An approximate analytical solution for transient gas flows in a vertically fractured well of finite fracture conductivity

An analytical solution in physical variable space is presented for transient gas flows during constant-rate production from a vertically-fractured well in an infinite homogeneous reservoir with finite fracture conductivity.The solution is based on the short-time asymptotic solution and a new approximate transient elliptical flow solution,which covers transient flows from the bilinear flow regime to the pseudo-radial flow regime.The solution covers the well-known asymptotic solutions in both short-and long-time limits of bilinear and pseudo-radial flows.The analytical model provides a practical and reliable engineering tool to evaluate the fractured reservoir properties,which can be programmed using a spreadsheet.

An adaptive physics-informed deep learning method for pore pressure prediction using seismic data

Accurate prediction of formation pore pressure is essential to predict fluid flow and manage hydrocarbon production in petroleum engineering.Recent deep learning technique has been receiving more interest due to the great potential to deal with pore pressure prediction.However,most of the traditional deep learning models are less efficient to address generalization problems.To fill this technical gap,in this work,we developed a new adaptive physics-informed deep learning model with high generalization capability to predict pore pressure values directly from seismic data.Specifically,the new model,named CGP-NN,consists of a novel parametric features extraction approach(1DCPP),a stacked multilayer gated recurrent model(multilayer GRU),and an adaptive physics-informed loss function.Through machine training,the developed model can automatically select the optimal physical model to constrain the results for each pore pressure prediction.The CGP-NN model has the best generalization when the physicsrelated metricλ=0.5.A hybrid approach combining Eaton and Bowers methods is also proposed to build machine-learnable labels for solving the problem of few labels.To validate the developed model and methodology,a case study on a complex reservoir in Tarim Basin was further performed to demonstrate the high accuracy on the pore pressure prediction of new wells along with the strong generalization ability.The adaptive physics-informed deep learning approach presented here has potential application in the prediction of pore pressures coupled with multiple genesis mechanisms using seismic data.

Machine learning for carbonate formation drilling: Mud loss prediction using seismic attributes and mud loss records

Due to the complexity and variability of carbonate formation leakage zones, lost circulation prediction and control is one of the major challenges of carbonate drilling. It raises well-control risks and production expenses. This research utilizes the H oilfield as an example, employs seismic features to analyze mud loss prediction, and produces a complete set of pre-drilling mud loss prediction solutions. Firstly, 16seismic attributes are calculated based on the post-stack seismic data, and the mud loss rate per unit footage is specified. The sample set is constructed by extracting each attribute from the seismic trace surrounding 15 typical wells, with a ratio of 8:2 between the training set and the test set. With the calibration results for mud loss rate per unit footage, the nonlinear mapping relationship between seismic attributes and mud loss rate per unit size is established using the mixed density network model.Then, the influence of the number of sub-Gausses and the uncertainty coefficient on the model's prediction is evaluated. Finally, the model is used in conjunction with downhole drilling conditions to assess the risk of mud loss in various layers and along the wellbore trajectory. The study demonstrates that the mean relative errors of the model for training data and test data are 6.9% and 7.5%, respectively, and that R2is 90% and 88%, respectively, for training data and test data. The accuracy and efficacy of mud loss prediction may be greatly enhanced by combining 16 seismic attributes with the mud loss rate per unit footage and applying machine learning methods. The mud loss prediction model based on the MDN model can not only predict the mud loss rate but also objectively evaluate the prediction based on the quality of the data and the model.

Experimental investigation and correlations for proppant distribution in narrow fractures of deep shale gas reservoirs

Hydraulic fracturing is a crucial stimulation for the development of deep shale gas reservoirs.A key challenge to the effectiveness of hydraulic fracturing is to place small proppants in complex narrow fractures reasonably.The experiments with varied particle and fluid parameters are carried out in a narrow planar channel to understand particle transport and distribution.The four dimensionless parameters,including the Reynold number,Shields number,density ratio,and particle volume fraction,are introduced to describe the particle transport in narrow fractures.The results indicate that the narrow channel probably induces fluid fingers and small particle aggregation in a highly viscous fluid,leading to particle settlement near the entrance.The low viscous fluid is beneficial to disperse particles further into the fracture,especially in the high-speed fluid velocity.The linear and natural logarithmic laws have relationships with dimensionless parameters accurately.The multiple linear regression method developed two correlation models with four dimensionless parameters to predict the bed equilibrium height and covered area of small particles in narrow fractures.The study provides fundamental insight into understanding small size proppant distribution in deep reservoirs.