A study of correlation between permeability and pore space based on dilation operation

CO2 and fracturing liquid injection into tight and shale gas reservoirs induces reactivity between minerals and injected materials, which results in porosity change and thus permeability change. In this paper, the dilation operation is used to simulate the change of the porosity and the corresponding change of permeability based on Lattice-Boltzmann is studied. Firstly we obtain digital images of a real core from CT experiment. Secondly the pore space of digital cores is expanded by dilation operation which is one of basic mathematical morphologies. Thirdly, the distribution of pore bodies and pore throats is obtained from the pore network modeling extracted by maximal ball method. Finally, the correlation between network modeling parameters and permeabilities is analyzed. The result is that the throat change leads to exponential change of permeability and that the big throats significantly influence permeability.Cited as: Zha, W., Yan, S., Li, D., et al. A study of correlation between permeability and pore space based on dilation operation. Advances in Geo-Energy Research, 2017, 1(2): 93-99, doi: 10.26804/ager.2017.02.0

Reconstruction of shale image based on Wasserstein Generative Adversarial Networks with gradient penalty

 Generative Adversarial Networks (GANs), as most popular artificial intelligence models in the current image generation field, have excellent image generation capabilities. Based on Wasserstein GANs with gradient penalty, this paper proposes a novel digital core reconstruction method. First, a convolutional neural network is used as a generative network to learn the distribution of real shale samples, and then a convolutional neural network is constructed as a discriminative network to distinguish reconstructed shale samples from real ones. Through this confrontation training method, realistic digital core samples of shale can be reconstructed. The paper uses two-point covariance function, Frechet Inception Distance and Kernel Inception Distance, to evaluate the quality of digital core samples of shale reconstructed by GANs. The results show that the covariance function can test the similarity between generated and real shale samples, and that GANs can efficiently reconstruct digital core samples of shale with high-quality. Compared with multiple point statistics, the new method does not require prior inference of the probability distribution of the training data, and directly uses noise vector to generate digital core samples of shale without using constraints of "hard data" in advance. It is easy to produce an unlimited number of new samples. Furthermore, the training time is also shorter, only 4 hours in this paper. Therefore, the new method has some good points compared with current methods.Cited as: Zha, W., Li, X., Xing, Y., He, L., Li, D. Reconstruction of shale image based on Wasserstein Generative Adversarial Networks with gradient penalty. Advances in Geo-Energy Research, 2020, 4(1): 107-114, doi: 10.26804/ager.2020.01.1

An equivalent single-phase flow for oil-water two-phase flow and its potential application in well test

In this work an equivalent single-phase flow model is proposed based on the oil-water two-phase flow equation with saturation-dependent parameters such as equivalent viscosity and equivalent formation volume factor. The equivalent viscosity is calculated from the oil-water relative permeability curves and oil-water viscosity. The equivalent formation volume factor is obtained by the fractional flow of the water phase. In the equivalent single-phase flow model, the equivalent viscosity and phase saturation are interdependent when the relative permeability curves are known. Four numerical experiments based on PEBI grids show that equivalent single-phase flow has a good agreement with the oil-water two-phase flow, which shows that the equivalent single-phase flow model can be used to interpret oil-water two-phase pressure data measured in the wellbore during the buildup period. Because numerical solution of single-phase flow model is several times faster than that of the two-phase flow model, whether the new model interprets the pressure data directly or offers good initial values for the true oil-water two-phase pressure data interpretation, it will obviously improve the efficiency of the interpretation of oil-water pressure data and decrease the burden of engineers.Cited as: Zha, W., Li, D., Lu, Z., Jia, B. An equivalent single-phase flow for oil-water two-phase flow and its potential application in well test. Advances in Geo-Energy Research, 2018, 2(2): 218-227, doi: 10.26804/ager.2018.02.0

Application of the ensemble Kalman filter for assisted layered history matching

Ensemble Kalman filter (EnKF) method has been used for automatic history matching the well production data such as production rate and watercut. However, the data of the connection watercut and connection rate are rarely used. In this work we conducted a history matching study based on the connection information using the EnKF for the first time to improve the matching accuracy. First, the initial implementation models are generated using the sequential Gaussian simulation method. Second, we choose the well watercut and connection watercut of each layer as production data respectively. During this step, the data such as permeability, pressure, saturation, and production data are normalized to improve the accuracy of history matching and reduce the simulation time. Finally, the case using the well watercut as historical production data is compared against the case using the connection watercut using EnKF. The results show that the well bottomhole pressure and connection watercut can be better matched using the connection watercut as the historical production data. In addition, the simulation time decreases significantly.Cited as: Zha, W., Gao, S., Li, D., Chen, K. Application of the ensemble Kalman filter for assisted layered history matching. Advances in Geo-Energy Research, 2018, 2(4): 450-456, doi: 10.26804/ager.2018.04.0

Application of the ensemble Kalman filter for assisted layered history matching

Ensemble Kalman filter (EnKF) method has been used for automatic history matching the well production data such as production rate and watercut. However, the data of the connection watercut and connection rate are rarely used. In this work we conducted a history matching study based on the connection information using the EnKF for the first time to improve the matching accuracy. First, the initial implementation models are generated using the sequential Gaussian simulation method. Second, we choose the well watercut and connection watercut of each layer as production data respectively. During this step, the data such as permeability, pressure, saturation, and production data are normalized to improve the accuracy of history matching and reduce the simulation time. Finally, the case using the well watercut as historical production data is compared against the case using the connection watercut using EnKF. The results show that the well bottomhole pressure and connection watercut can be better matched using the connection watercut as the historical production data. In addition, the simulation time decreases significantly

Effect of Matrix-Wellbore Flow and Porosity on Pressure Transient Response in Shale Formation Modeling by Dual Porosity and Dual Permeability System

A mathematical dual porosity and dual permeability numerical model based on perpendicular bisection (PEBI) grid is developed to describe gas flow behaviors in shale-gas reservoirs by incorporating slippage corrected permeability and adsorbed gas effect. Parametric studies are conducted for a horizontal well with multiple infinite conductivity hydraulic fractures in shale-gas reservoir to investigate effect of matrix-wellbore flow, natural fracture porosity, and matrix porosity. We find that the ratio of fracture permeability to matrix permeability approximately decides the bottom hole pressure (BHP) error caused by omitting the flow between matrix and wellbore and that the effect of matrix porosity on BHP is related to adsorption gas content. When adsorbed gas accounts for large proportion of the total gas storage in shale formation, matrix porosity only has a very small effect on BHP. Otherwise, it has obvious influence. This paper can help us understand the complex pressure transient response due to existence of the adsorbed gas and help petroleum engineers to interpret the field data better

Investigation of low water recovery based on gas-water two-phase low-velocity Non-Darcy flow model for hydraulically fractured horizontal wells in shale

Various mechanisms are employed to interpret the low water recovery during the shale-gas production period, such as extra-trapped water in the fracture network, water imbibition due to osmotic pressure and capillary pressure. These lead to the difficulty of water flow, which could be described by low-velocity non-Darcy's law known as threshold pressure gradient (TPG). In this paper we firstly employ the low-velocity non-Darcy's law to describe the water flow and use Darcy flow accounting for slip flow and free molecular flow mechanisms to model gas flow in the shale formation. The sensitive study using numerical simulation shows that the proposed flow model could model the low fracturing liquid recovery and that large pseudo TPG leads to lower fracturing liquid recovery. Thus, the proposed model would give new insight to model the low water recovery in shale formations