(753e) Deep Learning Based Hybrid Model of Hydraulic Fracturing Process

Many chemical processes undergo complex dynamics which can be explained using a model of the process. Models can either be based on first principle techniques (white box models) or can be data driven (black box models) [1]. One of the key difference between the methods is in the nature of the parameters. In first principles based models, the number of parameters are fixed and they carry physical meaning related to the process. On the contrary, in data-based models the number of parameters vary and their nature is flexible [2]. Hybrid models are a combination of the first principles and data based sub-models, and were first built using neural networks [2, 3]. The key idea was that the first principles knowledge about the process being modeled can be integrated with a neural network which can approximately estimate the unmeasured process parameters [3]. Since then, the field of neural networks has transformed from a single hidden layer to multiple hidden layers in a neural network which has shown tremendous ability to capture and represent complex data [4]. In this work, we combine the power of deep learning and first principles based knowledge of a hydraulic fracturing process to build a hybrid model which balances the advantages and disadvantages of a strictly first principles or neural networks based model.

Hydraulic fracturing is a highly complex and non-linear process of extracting oil/gas from rock formations which have low porosity and permeability. Its first principles based models consist of a system of nonlinear highly-coupled PDEs with time-dependent spatial domain and usually assume homogeneity of reservoir rock properties [5, 6]. But in reality the rock properties such as Young’s modulus, rock permeability and porosity etc. vary even within the same formation. Other process parameters such as fluid leak-off coefficient, proppant particle size are assumed to be constant throughout the process which is not true. The effect of these uncertainties cannot be undermined and they need to be integrated with the first principles based model in order to improve its prediction accuracy during the propagation of hydraulic fracture. We aim to achieve this by developing a hybrid model which includes a deep neural network that will approximate the uncertainties within the rock formation and a first principles based model that will explain the dynamics of the process. The overall structure of the hybrid model is similar to the first principles model which helps in interpreting the quantified uncertainties. We will demonstrate the superiority of this hybrid model in comparison to the strictly first principles based model in terms of prediction accuracy and also in comparison to strictly deep neural network based model in terms of reliability and extrapolation.

Literature cited:

[1] von Stosch, M., Oliveira, R., Peres, J., Feyo de Azevedo, S., 2014. Hybrid semi-parametric modeling in process systems engineering: Past, present and future. Comput. Chem. Eng. 60, 86-101.

[2] Thompson, M.L., Kramer, M.A., 1994. Modeling chemical processes using prior knowledge and neural networks. AIChE J. 40, 1328–1340.

[3] Psichogios, D.C., Ungar, L.H., 1992. A hybrid neural network-first principles approach to process modeling. AIChE J. 38, 1499-1511.

[4] Venkatasubramaniam, V., 2018. The promise of artificial intelligence in chemical engineering: Is it here, finally? AIChE J. 65, 466-478.

[5] Yang, S., Siddhamshetty, P., Kwon, J.S., 2017. Optimal pumping schedule design to achieve a uniform proppant concentration level in hydraulic fracturing. Comput. Chem. Eng. 101, 138-147.

[6] Economides, M.J., Nolte, K.G., 2000. Reservoir stimulation. Chichester, Wiley.