis of seismic probabilistic AVO inversion, and plays a K. Li et al. key role in reservoir modeling and geostatistics (Figueiredo et al., 2017(Figueiredo et al., , 2018Grana et al., 2012Grana et al., , 2013Gholami, 2015;Gonz� alez et al., 2008;Hastie et al., 2009;Bosch et al., 2010;Li et al., 2020). Bayesian inference is a popular statistical estimation method in reservoir characterization and fluid discrimination. ...
... In this work, the Gaussian mixture model pðm; μ k m ; C k m Þ is treated as the prior distribution pðmÞ for the subsurface model parameters describing the prior knowledge of m before the conditional seismic data has been collected, K. Li et al. where μ k m represents the prior mean of m for the k th Gaussian PDF, C k m represents the prior covariance matrix of m for the k th Gaussian PDF, λ k represents the prior proportions, or prior probabilities, of each fluid facies z k , which sum to one, and T is the total number of pore-fluid types (Hastie et al., 2009;Grana et al., 2012Grana et al., , 2013Li et al., 2020). In general, this prior knowledge, such as the variation function, prior mean and covariance, are collected from real logging data and well interpretation results by calculating the statistical characteristics of the well data. ...
Estimation of rock pore-fluid properties in subsurface reservoirs using seismic reflection data is an important topic in exploration geophysics. Prestack seismic inversion is a key approach for reservoir characterization and fluid discrimination. In this study, we propose a simultaneous estimation approach for discrete fluid facies (i.e., gas, oil, water) and continuous fluid indicators via a Bayesian seismic nonlinear inversion and the differential evolution Markov Chain Monte Carlo model. We derived one novel nonlinear exact PP-wave reflection coefficients equation characterized by Gassmann fluid term, shear modulus and density and the equation is more accurate and suitable for large incident angles. Besides, a mixture probability model is utilized as the prior probability density function (PDF) of the model parameters in the Bayesian seismic probabilistic inversion. Furthermore, the differential evolution Markov Chain Monte Carlo (DE-MCMC) model is developed to optimize the mixture posterior PDF in Bayesian seismic inference. The discrete fluid facies is estimated via the posterior weights of each probability component directly, which can reduce the uncertainty and the accumulation errors of seismic fluid discrimination. The main advantage of the DE-MCMC seismic probabilistic inversion is that it can simulate the posterior probability density distributions of the model parameters efficiently based on the simultaneous optimization of multiple Markov chains, which is helpful for the uncertainty assessment of the inversion results and fluid discrimination. Synthetic examples are provided to demonstrate the feasibility and stability of the proposed method. Furthermore, one field case of oil-gas exploration is presented to show the practicability of this method in reservoir fluid discrimination.
... Hansen et al. (2006) described the explicit solutions of geostatistics and Gaussian posterior probability density distribution to solve Bayesian linear inverse problem using sequential simulation algorithm. Grana et al. (2013) developed the seismic joint inversion of P-wave impedance and lithofacies, which is only applicable to the seismic linear inverse problem. However, the low-frequency regularization of P-wave impedance is not introduced in Grana et al. (2013Grana et al. ( , 2016, and the low-frequency background needs to be indirectly compensated to the final estimated results. ...
... Grana et al. (2013) developed the seismic joint inversion of P-wave impedance and lithofacies, which is only applicable to the seismic linear inverse problem. However, the low-frequency regularization of P-wave impedance is not introduced in Grana et al. (2013Grana et al. ( , 2016, and the low-frequency background needs to be indirectly compensated to the final estimated results. ...
Seismic Rock physics plays a bridge role between the rock moduli and physical properties of the hydrocarbon reservoirs. Prestack seismic inversion is an important method for the quantitative characterization of elasticity, physical properties, lithology and fluid properties of subsurface reservoirs. In this paper, a high order approximation of rock physics model for clastic rocks is established and one seismic AVO reflection equation characterized by the high order approximation (Jacobian and Hessian matrix) of rock moduli is derived. Besides, the contribution of porosity, shale content and fluid saturation to AVO reflectivity is analyzed. The feasibility of the proposed AVO equation is discussed in the direct estimation of rock physical properties. On the basis of this, one probabilistic AVO inversion based on differential evolution-Markov chain Monte Carlo stochastic model is proposed on the premise that the model parameters obey Gaussian mixture probability prior model. The stochastic model has both the global optimization characteristics of the differential evolution algorithm and the uncertainty analysis ability of Markov chain Monte Carlo model. Through the cross parallel of multiple Markov chains, multiple stochastic solutions of the model parameters can be obtained simultaneously, and the posterior probability density distribution of the model parameters can be simulated effectively. The posterior mean is treated as the optimal solution of the model to be inverted. Besides, the variance and confidence interval are utilized to evaluate the uncertainties of the estimated results, so as to realize the simultaneous estimation of reservoir elasticity, physical properties, discrete lithofacies and dry rock skeleton. The validity of the proposed approach is verified by theoretical tests and one real application case in eastern China.
... The core problem of reservoir modelling is reservoir prediction between wells. Compared with other geological bodies, oil and gas reservoirs are controlled by a variety of parameters, such as complex rock structures, spatial configurations and spatial changes in reservoir parameters, which leads to multiple solutions of stochastic modelling [25][26][27][28]. The accuracy of reservoir stochastic modelling depends on the number of well points involved in interpolation. ...
For 3D geological modelling of oil and gas reservoirs, well pattern density is directly related to the number of samples involved in the calculation, which determines the variation function of stochastic modelling and has great impacts on the results of reservoir modelling. This paper focuses on the relationship between well pattern density and the variogram of stochastic modelling, selects the large Sulige gas field with many well pattern types as the research object, and establishes a variogram database of stochastic models for different well pattern densities. First, the well pattern in the study area is divided into three different types (well patterns A, B, and C) according to well and row space. Several different small blocks (model samples) are selected from each type of well pattern to establish the model, and their reasonable variogram values (major range, minor range and vertical range) are obtained. Then, the variogram values of all model samples with similar well pattern densities are analysed and counted, and the variogram database corresponding to each type of well pattern is established. Finally, the statistical results are applied to the modelling process of other blocks with similar well pattern density to test their accuracy. The results show that the reservoir model established by using the variation function provided in this paper agrees well with the actual geological conditions and that the random model has a high degree of convergence. This database has high adaptability, and the model established is reliable.
