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
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