A machine learning framework for rapid forecasting and history matching in unconventional reservoirs

Abstract

We present a novel workflow for forecasting production in unconventional reservoirs using reduced-order models and machine-learning. Our physics-informed machine-learning workflow addresses the challenges to real-time reservoir management in unconventionals, namely the lack of data (i.e., the time-frame for which the wells have been producing), and the significant computational expense of high-fidelity modeling. We do this by applying the machine-learning paradigm of transfer learning, where we combine fast, but less accurate reduced-order models with slow, but accurate high-fidelity models. We use the Patzek model (Proc Natl Acad Sci 11:19731-19736, https://doi.org/10.1073/pnas.1313380110 , 2013) as the reduced-order model to generate synthetic production data and supplement this data with synthetic production data obtained from high-fidelity discrete fracture network simulations of the site of interest. Our results demonstrate that training with low-fidelity models is not sufficient for accurate forecasting, but transfer learning is able to augment the knowledge and perform well once trained with the small set of results from the high-fidelity model. Such a physics-informed machine-learning (PIML) workflow, grounded in physics, is a viable candidate for real-time history matching and production forecasting in a fractured shale gas reservoir.

Figure 1

PIML workflow for reservoir management. Short-term production data is supplied to the machine-learning inverse model which predicts appropriate site parameters that are then used as inputs to the forward model. Note that the forward model could be either physics based or again a machine-learning model.

Figure 2

A magnified look at the steps to produce an ML inverse model illustrating how the transfer learning paradigm uses both synthetic data from reduced-order models as well as high-fidelity models. Note that in this workflow, we used Patzek model as the reduced-order model, but the same workflow can be used with other reduced-order model choices that may be physics-based or even data-driven.

Figure 3

The DFN model with an octree-refined continuum mesh has $5\times {10}^5$ cells, despite using upscaling for permeability and porosity. There is large contrast in permeability and porosity since fractures are more permeable than the matrix, resulting in a stiff system after numerical discretization. Thus, it is difficult to simulate gas flow and transport for long periods of time, rendering the approach infeasible as a tool to generate large datasets or as a fast forward model for forecasting.

Figure 4

Benchmarking our model using actual dynamic production data from the MIP-3H well at the MSEEL site. The well boundary is assigned the same pressure as the well at the site (blue line) and we measure the amount of gas that is removed from the system. The agreement between the production from our simulated system (red line) agrees quite well with the field data (magenta line). Some differences are to be expected due to the assumptions in the model, but they do not appear to affect the first order behavior, especially for the first few years of production. At later times, the model diverges slightly, which could be due to second order effects (e.g., fracture mechanics and stimulation, interacting wells) that are not included in the model.

Figure 5

The Patzek reduced-order model can accurately fit the production data obtained from the high-fidelity model runs. This is evident from the root mean square (RMS) error of the fit, which is less than ${10}^{-5}$ in each of these plots.

Figure 6

The normalized cumulative production obtained from 150 high-fidelity simulations for a time-span of 10 years is shown. The production curves show an appreciable spread corresponding to the variance in the data. The simulations correspond to 150 samples of various parameters determined by the model of the fracture network. The fracture network model is based on data from the MSEEL site.

Figure 7

Parameter prediction from the ANN with parameter loss function (7) before (left) and after (right) transfer learning. Observe that training with synthetic data from the Patzek reduced-order model yields reasonable performance which improves remarkably after transfer learning. The distribution of the true parameters has a mean and standard deviation of 0.07 and 0.23 for $\overline{\alpha }$ and 0.49 and 0.22 for $\overline{M}$.

Figure 8

Predicted production profile obtained with Patzek reduced-order model from the ANN with parameter loss function (7) before (left) and after (right) transfer learning. In the previous figure, we observed that before transfer learning, the predicted parameters were reasonable. However, here we see that training with synthetic data from the Patzek reduced-order model is not able to capture the production profile generated by a high-fidelity model, but transfer learning with synthetic data from 100 DFN simulations is able to correct the discrepancy.

Figure 9

Parameter prediction from the ANN with production loss function (8) before (left) and after (right) transfer learning. The training with synthetic data from the Patzek reduced-order model is not geared to predict the parameters accurately, but instead to match the production.

Figure 10

Predicted production profile obtained with Patzek reduced-order model from the ANN with parameter loss function (8) before (left) and after (right) transfer learning with data from 100 DFN simulations. Observe that training with small amount of high-fidelity data from DFN simulations allows the ANN to capture the production profile generated by a high-fidelity model, but without transfer learning, the predicted results are not useful.