Source-linked AI summary
CCSNet: a deep learning modeling suite for CO$_2$ storage
Gege Wen, Catherine Hay, Sally M. Benson
TL;DR
Multiphase-flow simulation is computationally expensive, while uncertainty assessments and history matching can require many runs. CCSNet applies deep learning to 2d-radial CO2 storage problems and accurately predicts key injection outputs with high computational efficiency.
Problem
Multiphase-flow simulation is computationally expensive, and uncertainty-driven probabilistic assessment and history matching can require many runs; existing surrogate models are often task-specific.
Source: §1 · p. 2Method
CCSNet uses deep-learning models to provide solutions across CO2 storage problems in 2d-radial systems as an alternative to conventional numerical simulation.
Source: §1 · pp. 2–3Results
CCSNet accurately calculates key injection-phase outputs, including plume extent, pressure buildup, sweep efficiency, and solubility trapping, with high computational efficiency.
Source: §5 · p. 23Takeaways & Limitations
Its efficiency supports quick reservoir-specific estimates for screening prospective storage sites and optimization when site-specific geological data are available.
Source: §5 · p. 23Solubility-trapping estimates are a lower bound because CO2 continues dissolving after injection stops.
Source: §4.2.2 · p. 22
Abstract
from arXiv · showhide
Numerical simulation is an essential tool for many applications involving subsurface flow and transport, yet often suffers from computational challenges due to the multi-physics nature, highly non-linear governing equations, inherent parameter uncertainties, and the need for high spatial resolutions to capture multi-scale heterogeneity. We developed CCSNet, a general-purpose deep-learning modeling suite that can act as an alternative to conventional numerical simulators for carbon capture and storage (CCS) problems where CO$_2$ is injected into saline aquifers in 2d-radial systems. CCSNet consists of a sequence of deep learning models producing all the outputs that a numerical simulator typically provides, including saturation distributions, pressure buildup, dry-out, fluid densities, mass balance, solubility trapping, and sweep efficiency. The results are 10$^3$ to 10$^4$ times faster than conventional numerical simulators. As an application of CCSNet illustrating the value of its high computational efficiency, we developed rigorous estimation techniques for the sweep efficiency and solubility trapping.
1. Introduction
CCSNet uses deep learning to provide simulator-like solutions across realistic 2d-radial CO2 storage scenarios, with near-simulation accuracy and 10^3 to 10^4 times greater computational efficiency. Its outputs support estimation of sweep efficiency and solubility trapping.
1. Introduction
- Conventional multiphase-flow simulation is computationally expensive because of multiphysics, nonlinear PDEs, multiscale permeability heterogeneity, and high spatial-resolution requirements.Geological uncertainty also drives large simulation workloads for probabilistic assessment and history matching.Source: §1 · pp. 1–2
- CCSNet provides solutions for a whole class of CO2 storage problems, rather than serving only as a task-specific surrogate.It targets injection of supercritical CO2 into saline aquifers in 2d-radial systems through a vertical well.Source: §1 · pp. 2–3
- Physics-informed models have not yet accurately approximated the hyperbolic PDEs governing most multiphase-flow problems, while supervised models have shown promise for specific uncertainty-quantification and history-matching tasks.Source: §1 · p. 2
- CCSNet is nearly as accurate as numerical simulation across realistic cases while being 10^3 to 10^4 times more computationally efficient.The authors use stochastic sampling to develop an estimation technique for sweep efficiency and solubility trapping.Source: §1 · p. 3
- Its CNN sequence predicts CO2 gas saturation, pressure buildup, CO2 molar fractions, and gas- and liquid-phase fluid densities.These outputs allow evaluation of conservation equations without explicitly including them in the loss function.Source: §1 · p. 3
- CCSNet is trained on highly resolved, full-physics simulations spanning realistic reservoir conditions, fluid and rock properties, geological attributes, multiphase-flow properties, and injection designs.Source: §1 · p. 3
2. Methodology
CCSNet’s methodology combines ECLIPSE-generated simulations of radial saline formations with temporal-3d CNNs to predict dynamic CO2-storage outputs. The section specifies the governing-flow assumptions, sampled training scenarios, model inputs and outputs, and training strategy.
2.1. Governing equations
- The governing formulation sums component mass accumulation and advective flux across phases, with phase fluxes governed by Darcy’s law; molecular diffusion and hydrodynamic dispersion are omitted.Phase pressure is the reference pressure plus capillary pressure.Source: §2.1 · pp. 3–5
2.2. Training data set generation
- ECLIPSE simulations generated training data for a 200 m-thick, 100,000 m-radius radial reservoir with central, constant-rate CO2 injection.The modeled volume is isothermal, initially contains pure water, and has no-flow top and bottom boundaries; the large radius approximates an infinite-acting radial boundary.Source: §2.2 · p. 5
2.2.1. Reservoir conditions
- CCSNet accommodates 15–200 m formation thicknesses and samples initial pressure from 100–300 bar and temperature from 35–170°C.Layers beyond actual formation thickness receive permeability of 10^-7 mD; temperature values are generated by sampling geothermal gradients from 18–50°C/km.Source: §2.2.1 · p. 6
2.2.2. Geological model
- Training geology spans permeability from 10^-3 mD to 10^2 D, varied horizontal and vertical correlations, and Gaussian, non-Gaussian, multimodal, and uniform distributions.The passage describes permeability maps representing different depositional environments.Source: §2.2.2 · pp. 6–7
2.2.3. Rock properties; 2.2.4. Injection design
- Rock and injection scenarios vary irreducible water saturation from 0.1–0.3, capillary-curve scaling from 0.3–0.7, injection rates from 0.02–2 MT/year, and perforation thickness from 15–200 m.Corey curves model relative permeability, van Genuchten functions model capillary pressure, and the capillary entry pressure is scaled by permeability using the Leverett J-function.Source: §2.2.3 · p. 7, §2.2.4 · p. 8
2.3. Model architectures
- Temporal-3d CNNs use 3d convolutions and an encoder–processor–decoder with 3d-ResConv blocks to map inputs to dynamic saturation, pressure, and dissolved-fraction predictions.They were trained on non-uniform spatial and temporal dimensions; the authors report superior performance to U-Net architectures and hypothesize that input and output occupy different spatial and temporal spaces.Source: §2.3 · p. 8
2.4.1. Outputs; 2.4.2. Inputs
- Outputs are configured as 96 × 200 × 24 temporal volumes, while CNN inputs use the same shape and combine reservoir, geological, rock, and injection variables.Molar-fraction models additionally receive predicted gas saturation and pressure; density models receive formation temperature, pressure, and phase molar fraction. Plume-focused augmentation preserves detail in yCO2 and density predictions.Source: §2.4.1 · pp. 9–10, §2.4.2 · p. 10
2.5. Training strategy
- Training used a 10/1 split of 19,000 training and 1,900 validation samples, MSE loss, Adam, L2 regularization of 0.001, and a learning rate reduced from 10^-4 to 10^-7.Convolutional kernels used Glorot normal initialization; models ran on NVIDIA V100 GPUs for a few days to a week.Source: §2.4.2 · p. 10, §2.5 · p. 11
3. Results
CCSNet’s CNNs predict dynamic CO2 saturation and pressure fields, while linked phase-property models enable mass-balance evaluation. The results show accurate predictions and mass balances, with errors that are largest early in injection.
3.1. CO 2 gas saturation distribution
- The Saturation CNN predicts dynamic CO2 saturation distributions in ∼0.05s, more than 104 times faster than conventional simulators, and closely matches simulated plumes, including dry-out and heterogeneous cases.It performs well throughout the prediction period and saturation range, including an example among the lowest 5% of validation scores.Source: §3.1 · pp. 11, 12, 14, Figure 3 · p. 13
3.2. Pressure buildup
- The Pressure CNN independently predicts pressure buildup in ∼0.04s across cases ranging from almost 400 bars near injection wells to 0 bars near reservoir boundaries, with poorest performance at the smallest buildups.It captures dynamic pressure propagation throughout injection; performance correlates with pressure-buildup magnitude.Source: §3.2 · p. 14, Figure 4 · p. 15
3.3. Mass balance analysis
- Six deep-learning models provide the saturation, pressure-derived porosity, phase molar fractions, and fluid densities needed to evaluate CO2 mass balance without explicitly encoding governing equations in the loss.The Pressure CNN is combined with rock compressibility to predict porosity; separate models predict liquid- and gas-phase molar fractions and densities.Source: §3.3 · p. 16
3.3.1. xCO 2 CNN
- The xCO2 CNN predicts dissolved CO2 molar fraction, performing better in relatively homogeneous reservoirs than heterogeneous cases where dissolved CO2 migrates ahead of the plume at varying velocities.Using Pressure CNN and Saturation CNN predictions alongside the original inputs significantly reduced over-fitting compared with training on original inputs alone.Source: §3.3.1 · pp. 16–17, Figure 5 · p. 17
3.3.2. yCO 2 CNN
- The yCO2 CNN provides excellent training- and validation-set predictions of gas-phase CO2 molar fraction from temperature, predicted gas saturation, and predicted pressure.Source: §3.3.2 · p. 17
3.3.3. Fluid density CNNs
- Two fluid-density CNNs produce highly accurate liquid- and gas-phase density predictions from temperature, predicted pressure, and the corresponding predicted phase molar fraction.Source: §3.3.3 · p. 18
3.3.4. Error analysis
- CCSNet generates accurate CO2 mass balances throughout injection, with the largest errors in the first several days; the results indicate supervised predictions can satisfy conservation laws given sufficient data and training.Errors become smaller as injection proceeds and a larger fraction of CO2 mass is in the gas phase.Source: §3.3.4 · p. 18, Figure 6 · p. 18
4. Discussion
CCSNet produces a simulator’s full set of outputs in about 0.22 seconds, enabling rapid sampling to estimate sweep efficiency and solubility trapping. The estimates show how these outcomes vary with reservoir and operational properties, subject to the study’s modeling conditions.
4.1. Comparative computational efficiency
- CCSNet’s full model sequence takes ∼0.22s, with speed-ups of 10^3 to 10^4 over ECLIPSE depending on the analysis.Sweep efficiency prediction takes ∼0.05s; calculating solubility trapping takes ∼0.15s. ECLIPSE averages 10 minutes per simulation in the reported comparison.Source: Table 2 · p. 19, §4.1 · p. 19
4.2. Applications with fast prediction
- CCSNet enabled exhaustive sampling for sweep efficiency in ∼4 minutes and solubility trapping in ∼12 minutes, using 5,000 runs per estimation approach.The sampled cases used homogeneous reservoirs and were limited to maximum pressure buildup of 75% of initial reservoir pressure; the approach reduced sampling time from ∼35 days.Source: §4.2 · p. 20
4.2.1. Sweep efficiency estimation
- Sweep efficiency ranged from 0.01 to 0.2, and Equation 11 predicted it well for Bond numbers of 10 to 450 under the 75% overpressure constraint.For the homogeneous reservoirs studied, Bond number had the largest influence: lower Bond numbers, higher injection rates, and lower Swi increased sweep efficiency; injection depth and interval had no significant influence, a finding expected to change for heterogeneous reservoirs.Source: §4.2.1 · pp. 20–22, Figure 7 · p. 21
4.2.2. Solubility trapping estimation
- Estimated solubility trapping ranged from 0.05 to nearly 0.15 and increased with lower permeability, higher temperature, lower pressure, and lower Bond number.The authors attribute the temperature and pressure trends to CO2 density and plume volume. Estimates cover the injection phase only and are a lower bound because dissolution continues afterward; pure-water reservoirs were assumed, while dissolved salts reduce solubility trapping.Source: §4.2.2 · pp. 22–23
5. Conclusion and future work
CCSNet provides an accurate, computationally efficient alternative for predicting CO2 storage injection performance, while its current scope is limited to 2d-radial systems with isotropic rock properties. The conclusion highlights site-screening and operational-planning uses, and describes a web application for running CCSNet predictions.
5. Conclusion and future work
- CCSNet accurately predicts key CO2 injection outputs with high computational efficiency as an alternative to numerical simulators, but is currently limited to 2d-radial systems with isotropic rock properties.It does not yet model post-injection processes such as residual gas trapping or mineral trapping.Source: §5 · p. 23
- CCSNet can be extended with additional inputs and features, including directional permeability, porosity, and relative-permeability curves that include residual gas trapping.Idle input-volume slices can be repurposed for these parameters.Source: §5 · p. 23
- CCSNet enables rapid, reservoir-specific estimates of sweep efficiency and solubility trapping for screening prospective storage sites using publicly available data.With site-specific heterogeneity data, it could also support optimization of injection depths and rates, probabilistic plume-footprint and pressure-buildup predictions, and inverse modeling of monitoring data for regulatory applications.Source: §5 · p. 23
Web application
- A web application hosts CCSNet and lets users customize input combinations, upload permeability maps, and generate predictions such as gas saturation, pressure buildup, solubility trapping, and sweep efficiency.The manuscript states that the application would be released to the public upon publication.Source: Web application · p. 24
Appendix A. Grid resolution
CCSNet’s grid uses fine spatial and temporal resolution near the injection well and progressively coarser resolution as the CO2 plume migrates away. The temporal schedule spans 30 years in 24 snapshots and supports finer monitoring early in injection.
Appendix A. Grid resolution
- The vertical grid spacing is 2.0833 m, while radial spacing grows as dr = 3.6 m × a^(i−1), with a = 1.035012 across 200 radial cells.The vertical dimension is dz = 200 m/96; the radial index i ranges from 1 to 200.Source: Appendix A · p. 25
- The 30-year simulation uses 24 time snapshots with intervals dt = 1.421245^(i−1) days, where i ranges from 1 to 24.The intervals gradually coarsen from days to years.Source: Appendix A · p. 25
- Fine early time steps capture plume variability near the well, while coarser later steps suffice as the plume moves into regions with coarser spatial grids.The temporal design also supports operational needs for finer monitoring at the beginning of injection.Source: Appendix A · p. 25
Appendix B. Statistical characteristics of permeability maps
The permeability maps were generated with SGeMS using user-defined spatial characteristics, and individual cell values ranged from 10^-3 mD to 10^2 D.
Appendix B. Statistical characteristics of permeability maps
- SGeMS [66] was used to generate maps with user-defined medium appearance, spatial correlation, mean, and contrast ratio (k_high/k_low).SGeMS is described as an open-source package for geostatistical modeling.Source: Table B.3 · p. 26
- Individual-cell permeability values ranged from 10^-3 mD to 10^2 D.Source: Table B.3 · p. 26
Appendix C. Mass balance analysis
CCSNet calculates mass balance from predictions of saturation, fluid density, phase CO2 molar fractions, and pressure-adjusted pore volume. Small predicted saturation and xCO2 values are cut off to prevent their amplification in large grid cells far from the injection well.
Appendix C. Mass balance analysis
- CCSNet combines predicted gas saturation, fluid densities, and phase CO2 molar fractions to calculate the components used in its discretized mass accumulation term.The Saturation CNN, fluid density CNNs, and xCO2 and yCO2 CNNs provide these quantities across spatial grid cells and gas or liquid phases.Source: Appendix C · p. 27
- The Pressure CNN supplies cell pressures used to adjust pore volume for rock compressibility, with Ct = 5 × 10^-4 bar^-1 and reference pressure 1.0132 bar.The pore-volume adjustment uses φn(Pn) = φn(Pn,ref)(1 + X + X^2/2), where X = Ct(Pn − Pn,ref).Source: Appendix C · p. 27
- Gas saturation below 1e-2 and xCO2 below 8e-4 are cast to zero to prevent tiny predictions from being amplified in large grid cells far from the injection well.Neural-network outputs rarely equal true zero, and the resulting small values can be amplified by large grid-cell volumes in the mass-balance calculation.Source: Appendix C · p. 27
Appendix D. Saturation CNN architecture
Appendix D specifies the saturation CNN architecture, its layer notation, and its parameter count.
Appendix D. Saturation CNN architecture
- The saturation CNN has 40,399,489 total parameters, including 40,386,817 trainable and 12,672 non-trainable parameters.The table also defines the layer notation and operations, including Conv3D, batch normalization, identity additions, nearest-neighbor upsampling, and reflection padding.Source: Table D.4 · p. 28
Appendix E. Pressure CNN architecture
Appendix E defines the notation and operations used in the Pressure CNN architecture and reports its parameter counts.
Appendix E. Pressure CNN architecture
- The Pressure CNN has 33,316,481 total parameters, including 33,305,857 trainable and 10,624 non-trainable parameters.Source: Table E.5 · p. 29
- Conv3D denotes a 3D convolutional layer, while c, k, and s denote output channels, kernel size, and stride size.Source: Table E.5 · p. 29
- UnSampling expands matrix dimensions by nearest-neighbor interpolation, and Padding uses reflection padding.Source: Table E.5 · p. 29
Appendix F. xCO2, yCO2, and fluid densities CNN architecture
Table F.6 specifies the CNN architecture for predicting xCO2, yCO2, and gas- and liquid-phase densities.
Appendix F. xCO2, yCO2, and fluid densities CNN architecture
- The architecture has 8,337,057 total parameters, including 8,331,745 trainable and 5,312 non-trainable parameters.Its table key defines Conv3D, channel count, kernel size, stride, batch normalization, ReLU, identity addition, nearest-neighbor upsampling, and reflection padding.Source: Table F.6 · p. 30
Appendix G. Multivariate regression
The appendix develops regression models for sweep efficiency and solubility trapping from dimensionless variables. It uses forward selection and diagnostic plots to identify optimal models for both outcomes.
Appendix G. Multivariate regression
- The data were split randomly into 80% training and 20% validation sets to relate the outcomes to dimensionless numbers and reservoir properties.Variables included Nb, Nc, Ng, permeability, initial pressure, injection rate, perforation dimensions, Swi, and capillary-pressure scaling; combinations and reciprocals were also investigated.Source: Appendix G · p. 31
- Forward selection assessed linear and nonlinear regressions using R2, Adjusted R2, and RMSE, with Adjusted R2 penalizing additional variables.Normal Q-Q, scale-location, residuals-versus-fitted, and Cook’s distance plots examined residual normality, constant variance, nonlinearity, and influential outliers.Source: Appendix G · p. 31
- The optimal sweep-efficiency model uses Nb, rinj/rref, and Swi; the solubility-trapping model uses Swi, Nb, λ, kref/k, P/Pref, and T/Tref.Table G.7 summarizes model parameters and criterion results, as well as prediction ranges, constants, and term standard errors.Source: Appendix G · p. 31, Table G.7 · p. 32