We assemble a multiscale physical model of gas production in a mudrock (shale). We then tested our model on 45 horizontal gas wells in the Barnett with 12–15 years on production. When properly used, our model may enable shale companies to gain operational insights into how to complete a particular well in a particular shale. Macrofractures, microfractures, and nanopores form a multiscale system that controls gas flow in mudrocks. Near a horizontal well, hydraulic fracturing creates fractures at many scales and increases permeability of the source rock. We model the physical properties of the fracture network embedded in the Stimulated Reservoir Volume (SRV) with a fractal of dimension D < 2 . This fracture network interacts with the poorly connected nanopores in the organic matrix that are the source of almost all produced gas. In the practically impermeable mudrock, the known volumes of fracturing water and proppant must create an equal volume of fractures at all scales. Therefore, the surface area and the number of macrofractures created after hydrofracturing are constrained by the volume of injected water and proppant. The coupling between the fracture network and the organic matrix controls gas production from a horizontal well. The fracture permeability, k f , and the microscale source term, s, affect this coupling, thus controlling the reservoir pressure decline and mass transfer from the nanopore network to the fractures. Particular values of k f and s are determined by numerically fitting well production data with an optimization algorithm. The relationship between k f and s is somewhat hyperbolic and defines the type of fracture system created after hydrofracturing. The extremes of this relationship create two end-members of the fracture systems. A small value of the ratio k f / s causes faster production decline because of the high microscale source term, s. The effective fracture permeability is lower, but gas flow through the matrix to fractures is efficient, thus nullifying the negative effect of the smaller k f . For the high values of k f / s , production decline is slower. In summary, the fracture network permeability at the macroscale and the microscale source term control production rate of shale wells. The best quality wells have good, but not too good, macroscale connectivity.

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In recent years, many machine-learning models have been developed to predict future production of oil in gas in "shales". Long-short term memory (LSTM), the most widely used model, relies on the long-term production history for a reasonably accurate production forecast. All analytical and machine learning models, including LSTM, fail miserably in the absence of long production history. Our goal is to present a novel method of production forecasting using only 24 months of production data. The first and secondorder derivatives of the distance traveled give speed and acceleration to describe the trajectory and dynamics of a moving vehicle. Similarly, higher-order derivatives of hydrocarbon/water production rate vs. time uncover hidden patterns and fluctuations in a well that act as differential markers of its future recovery factor (RF). In this paper, we couple production data and their higher-order derivatives with other known parameters for a well, i.e., well length and initial production. The time-series data are passed into a Convolutional Neural Network (CNN) with two hidden layers of 16 nodes each, and one output layer. The model is trained to predict recovery factor (RF) in the 10th year of production. We analyze the first 24 months of production data for the Barnett (1500), Marcellus (800), Haynesville (800), and Eagle Ford (1000) shale wells. All wells have a minimum pressure interference time of 34 months. The production rate vs. time and its first, second, and third-order derivatives are coupled with the well length and initial production rate, and the data are normalized with their respective maxima. For the Barnett wells, the CNN model predicts recovery factors in their 10th year of production with an average accuracy of 90%. For the Marcellus, Haynesville, and Eagle Ford wells, the prediction accuracy in the 8th year of production is 89%, 92%, and 91%, respectively. Further, we divide the wells into three groups (A, B, C) depending on the range of their recovery factor (A:RF=0-0.3, B:RF=0.3-0.6, and C:RF=0.6-0.9). We show that the clusters of wells grouped by their RFs strongly correlate with the distribution of the higher-order de rivatives of production from these wells. Thus, we posit that the detailed production history and its derivatives are the most important variables that define distributions of maximum recoverable hydrocarbon from a source rock. Our novel method uses only 24 months of production data to predict future recovery factor with an outstanding average accuracy of 90%. We show that the higher-order derivatives of high-resolution production data available from the operators could be an excellent tool for well screening and predicting future production with reasonable accuracy.

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