No abstract

The estimation of the formation permeability is considered a vital process in assessing reservoir deliverability. The prediction of such a rock property with the use of the minimum number of inputs is mandatory. In general, porosity and permeability are independent rock petrophysical properties. Despite these observations, theoretical relationships have been proposed, such as that by the Kozeny–Carmen theory. This theory, however, treats a highly complex porous medium in a very simple manner. Hence, this study proposes a comprehensive ANN model based on the back propagation learning algorithm using the FORTRAN language to predict the formation permeability from available well logs. The proposed ANN model uses a weight visualization curve technique to optimize the number of hidden neurons and layers. Approximately 500 core data points were collected to generate the model. These data, including gamma ray, sonic travel time, and bulk density, were collected from numerous wells drilled in the Western Desert and Gulf areas of Egypt. The results show that in order to predict the permeability accurately, the data set must be divided into 60% for training, 20% for testing, and 20% for validation with 25 neurons. The results yielded a correlation coefficient (R2) of 98% for the training and 96.5% for the testing, with an average absolute percent relative error (AAPRE) of 2.4%. To validate the ANN model, two published correlations (i.e., the dual water and Timur’s models) for calculating permeability were used to achieve the target. In addition, the results show that the ANN model had the lowest mean square error (MSE) of 0.035 and AAPRE of 0.024, while the dual water model yielded the highest MSE of 0.84 and APPRE of 0.645 compared to the core data. These results indicate that the proposed ANN model is robust and has strong capability of predicting the rock permeability using the minimum number of wireline log data.

Unlike conventional gas reservoirs, fluid flow in shale gas reservoirs is characterized by complex interactions between various factors, such as stress sensitivity, matrix shrinkage, and critical desorption pressure. These factors play a crucial role in determining the behavior and productivity of shale gas reservoirs. Stress sensitivity refers to the stress changes caused by formation pressure decline during production, where the shale gas formation becomes more compressed and its porosity decreases. Matrix shrinkage, on the other hand, refers to the deformation of the shale matrix due to the gas desorption process once the reservoir pressure reaches the critical desorption pressure where absorbed gas molecules start to leave the matrix surface, causing an increase in shale matrix porosity. Therefore, the accurate estimation of gas reserves requires careful consideration of such unique and complex interactions of shale gas flow behavior when using a material balance equation (MBE). However, the existing MBEs either neglect some of these important parameters in shale gas reserve analysis or employ an iterative approach to incorporate them. Accordingly, this study introduces a straightforward modification to the material balance equation. This modification will enable more accurate estimation of shale gas reserves by considering stress sensitivity and variations in porosity during shale gas production and will also account for the effect of critical desorption pressure, water production, and water influx. By establishing a linear relationship between reservoir expansion and production terms, we eliminate the need for complex and iterative calculations. As a result, this approach offers a simpler yet effective means of estimating shale gas reserves without compromising accuracy. The proposed MBE was validated using an in-house finite element poro-elastic model which accounts for stress re-distribution and deformation effects during shale gas production. Moreover, the proposed MBE was tested using real-field data of a shale gas reservoir obtained from the literature. The results of this study demonstrate the reliability and usefulness of the modified MBE as a tool for accurately assessing free and adsorbed shale gas volumes.

Shale gas reservoirs are one of the most rapidly growing forms of natural gas worldwide. Gas production from such reservoirs is possible by using extensive and deep well fracturing to contact bulky fractions of the shale formation. In addition, the main mechanisms of the shale gas production process are the gas desorption that takes place by diffusion of gas in the shale matrix and by Darcy’s type through the fractures. This study presents a finite element model to simulate the gas flow including desorption and diffusion in shale gas reservoirs. A finite element model is used incorporated with a quadrilateral element mesh for gas pressure solution. In the presented model, the absorbed gas content is described by Langmuir’s isotherm equation. The non-linear iterative method is incorporated with the finite element technique to solve for gas property changes and pressure distribution. The model is verified against an analytical solution for methane depletion and the results show the robustness of the developed finite element model in this study. Further application of the model on the Barnett Shale field is performed. The results of this study show that the gas desorption in Barnett Shale field affects the gas flow close to the wellbore. In addition, an artificial neural network model is designed in this study based on the results of the validated finite element model and a back propagation learning algorithm to predict the well gas rates in shale reservoirs. The data created are divided into 70% for training and 30% for the testing process. The results show that the forecasting of gas rates can be achieved with an R2 of 0.98 and an MSE = 0.028 using gas density, matrix permeability, fracture length, porosity, PL (Langmuir’s pressure), VL (maximum amount of the adsorbed gas (Langmuir’s volume)) and reservoir pressure as inputs.

This paper presents a new and innovative approach for the estimation of relative permeability of porous fractured carbonate rocks. The presented method differs from previous studies in that the relative permeability estimation for three different systems that exists in fractured rocks is measured. Fracture, matrix, as well as fracture-matrix porous systems are all taking into account with laboratory measurements of relative permeability and capillary pressure. In this study, both steady and un-steady states are used for the estimation of relative permeability in addition to the produced water during drainage flooding. Fracture surface topography is imaged by the use of surface scanning technique to determine the asperities of the surface and their heights. Simulation based on Reynolds equation is considered when developing the mathematical formulation of multiphase flow simulation. The developed mathematical model based on the integration of Darcy, cubic law and Reynolds to account for the variation of different porosity systems. The results simulated numerically are in a good agreement with the laboratory.