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An a priori model for multipoint statistics (MPS) modeling approaches is a training image. Before using MPS modeling, it must be determined whether the training images satisfy the spatial statistical stationarity. Modeling can be performed using the regular MPS approach if a training image is stationary. Otherwise, an enhanced method of nonstationary modeling is required. For instance, partition-based nonstationary modeling is an option. This study proposes a nonstationary evaluation metric based on pattern tile distances. It is possible to more accurately quantify the characteristics of the various distributions of spatial structure features in the entire space and achieve the goal of quantitatively evaluating the nonstationary metrics of training images by quantifying the distances of lower-level subpatterns in the pattern. Furthermore, an automatic partitioning approach based on pattern tile discrepancy is proposed for nonstationary training images to avoid the subjective and inefficient issues of manual partitioning when the training images cannot meet the stationary requirement of MPS modeling.

AbstractA new modeling method is proposed to address the shortcomings of conventional geological modeling methods in simultaneously characterizing the geometry, stacking patterns, and well data of the channel bar in braided river. The channel bar model is reconstructed based on the target body, which is defined by the channel bar’s geometric parameters points, lines, and surfaces. In the simulation process, the distributions of sandstone and mudstone are simulated first. Then, the channel bars at the well are simulated based on the channel bars identified on the well and the thickness of the sandstone, the priori geometries, and sizes of the channel bars. It is judged whether the proportion of the simulated channel bars has reached the global proportion. If not, a randomly selected point between wells is used as a virtual well, and the sandstone thickness is used to determine whether it is a single or composite channel bar. The process is repeated until the proportion of channel bars reaches the set proportion. Take the N gas field as an example. The analysis of the geometry, variance function, thickness distribution histogram, and volume distribution histogram of the simulation results shows that the new method can better characterize the channel bar’s geometry, sizes, and stacking patterns than the multipoint geostatistical modeling method Snesim.

AbstractThe proportion of different lithofacies is essential to determine the net-gross ratio, which directly affects the calculation of oil and gas reserves. Under the condition of few wells, the reliability of different lithofacies proportions obtained using well data is poor because it is difficult to estimate the uncertainty variation range of different lithofacies proportions. The present study overcomes this problem using an uncertainty evaluation method for reservoir lithofacies proportion. First, different lithofacies proportions of the reservoir are determined using the well and seismic data and are considered as the most likely estimated. Based on the lithofacies proportion, the lithofacies models of the study area are developed. Second, uniform and random methods are applied to sample the lithofacies models, and then, the probability distribution functions of different lithofacies proportions are derived. Third, the three levels of lithofacies proportions in the study area are calculated using the method of quantile and discretization of the probability distribution. Finally, we take M gas field as a sample and compare the test results of the fixed and random well structures. The results show that the sampling results of the fixed well structure model significantly deviate under the influence of the extension direction of the channel and well pattern distribution. Therefore, it is suggested to use random well structure to determine the uncertainty distribution range of lithofacies proportion.

AbstractTraining image (TI) is important for multipoint statistics simulation method (MPS), since it captures the spatial geological pattern of target reservoir to be modeled. Generally, one optimal TI is selected before applying MPS by evaluating the similarities between many TIs and the well interpretations of target reservoir. In this paper, we propose a new training image optimization approach based on the convolutional neural network (CNN). First, candidate TIs were randomly sampled several times to obtain the sample dataset. Then, the CNN was used to conduct transfer learning for all samples, and finally, the optimal TI of the conditioning well data is selected through the trained CNN model. By taking advantage of the strong learning ability of CNN in image feature recognition, the proposed method can automatically identify differences in spatial features between the conditioning well data and the samples of the training image. Hence, it effectively resolves the difficulty of spatial matching between discrete datapoints and grid structures. We demonstrated the applicability of our model via 2D and 3D training image selection examples. The proposed methods effectively selected the appropriate TI, and then the pretreatment techniques for improving the accuracy of continuous TI selection were achieved. Moreover, the proposed method was successfully applied to training image selection of a discrete fracture network model. Finally, sensitivity analysis was carried out to show that sufficient conditioning data volume can reduce the uncertainty of the optimization results. By comparing with the improved MDevD method, the advantages of the new method are verified in terms of efficiency and reliability.