Fast and scalable metamodelling of reservoir flows via machine learning techniques
Student:
Pavel Temirchev
Ph.D. student, 4th year
English for PhD Exam
Intro: Hydrodynamical Reservoir Simulation
Finite-Differences modelling
The standard approach (ECLIPSE, TNAVIGATOR, OPM-FLOW)
\sim O(n^\alpha), \;\;\;\; \alpha=2\div3
\text{PDE\_solver}(s_0, \theta, u)
Time
initial reservoir state:
pore pressure, saturation fields
porosity, permeability, relative permeability and PVT tables
control applied on wells:
BHP, injection rates
The computational complexity depends on the number of computational cells (the complexity of matrix inversion)
\theta
u_0
s_0
\frac{\partial s_0}{\partial t}
\frac{\partial s_1}{\partial t}
\frac{\partial s_2}{\partial t}
u_1
u_2
u_3
Objective
Create a fast and scalable reservoir model based on machine learning algorithms:
- 3D, 3-phase flow
- Arbitrary reservoir and wells' geometry
- Generalizable between reservoirs
Problem
Conventional reservoir simulation is too slow.
Prior art
ROMs:
- Dynamic Mode Decomposition
P.J. Schmid (2010). “Dynamic mode decomposition of numerical and experimental data”
J.L. Proctor, S.L. Brunton, J.N. Kutz (2014). “Dynamic mode decomposition with control” - Galerkin-POD projection
T. Lassila, A. Manzoni, A. Quarteroni, G. Rozza (2014). “Model order reduction in fluid dynamics: challenges and perspectives”
S. Chaturantabut, D.C. Sorensen (2010). “Nonlinear model reduction via discrete empirical interpolation” - Deep Residual Recurrent Neural Networks
J.N. Kani, A.H. Elsheikh (2018). “Reduced order modeling of subsur-face multiphase flow models using deep residual recurrent neural networks” - Embed to Control
M. Watter, J. Springenberg, J. Boedecker, M. Riedmiller (2015). “Embed to control: A locally linear latent dynamics model for control from raw images”
Z.L Jin, Y. Liu, L.J. Durlofsky (2020). “Deep-learning-based surrogate model for reservoir simulation with time-varying well controls” - LSTM + Variational Autoencoder model
P. Temirchev, M. Simonov, R. Kostoev, E. Burnaev, I. Oseledets, A. Akhmetov, A. Margarit, A. Sit- nikov, D. Koroteev (2020). “Deep neural networks predicting oil movement in a development unit”
Supervised Machine Learning
"Cat"
"Cat"
"Dog"
"Giraffe"
Object
Target variable
The training set of reservoirs
Object - a reservoir
Target variable
- forecast of pore pressure and saturations (States)
- forecast of the production rates (Rates)
Problem: how to find the target variable for an object?
Solution: let us compute it on the commercial simulator (tNavigator).
- initial pore pressure and saturations (initial State)
- porosity and permeability (Rock)
- PVT, RPP (Tables)
- reservoir geometry (Grid)
- wells and their working schedule (Wells)
tNavigator
NDE-b-ROM metamodel:
Neural Differential Equations based Reduced Order Model
Time
\theta
u_{0:T}
s_0
\frac{\text{d}z_1}{\text{d}t}
\frac{\text{d}z_2}{\text{d}t}
z_1
z_2
z_3
ENCODER
\hat\theta
\hat{u}_{0:T}
z_0
\frac{\text{d}z_0}{\text{d}t}
DECODER
Tightly approximates
commercial solutions
oil field Х
nde-b-rom
finite-difference
forecast
time
Tightly approximates
commercial solutions
oil field Х: production rates
Computational time results
Compared with commercial simulator tNavigator
Time, sec
Model
NDE-b-ROM
tNavigator
1 GPU 20 sec
40 CPU 2400 sec
Tested on:
- large real oil reservoir
with more than 3.000.000 of active cells - non-linear well trajectories, fish-bones
- 40 years of simulation
Publications
Conclusions
- We constructed the scalable reservoir model NDE-b-ROM based on Deep Learning techniques
- The computational time improvement is around 100x times
- The framework data processing was developed
- The API similar to conventional hydrodynamical models was developed
- History-matching and optimization procedures are under research
exam_presentation
By cydoroga
