=Paper= {{Paper |id=Vol-2587/article_10 |storemode=property |title=Physics-Informed Machine Learning for Real-time Reservoir Management |pdfUrl=https://ceur-ws.org/Vol-2587/article_10.pdf |volume=Vol-2587 |authors=Maruti K. Mudunuru,Daniel O’Malley,Shriram Srinivasan,Jeffrey D. Hyman,Matthew R. Sweeney,Luke Frash,Bill Carey,Michael R. Gross,Nathan J. Welch,Satish Karra,Velimir V. Vesselinov,Qinjun Kang,Hongwu Xu,Rajesh J. Pawar,Tim Carr,Liwei Li,George D. Guthrie,Hari S. Viswanathan |dblpUrl=https://dblp.org/rec/conf/aaaiss/MudunuruOSHSFCG20 }} ==Physics-Informed Machine Learning for Real-time Reservoir Management== https://ceur-ws.org/Vol-2587/article_10.pdf

Physics-informed Machine Learning for Real-time Unconventional Res-
ervoir Management
Maruti K. Mudunuru, Daniel O’Malley, Shriram Srinivasan, Jeffrey D. Hyman, Matthew R.
Sweeney, Luke Frash, Bill Carey, Michael R. Gross, Nathan J. Welch, Satish Karra, Velimir V.
Vesselinov, Qinjun Kang, Hongwu Xu, Rajesh J. Pawar, Tim Carr, Liwei Li, George D. Guthrie,
Hari S. Viswanathan
Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM-87544.
Department of Geology & Geography, West Virginia University, Morgantown, WV 26506.
{maruti,omalled,shrirams,jhyman,msweeney2796,lfrash,bcarey,michael_gross,nwelch,satkarra,vvv,qkang,hxu,ra-
jesh,geo,viswana}@lanl.gov, {tim.carr,liwei.li}@mail.wvu.edu

Abstract rock formations that have high porosity and permeability
We present a physics-informed machine learning (PIML) (Bahadori, 2017). These rock formations are found below an
workflow for real-time unconventional reservoir manage- impermeable rock. However, energy extraction from uncon-
ment. Reduced-order physics and high-fidelity physics model ventional hydrocarbon resources (Ahmmed and Meehan,
simulations, lab-scale and sparse field-scale data, and ma-
2016) involves using advanced drilling and stimulation
chine learning (ML) models are developed and combined for
real-time forecasting through this PIML workflow. These techniques (e.g., long horizontal laterals and multi-stage hy-
forecasts include total cumulative production (e.g., gas, wa- draulic fracturing) to extract crude oil and natural gas that
ter), production rate, stage-specific production, and spatial are trapped in the pores of relatively impermeable sediment-
evolution of quantities of interest (e.g., residual gas, reservoir ary rocks (e.g., shale, tight sandstones).
pressure, temperature, stress fields). The proposed PIML
Typically, unconventional reservoirs have porosity in the
workflow consists of three key ingredients: (1) site behavior
libraries based on fast and accurate physics, (2) ML-based range of 0.04-0.08 and matrix permeability on the order of
inverse models to refine key site parameters, and (3) a fast nanodarcies (10-16-10-20 m2) (Rezaee, 2015; Belyadi et al.,
forward model that combines physical models and ML to 2019). Instead of the porous flow that dominates conven-
forecast production and reservoir conditions. First, synthetic tional reservoirs, fracture flow dominates unconventional
production data from multi-fidelity physics models are inte-
reservoirs, with natural fractures dissecting the matrix and
grated to develop the site behavior library. Second, ML-based
inverse models are developed to infer site conditions and en- intersecting with the hydraulic fractures. As result, energy
able the forecasting of production behavior. Our preliminary extraction is more difficult than conventional reservoirs.
results show that the ML-models developed based on PIML Model-based optimization of unconventional reservoirs is
workflow have good quantitative predictions (>90% based on also challenging because due to the long horizontal laterals
R2-score). In terms of computational cost, the proposed ML-
there is insufficient site data to inform high-fidelity physics
models are 𝒪𝒪(104 ) to 𝒪𝒪(107 ) times faster than running a
high-fidelity physics model simulation for evaluating the models (Mohaghegn, 2017; Belyadi et al., 2019). Despite
quantities of interest (e.g., gas production). This low compu- these challenges and due to the abundance of unconven-
tational cost makes the proposed ML-models attractive for tional resources, with reserves projected to last for many
real-time history matching and forecasting at shale-gas sites decades, energy extraction from these resources have gained
(e.g., MSEEL – Marcellus Shale Energy and Environmental
prominence in recent years (Briefing, 2013 and Weijermars,
Laboratory) as they are significantly faster yet provide accu-
rate predictions. 2014). Current extraction efficiency from unconventional
reservoir is very low (~5-10%) for tight oil and ~20% for
1. Introduction
shale gas (Sandrea, 2007; Muggeridge et al., 2014) com-
Energy extraction from conventional resources involves pared to conventional reservoirs (~20-40%) (Zitha et al.,
producing crude oil, natural gas, and its condensates from 2008). This is because the impact of resource development

Copyright © 2020, for this paper by its authors. Use permitted under Crea-
tive Commons License Attribution 4.0 International (CCBY 4.0).
processes (e.g., slow drawdown or fast drawdown) and un- training regimes, and the exploration of novel production
derlying physics that determine the energy extraction from strategies fundamentally requires extrapolation (where ML
the impervious rocks are poorly understood (Rezaee, 2015; struggles) as opposed to interpolation (where ML excels).
Belyadi et. Al., 2019). State-of-the-art workflows for uncon- The physics-based workflows adopted for modeling con-
ventional reservoir management are data-driven, which per- ventional reservoirs use extensively available site-character-
form poorly beyond their training regimes. Hence, innova- ization data (which is acquired over months or years) for
tive extraction strategies (e.g., pressure-drawdown manage- history-matching. Even though large unconventional reser-
ment) coupled with advanced workflows (e.g., physics-in- voir data (e.g, fiber-optics) are sampled at sparse locations,
formed machine learning) are needed to improve the hydro- simply combining all the data together would not improve
carbon recovery efficiency (Seales et al., 2017; Lougheed et the accuracy of real-time forecasting. This is because reser-
al., 2017; Mirani et al., 2018). In this paper, we present a voir conditions change considerably from one basin to an-
physics-informed machine learning (PIML) workflow other basin. Therefore, physical constraints need to be incor-
(Fig.1) to address unconventional production for real-time porated in workflows. Existing workflows employ high-fi-
reservoir management. One of the goals of this PIML work- delity physics models to perform simulations, which are ex-
flow (Fig.2) is to develop fast and accurate ML-models pensive to run. For example, it takes several days to months
grounded in physics for real-time history matching and pro- to run reservoir-scale model simulations (Rezaee, 2015;
duction forecasting in a fracture shale gas reservoir. Rajput and Thakur, 2016; Belyadi et al., 2019) with degrees-
of-freedom in the 𝒪𝒪(108 ) on state-of-the-art HPC machines.
1.1 State-of-the-art Workflows and Key Gaps As a result, these conventional reservoir workflows are not
Current workflows for unconventional reservoirs are pre- ideal for usage in comprehensive uncertainty quantification
dominantly based on production decline curve analysis and studies, which require 1000s of forward model runs. To
its extensions (Wu et al., 2013; Sun 2015), data-driven ma- overcome the key gaps associated with existing workflows,
chine learning (ML) approaches (Holdaway 2014; Chaki we propose a PIML workflow (Fig.1 and Fig.2) to accelerate
2015; Puyang et al., 2015; Carvajal et al. 2017; Mohaghegn, the development of ML-models while constraining it with
2017), and/or extension of physics-based conventional res- physics. The aim is (1) to develop a library from a combina-
ervoir workflows (Rezaee, 2015; Rajput and Thakur, 2016; tion of site observations and physics-based models that is
Belyadi et al., 2019). Decline curve analysis provides em- representative of unconventional reservoir site behavior,
pirical models to forecast production data based on the past and (2) to develop fast and accurate ML-models for real-
production history. This type of approach lacks physics and time history matching to refine key site parameters and fore-
in-depth knowledge of the site behavior is not included in cast production quantities of interest (QoIs) with uncertainty
the forecasting models. The data-driven ML approaches per- estimates. Key production QoIs include, total cumulative
form poorly when faced with uncertain, missing, and sparse production of hydrocarbons, gas and water production rates,
data – common problems with existing datasets related to stage-specific production, and spatial evolution of residual
unconventional reservoirs. Moreover, the data-driven ML gas, reservoir pressure, temperature, and stress fields based
analyses perform poorly in making forecasts outside of their on a user-defined pressure-drawdown strategy.

Figure-1: Physics-informed machine learning (PIML) workflow for reservoir management.
inverse model, then the smaller number of runs from the
high-fidelity model are used to fine-tune the inverse
model. This effectively represents a multi-fidelity ap-
2. Physics-informed Machine Learning proach to training the ML inverse model. This ML-in-
2.1 Innovation and proposed approach verse model provides capabilities for real-time history
matching to update the key parameters (e.g., rock perme-
The proposed approach to develop the PIML workflow
ability, rock porosity, gas transport properties). Sensitiv-
consists of three key steps: (Step-1) Development of site
ity analysis (e.g., Sobel indices, Random Forests) is per-
behavior libraries based on fast and accurate physics,
formed to provide quantitative information on the key
(Step-2) Development of ML-based inverse models to in-
sensitive parameters (e.g, matrix permeability and poros-
fer key site parameters, and (Step-3) Development of fast
ity, fracture network parameters) that influence shale gas
forward models that combine physical models with ML
production rates.
to forecast production and reservoir conditions.
PIML Workflow Step-3: The physics-based reduced
PIML Workflow Step-1: Development of a site be-
order forward model uses these calibrated parameters for
havior library involves generating synthetic data for a
real-time forecasting. This model is trained on the site li-
range of possible site characteristics. This includes a large
braries along with evolving production data. Moreover, it
number of runs from a fast physics-based reduced-order
allows for various operational decisions (e.g, slow draw-
model and a smaller number of runs from a high-fidelity,
down vs. fast drawdown) to be evaluated relative to future
full physics model. The fast physics models (e.g., Patzek
outcomes. The ML-inverse and physics-based reduced
models) allow us to quickly model and build a site library
order forward model can be combined to provide uncer-
on the evolving reservoir data. These models allow us to
tainty estimates on the production quantities of interest
efficiently explore the parameter space. Moreover, com-
(e.g., remaining hydrocarbon-in-place, spatial evolution
bining fast physics models with ML allows us to identify
of pressure and temperature, shale gas and water produc-
the important physical processes or dominant mecha-
tion as a function of time).
nisms that must be represented during full physics simu-
lations. The dominant mechanisms at different stages of 2.2 Key Challenges
production include The key challenges to accelerate the proposed PIML work-
• Early stages of production (<1 year): Primary frac- flow include:
ture creation, geometry, and network connectivity, 1Q. How do we enhance the information content and fill the
primary fracture behavior, propped fracture behavior, gaps in the limited unconventional site-data for PIML
anisotropic permeability of fractures. analyses? Specifically, how to use the short-time gas pro-
• Middle stages of production (~1-5 years): Second- duction data (e.g., 30-120 days) to forecast the long-term
ary fractures and their permeabilities, shear fracture performance (e.g., 1-5 years) of an unconventional shale
geometries, and geochemical impacts of hydraulic flu- gas well?
ids and formation water. 2Q. What is the minimum number of high-fidelity physics
• Late stages of production (~5-10 years): Matrix po- model simulations (e.g., PFLOTRAN, FEHM, dfnWorks)
rosity and transport properties, water imbibition im- needed to develop a gas production library that is repre-
pacts, adsorbed gas properties, pore structure distribu- sentative of shale gas sites behavior? How do we improve
tion. the full physics models to accurately represent the site be-
These mechanisms are not accounted for in the fast phys- havior?
ics models but are needed to describe the reservoir behav- 3Q. How can we use the information learned from reduced-
ior at different stages of gas and water production. How- order physics models (e.g., Patzek model, graph-based
ever, simulating these mechanisms using full physics models) to inform high-fidelity physics model simula-
models for entire parameter space is computationally in- tions?
tractable. As a result, a fast physics model library along 4Q. What are the key sensitive parameters (e.g., matrix and
with ML are used to guide and improve the development fracture properties) in high-fidelity physics models that
of the full physics model library (which consist of complex influence short-term and long-term gas production rates?
3D simulations of matrix-fracture interactions) for char- 5Q. What are the key operational parameters (e.g., pressure
acterizing site behavior. drawdown strategies) that can be used to inform decisions
PIML Workflow Step-2: The ML-inverse model is in real-time, leading to optimized production?
developed on this site behavior library using a transfer
learning approach (Pan et al., 2009; Goodfellow et al., 2.3 Our Hypothesis
2016; Yamada et al., 2018) where the numerous runs Our hypotheses/approaches to address the key challenges
from the reduced order model are used to train an initial include:
1A. Augment limited unconventional reservoir data (e.g., PetroMehras) can be used to generate synthetic data for the
short-term production data, well logs) with lab-scale ex- site behavior library.
perimental data, reduced-order physics simulation data, The reduced-order physics models (Patzek et al., 2013) to
and high-fidelity physics simulation data. Short-term pro- generate synthetic data are given by
duction data (e.g., 30-120 days) contains statistical infor- 𝜕𝜕𝑚𝑚
� � ) 𝜕𝜕𝑚𝑚
𝜕𝜕 𝛼𝛼(𝑚𝑚 �
mation (e.g., matrix and fracture network properties) that − � �=0 (1)
̃
𝜕𝜕𝑡𝑡 𝜕𝜕𝑥𝑥� 𝛼𝛼𝑖𝑖 𝜕𝜕𝑥𝑥�
can help us predict the long-term production data (e.g., 1-
5 years). where 𝑡𝑡̃ is the dimensionless time, 𝑥𝑥� is the dimensionless
2A. Reduced-order physics models provide information on distance, and 𝑚𝑚 � is the real gas pseudopressure. Eq.(1) cor-
the key sensitive parameters needed to inform high-fidel- responds to reduced-order physics of gas flow in fractured
ity physics model simulations. As we obtain more produc- porous rock. These are given as follows
tion data and/or site data, a ML-based active-feedback 𝑡𝑡 𝑑𝑑 2 𝑥𝑥 𝑘𝑘
loop is used to improve full physics models. In this active 𝑡𝑡̃ = 𝜏𝜏 = 𝑥𝑥� = 𝛼𝛼𝑖𝑖 = �
𝜏𝜏 𝛼𝛼𝑖𝑖 𝑑𝑑 𝜙𝜙𝑠𝑠𝑔𝑔 𝜇𝜇𝑔𝑔 𝑐𝑐𝑔𝑔 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 𝑝𝑝,𝑇𝑇
feedback loop, ML-inverse model is used to update and
constrain the key parameters based on newly available 1 �𝑐𝑐𝑔𝑔 𝑝𝑝�𝜇𝜇𝑔𝑔 𝑍𝑍𝑔𝑔
reservoir data. Based on these updated key parameters, 𝑚𝑚
�= � � 𝑚𝑚(𝑥𝑥, 𝑡𝑡)
2 𝑝𝑝2
site-behavior libraries are also updated to account for new 𝑖𝑖
production data. 𝑝𝑝
3A. Transfer learning can be used to provide link and trans- 𝑝𝑝 𝑑𝑑𝑑𝑑
𝑚𝑚(𝑝𝑝, 𝑥𝑥, 𝑡𝑡) = 2 �
fer information from reduced-order physics to high-fidel- 𝜇𝜇𝑔𝑔 𝑍𝑍𝑔𝑔 (𝑝𝑝, 𝑇𝑇)
ity physics. 𝑝𝑝𝑏𝑏ℎ𝑝𝑝

4A. Sensitivity analysis (e.g., Sobel indices, Random For-
ests) can provide quantitative information on the key sen- 𝑘𝑘(𝑝𝑝) (2)
𝛼𝛼�𝑚𝑚(𝑝𝑝)� = �
sitive parameters (e.g, matrix permeability, matrix lithol- �𝜙𝜙𝑠𝑠𝑔𝑔 + (1 − 𝜙𝜙)𝒦𝒦𝑎𝑎 �𝜇𝜇𝑔𝑔 𝑐𝑐𝑔𝑔 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑝𝑝,𝑇𝑇
ogy, fracture length and orientation, stage spacing, hydro-
carbon-in-place) that influence short-term and long-term where 𝜏𝜏 is the characteristic inference time, 𝑑𝑑 is the half-
gas production rates through feature importance. distance between the hydrofractures, 𝛼𝛼𝑖𝑖 is the initial hydrau-
5A. Maximizing early production may not maximize total lic diffusivity, 𝑘𝑘 is the fractured rock effective permeability
recovery efficiency. Optimal pressure management strat- dependent on reservoir pressure, 𝜙𝜙 is the fractured rock ef-
egies are needed to enhance recovery efficiency. One of fective porosity, 𝑠𝑠𝑔𝑔 is the fraction of pore space occupied by
our hypotheses is that slower drawdown rates can lead to the gas, 𝜇𝜇𝑔𝑔 is the gas viscosity, 𝑐𝑐𝑔𝑔 is the isothermal com-
improved recovery efficiency in long-term shale gas pro- pressibility of gas, 𝒦𝒦𝑎𝑎 is the differential equilibrium parti-
duction (e.g., 5-10 years). tioning coefficient of gas, and 𝑍𝑍𝑔𝑔 is the compressibility fac-
tor of gas. These gas properties are dependent on evolving
2.4 Details of the Proposed Approach reservoir pressure and temperature. Eq. (1) is a nonlinear
Fig.1 shows the overall PIML workflow for reservoir pressure diffusion equation, which is solved numerically.
management. Short-time production data is fed to ML-in- The cumulative production of gas mass is given as follows
verse model to perform history-matching and infer key site 𝑡𝑡̃
parameters. These key parameters are then fed to ML-for- 𝜕𝜕𝑚𝑚
�
𝔐𝔐(𝑡𝑡̃) = ℳ � � 𝑑𝑑𝑡𝑡 ′ (3)
ward model to forecast long-term production QoIs. Fig.2 𝜕𝜕𝑥𝑥� 𝑥𝑥�=0
0
and Fig.3 provide more details on our PIML workflow. where ℳ is the initial hydrocarbon-in-place.
These figures show how the site behavior library is con- The expensive full physics models to simulate gas flow
structed and used to develop ML-models for history match- and transport in fractured porous media (Rezaee, 2015;
ing and real-time forecasting. Physically-realistic synthetic Salama et al., 2017; Belyadi et al., 2019) are given by
data is generated for a range of possible site characteristics
𝜕𝜕𝜕𝜕𝑠𝑠𝑔𝑔 𝜌𝜌𝑔𝑔
using multi-fidelity physics models. This synthetic data pro- + 𝛻𝛻 ∙ 𝜌𝜌𝑔𝑔 𝒒𝒒 = 0 (4)
vides insights on relevant features on poorly constrained site 𝜕𝜕𝜕𝜕
parameters and production scenarios that are not-yet ob- 𝑘𝑘(𝑝𝑝)
𝒒𝒒 = − 𝛻𝛻�𝑝𝑝 − 𝜌𝜌𝑔𝑔 𝑔𝑔𝑔𝑔� (5)
served. The site behavior library can be updated actively as 𝜇𝜇𝑔𝑔
the field-scale data becomes available overtime. This allows 𝜕𝜕𝜕𝜕𝜕𝜕 (6)
+ 𝛻𝛻 ∙ (𝑐𝑐𝒒𝒒 − 𝜙𝜙𝜙𝜙𝜙𝜙𝜙𝜙𝜙𝜙𝜙𝜙) = 0
us to update or prune parameter combinations that are in- 𝜕𝜕𝜕𝜕
consistent with site characteristics. Note that any simulation where 𝜌𝜌𝑔𝑔 is the density of the gas which is dependent on the
platform (e.g., ECLIPSE, INTERSECT, tNavigator, CMG reservoir pressure, 𝒒𝒒 is the Darcy flux, 𝑐𝑐 is the gas concen-
suite, Landmark Nexus, MRST, BOAST, OPM) (see ref.
tration, 𝜆𝜆 is the tortuosity, and 𝐷𝐷 is the fracture rock effec- model. The loss function for this ML-inverse model is de-
tive diffusivity. Eq.(4) and Eq.(5) model the gas flow under fined in terms of how well it works in combination with the
varying reservoir and bottom hole pressures. The underlying reduced-order physics model at predicting future produc-
assumptions include Darcy’s flow and Fick’s law. Adsorp- tion. Note that the second library can also be augmented
tion and non-pore refinement effects on phase behavior are with field production data to improve the realism of the ML-
ignored. Eq.(6) models the gas transport from fractured inverse model. This fine-tuning represents a multi-fidelity
stage to horizontal well based on the initial hydrocarbon-in- approach to machine learning where a large dataset is gen-
place. The amount of gas extracted from the pair of hydro- erated with a reduced-order physics model and a smaller da-
fractures at a given section of the well is equal to 𝑐𝑐𝒒𝒒. Differ- taset is generated with a high-fidelity, expensive full physics
ent types of equation of state (EOS) models are used to eval- model. This multi-fidelity approach allows us to perform
uate the gas density. These include ideal gas law, exponen- real-time history matching on new production data to deter-
tial pressure-dependent model, and Redlich-Kwong-Soave mine critical site parameters that can be used to accurately
model. The corresponding EOS model expressions are given predict future production.
by
𝑝𝑝𝑀𝑀𝑔𝑔
𝜌𝜌𝑔𝑔 = 3. Results
𝑅𝑅𝑅𝑅
Fig.4 shows a DFN model of a single stage based on field
𝜌𝜌𝑔𝑔 = 𝜌𝜌0 𝑒𝑒 𝛽𝛽×(𝑝𝑝−𝑝𝑝0)
data from the Marcellus Shale Energy and Environment La-
𝑝𝑝𝑀𝑀𝑔𝑔 boratory (MSEEL) shale gas site. This model was built us-
𝜌𝜌𝑔𝑔 = (7) ing dfnWorks, which is a computationally expensive full
𝑍𝑍𝑔𝑔 (𝑝𝑝, 𝑇𝑇)𝑅𝑅𝑅𝑅
physics software suite used to generate high-resolution rep-
Note that it is possible to incorporate nanopore confinement resentations of DFNs (Hyman et al., 2015). This high-fidel-
effects (e.g,shifts in bubble or dew points) into EOS models ity meshing of the fracture network is critical to accurately
to account for density changes. For example, see ref. Islam capture the physical processes in a fractured shale gas reser-
et al., 2015, Tan and Piri, 2015, and Liu and Zhang, 2019. voir. To capture the matrix effects, we generate an octree-
Through these multi-fidelity physics models, the reser- refined continuum mesh (grey color in Fig.4) based on the
voir physical behavior is captured accurately. Gas flow and DFN. The original DFN model in Fig.4 consists of three hy-
transport mechanisms are accounted through conservation draulic fractures and a swarm of natural fractures that are
of mass and equation of state for real gases. State-of-the-art connected to hydraulic fractures. While generating the con-
simulators (e.g., PFLOTRAN, dfnWorks) are used to de- tinuum mesh, the DFN model is simultaneously upscaled to
velop high-fidelity simulation data. These simulators use fi- account for matrix-fracture interactions, which results in ac-
nite volume methods and Newton-Raphson method to solve curate permeability and porosity values that are needed to
the discretized system of nonlinear equations given by simulate gas flow and transport in fractured shale. The final
Eq.(4)-(7). Moreover, these simulators account for accurate mesh contains approximately 500,000 mesh cells.
meshing of fractures, matrix, and upscaling of fracture net- Fig.5 shows the flow and transport simulation using
work properties for reservoir-scale high-fidelity physics PFLOTRAN with a Barton-Bandis stress relationship (Bar-
simulations. ton and Bandis, 1990). This figure shows the drainage over
Fig.3 shows the PIML workflow to create efficient in- a period of 10 years. For gas flow simulations (left), the well
verse models to infer key site parameters from production is maintained at 12MPa and the reservoir initial pressure is
information. First, we sample the relevant regions in param- at 21MPa. For gas transport simulations (right), the initial
eter space. Two site behavior libraries are developed based hydrocarbon-in-place is assumed to spread in the entire frac-
on this sampling. One comes from running the reduced-or- ture stage and the figure shows the transport of hydrocarbon
der physics model with a large set of samples and the other to the well over time at two different vertical heights. The
comes from running the full physics model with a smaller main inference from these simulations is that the character-
set of samples. The first library (based on the reduced-order istic behavior of drainage is tied to hydraulic fractures. Our
physics model) is used to train an initial ML-inverse model. future work involves accounting for heterogeneity of hydro-
The ML-inverse model is then fine-tuned with the library carbon distribution in the matrix for production forecasts.
from the high-fidelity physics model using transfer learning, Fig.6 shows encouraging results of long-term production
producing a final ML-inverse model. During this fine-tuning forecasts using ML-forward models. The red color repre-
process the weights of the neural network are fine-tuned. sents the short-term production, which is used along with
The ML-inverse model takes past production as input and the site behavior library built on reduced-order physics mod-
produces physical parameters as output. These physical pa- els to infer key site parameters (e.g., initial hydrocarbon-in-
rameters can then be fed into the reduced-order physics place, hydraulic diffusivity). History-matching is performed
on the short-term production data. That is, the ML-inverse full physics models. The initial ML-inverse model trained
model is trained on 90 days of production data (red color). on the reduced physics site library and short-term produc-
Then, the resulting ML-model with site behavior library tion data provided us key site parameters, which are hydrau-
based on reduced-order physics is used to predict future pro- lic diffusivity and initial hydrocarbon-in-place. This initial
duction (green color). The markers represent the long-term ML-inverse model is then fine-tuned with the library from
production data and the solid green color line represents the the expensive full physics models using transfer learning.
ML-model forecasts. Quantitatively, the prediction accu- The expensive full physics model simulations were devel-
racy based on R2-score is > 90%. From this figure, it is clear oped using dfnWorks and PFLOTRAN simulators. These
that ML-model predictions, which are combined with phys- high-fidelity simulations account for matrix-fracture inter-
ics are able to accurately represent the long-term production action, which is needed to accurately simulate gas flow and
data. transport in fractured shale reservoirs. Moreover, from these
simulations we inferred that the characteristic behavior of
3.1 Discussion drainage is tied to hydraulic fractures. This high-fidelity
We note that if another site/formation (e.g., Woodford, simulation library was used to fine-tune the ML-inverse
Haynesville, Fayetteville, Barnett, Utica, EagleFord) has a model. Our ongoing work seeks to advance and test the
similar parameter range, we can use a set of ML techniques PIML workflow, site behavior libraries, and ML-models for
derived from transfer learning to model this site/formation. pressure management (e.g., slow drawdown vs. fast draw-
Transfer learning helps us to transfer knowledge gained down) to optimize recovery at MSEEL. Our preliminary re-
from one site (e.g., Marcellus) to another site (e.g., Wood- sults shown in this paper are encouraging for use of site be-
ford, Barnett). But the developed ML-models for one site havior libraries with ML-inverse model to address this prob-
(e.g., MSEEL) need fine-tuning (or minimal retraining the lem.
neural networks) to transfer knowledge across shale
sites/formations. This is not burdensome when compared to
developing a new site behavior library and ML-model for a Acknowledgements
different site altogether. The transfer learning approach is
This work was funded by the U.S. Department of Energy
attractive for tasks where reusability of ML-models for sim-
(DOE) – Office of Fossil Energy (FE) through its Oil and
ilar types is of great importance.
Natural Gas Research Storage Program as implemented by
If the production curve contains high frequency content
the National Energy Technology Laboratory. We would
or oscillations, which might need addressing, there are vari-
specifically like to thank Jared Ciferno for his support and
ous ways to incorporate this in the ML analyses and physics-
guidance. LANL is operated by Triad National Security,
based models. For example, from the production curve and
LLC, for the National Nuclear Security Administration of
bottom hole pressure, we can extract dominant frequencies
U.S. Department of Energy (Contract No.
or a range of frequencies we are interested in modeling
89233218CNA000001). The opinions expressed in this pa-
through Fast Fourier Transformation (FFT). This FFT trans-
per are those of the authors and do not necessarily reflect
formation of bottom hole pressure and production curve vs.
that of the sponsors.
time provides in-depth information on quantitative aspects
of high-frequency oscillations to be incorporated in physics
models (e.g., 𝑝𝑝𝑏𝑏ℎ𝑝𝑝 = 𝑎𝑎1 sin 𝜔𝜔1 𝑡𝑡 + 𝑎𝑎2 sin 𝜔𝜔2 𝑡𝑡 + References
… + 𝑎𝑎𝑛𝑛−1 sin 𝜔𝜔𝑛𝑛−1 𝑡𝑡 + 𝑎𝑎𝑛𝑛 sin 𝜔𝜔𝑛𝑛 𝑡𝑡 ) when developing the
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Figure-2: Details of PIML workflow. The workflow utilizes a library of data on site behavior to inform forecasting models. The
scale of physical parameters used in the development of site behavior libraries are stage spacing (~100-200m), hydraulic fracture
length (~100-150m), a stage may contain 3-4 hydraulic fractures and a swarm of natural fractures that are connected to hydraulic
fractures, fracture rock reservoir permeability (~0.1-0.9mD), fractured rock porosity (~0.04-0.08), reservoir pressures (~20-
30MPa), well flowing pressures (~5-15MPa), and gas properties (e.g., density, saturation, viscosity, compressibility).
Figure-3: PIML workflow to create an efficient set of ML-inverse models for real-time history-matching.

Figure-4: Discrete fracture network (DFN) and upscaled DFN models to simulate the physical behavior of the fractured reservoir.
Figure-5: Gas flow and transport in upscaled DFN model using PFLOTRAN simulator with Barton-Bandis stress relationship.

Figure-6: Long-term production forecasts using ML-forward model trained on reduced-order physics models.