Gaussian Mixture Model Deep Neural Network and Its Application in Porosity Prediction of Deep Carbonate Reservoir

To estimate the spatial distribution of porosity, model-driven or data-driven methods are usually used to establish the relationship between porosity and seismic elastic parameters. However, due to the strong heterogeneity and complex pore structures of carbonate reservoirs, porosity estimation of carbonates still represents a great challenge. The existing conventional model-driven and data-driven-based porosity estimation methods have high uncertainty. In order to characterize the complex statistical distribution of porosity, the nonlinear relationship between porosity and seismic elastic parameters, and the uncertainty of porosity estimation, we propose to use a Gaussian Mixture Model Deep Neural Network (GMM-DNN) to invert porosity from seismic elastic parameters. We use a Gaussian mixture model to describe the complex distribution of porosity, and apply a deep neural network (DNN) to establish the nonlinear relationship between seismic P-wave velocity, density and porosity. The outputs of the GMM-DNN provide an estimated probability distribution of porosity conditioned on the input seismic elastic parameters. The synthetic data example verifies the feasibility of this method. We further apply the GMM-DNN-based porosity inversion method to a deep complex carbonate reservoir in the Tarim Basin, Northwest China. The well logging data is used to train the GMM-DNN, then the P-wave velocity and density obtained by pre-stack AVO inversion are fed into the trained network to reasonably estimate the porosity distribution of the whole target reservoir and evaluate its uncertainties.

Porosity estimation based on rock skeleton general formula and comprehensive pore structure parameter – An application to a tight-sand reservoir

Most of current 3D reservoir’s porosity estimation methods are based on analyzing the elastic parameters inverted from seismic data. It is well-known that elastic parameters vary with pore structure parameters such as pore aspect ratio, consolidate coefficient, critical porosity, etc. Thus, we may obtain inaccurate 3D porosity estimation if the chosen rock physics model fails properly address the effects of pore structure parameters on the elastic parameters. However, most of current rock physics models only consider one pore structure parameter such as pore aspect ratio or consolidation coefficient. To consider the effect of multiple pore structure parameters on the elastic parameters, we propose a comprehensive pore structure (CPS) parameter set that is generalized from the current popular rock physics models. The new CPS set is based on the first order approximation of current rock physics models that consider the effect of pore aspect ratio on elastic parameters. The new CPS set can accurately simulate the behavior of current rock physics models that consider the effect of pore structure parameters on elastic parameters. To demonstrate the effectiveness of proposed parameters in porosity estimation, we use a theoretical model to demonstrate that the proposed CPS parameter set properly addresses the effect of pore aspect ratio on elastic parameters such as velocity and porosity. Then, we obtain a 3D porosity estimation for a tight sand reservoir by applying it seismic data. We also predict the porosity of the tight sand reservoir by using neural network algorithm and a rock physics model that is commonly used in porosity estimation. The comparison demonstrates that predicted porosity has higher correlation with the porosity logs at the blind well locations.

Optimizing Borehole Images to Predict Porosity in New Discovery Limestone Minahaki Formation Pia-001 Exploration Well Matindok Block Central Sulawesi

PIA-001 exploration well is located 4 km away from Donggi Gas Field, Central Sulawesi. The objective of the well is to unlock the hydrocarbon potential in Minahaki Formation. However, this is not an easy task to do. Minahaki Formation is mainly comprised of heterogeneous limestone facies, in which the primary and secondary porosity varies from facies to facies at different scales. Moreover, the diagenesis processes, such as dissolution and cementation alter each facies differently. These are the factors that introduce high uncertainty in the porosity distribution and estimation in Minahaki Formation. The conventional method to predict porosity utilizes conventional logs such as density, neutron and sonic log. However, this method is not suitable to be used in heterogeneous limestone. Its low vertical sampling rates relative to the porosity distribution, fails to predict accurately the porosity and productivity potential of these complex reservoirs. Hence, porosity needs to be generated using other type of data. The ideal data to tackle this complexity is by using electrical borehole image log which was logged within water based mud. This data is in high resolution and cover 360-degree view of borehole wall. On top of that, by using the newly developed carbonate textural and porosity estimation method, the porosity as well as the productivity potential can be accurately generated. This carbonate textural and porosity computation method has been performed in PIA-001 Well. It is observed that the secondary porosity in PIA-001 well comprises of vugs connected to fractures, vugs connected to bed boundary and connected vugs with some isolated vugs, with the total porosity ranges from 10-20%. Generally, this porosity trend shows good correlation with the porosity result from routine core analysis. Besides that, the porosity as well as the connectivity from this method is used to assist the DST interval selection. Based on this study, it can be concluded that electrical borehole image contributes to significant improvement in heterogeneous limestone porosity estimation. The porosity result also shows a good correlation with the porosity from routine core analysis and flow potential from DST Test. It is suggested to perform the same analysis to improve the success ratio in exploration well with the same reservoir challenges.