Upscaling the porosity-permeability relationship of a microporous carbonate for Darcy-scale flow with machine learning

Permeability modelling in a highly heterogeneous tight carbonate reservoir using comparative evaluating learning-based and fitting-based approaches

Permeability modelling is considered a complex task in reservoir characterization and a key component of reservoir simulation. A common method for permeability modelling involves performing static rock typing (SRT) using routine core analysis data and developing simple fitting-based mathematical relations that link permeability to reservoir rock porosity. In the case of carbonate reservoirs, which are associated with high heterogeneities, fitting-based approaches may fail due to porosity-permeability data scattering. Accurate modelling of permeability using petrophysical well log data seems more promising since they comprise a vast array of information about the intrinsic properties of the geological formations. Furthermore, well log data exhibit continuity throughout the entire reservoir interval, whereas core data are discrete and limited in availability and coverage. In this research work, porosity, permeability and log data of two oil wells from a tight carbonate reservoir were used to predict permeability at un-cored intervals. Machine learning (ML) and fitting models were used to develop predictive models. Then, the developed ML models were compared to exponential and statistical fitting modelling approaches. The integrated ML permeability model based on Random Forest method performed significantly superior to exponential and statistical fitting-based methods. Accordingly, for horizontal and vertical permeability of test samples, the Root Mean Squared Error (RMSE) values were 3.7 and 4.5 for well 2, and 1.7 and 0.86 for well 4, respectively. Hence, using log data, permeability modelling was improved as it incorporates more comprehensive reservoir rock physics. The outcomes of this reach work can be used to improve the distribution of both horizontal and vertical permeability in the 3D model for future dynamic reservoir simulations in such a complex and heterogeneous reservoir system.

Automated Classification of Well Test Responses in Naturally Fractured Reservoirs Using Unsupervised Machine Learning

Understanding the impact of fractures on fluid flow is fundamental for developing geoenergy reservoirs. Pressure transient analysis could play a key role for fracture characterization purposes if better links can be established between the pressure derivative responses (p′) and the fracture properties. However, pressure transient analysis is particularly challenging in the presence of fractures because they can manifest themselves in many different p′ curves. In this work, we aim to provide a proof-of-concept machine learning approach that allows us to effectively handle the diversity in fracture-related p′ curves by automatically classifying them and identifying the characteristic fracture patterns. We created a synthetic dataset from numerical simulation that comprised 2560 p′ curves that represent a wide range of fracture network properties. We developed an unsupervised machine learning approach that can distinguish the temporal variations in the p′ curves by combining dynamic time warping with k-medoids clustering. Our results suggest that the approach is effective at recognizing similar shapes in the p′ curves if the second pressure derivatives are used as the classification variable. Our analysis indicated that 12 clusters were appropriate to describe the full collection of p′ curves in this particular dataset. The classification exercise also allowed us to identify the key geological features that influence the p′ curves in this particular dataset, namely (1) the distance from the wellbore to the closest fracture(s), (2) the local/global fracture connectivity, and (3) the local/global fracture intensity. With additional training data to account for a broader range of fracture network properties, the proposed classification method could be expanded to other naturally fractured reservoirs and eventually serve as an interpretation framework for understanding how complex fracture network properties impact pressure transient behaviour.

Upscaling Porous Media Using Neural Networks: A Deep Learning Approach to Homogenization and Averaging

In recent years machine learning algorithms have been gaining momentum in resolving subsurface flow issues related to hydrocarbon flows, Carbon capture utilization and storage, hydrogen storage, geothermal flows, and enhanced oil recovery. This paper presents and attempts to solve subsurface flow problem using neural upscaling method. The neural upscaling method, described in the present work, is a machine learning approach to calculate effective properties in each grid block for subsurface flow modeling. This method is intended to be more accurate than traditional analytical upscaling methods (which are only accurate for layered or homogeneous media) and numerical upscaling methods (which are more accurate for heterogeneous media but involve higher computational cost and are dependent on boundary conditions). The neural upscaling method is based on learning from a large number of geological realizations, which allows it to account for uncertainty in geology. It is also computationally fast and accurate. The method is demonstrated through a series of 2D test cases, and its accuracy is compared to that of analytical and numerical upscaling methods.

Machine learning to predict effective reaction rates in 3D porous media from pore structural features

Large discrepancies between well-mixed reaction rates and effective reactions rates estimated under fluid flow conditions have been a major issue for predicting reactive transport in porous media systems. In this study, we introduce a framework that accurately predicts effective reaction rates directly from pore structural features by combining 3D pore-scale numerical simulations with machine learning (ML). We first perform pore-scale reactive transport simulations with fluid–solid reactions in hundreds of porous media and calculate effective reaction rates from pore-scale concentration fields. We then train a Random Forests model with 11 pore structural features and effective reaction rates to quantify the importance of structural features in determining effective reaction rates. Based on the importance information, we train artificial neural networks with varying number of features and demonstrate that effective reaction rates can be accurately predicted with only three pore structural features, which are specific surface, pore sphericity, and coordination number. Finally, global sensitivity analyses using the ML model elucidates how the three structural features affect effective reaction rates. The proposed framework enables accurate predictions of effective reaction rates directly from a few measurable pore structural features, and the framework is readily applicable to a wide range of applications involving porous media flows.

A Lab on a Chip Experiment for Upscaling Diffusivity of Evolving Porous Media

Reactive transport modelling is a powerful tool to assess subsurface evolution in various energy-related applications. Upscaling, i.e., accounting for pore scale heterogeneities into larger scale analyses, remains one of the biggest challenges of reactive transport modelling. Pore scale simulations capturing the evolutions of the porous media over a wide range of Peclet and Damköhler number in combination with machine learning are foreseen as an efficient methodology for upscaling. However, the accuracy of these pore scale models needs to be tested against experiments. In this work, we developed a lab on a chip experiment with a novel micromodel design combined with operando confocal Raman spectroscopy, to monitor the evolution of porous media undergoing coupled mineral dissolution and precipitation processes due to diffusive reactive fluxes. The 3D-imaging of the porous media combined with pore scale modelling enabled the derivation of upscaled transport parameters. The chemical reaction tested involved the replacement of celestine by strontianite, whereby a net porosity increase is expected because of the smaller molar volume of strontianite. However, under our experimental conditions, the accessible porosity and consequently diffusivity decreased. We propose a transferability of the concepts behind the Verma and Pruess relationship to be applied to also describe changes of diffusivity for evolving porous media. Our results highlight the importance of calibrating pore scale models with quantitative experiments prior to simulations over a wide range of Peclet and Damköhler numbers of which results can be further used for the derivation of upscaled parameters.

A case study of petrophysical rock typing and permeability prediction using machine learning in a heterogenous carbonate reservoir in Iran

Petrophysical rock typing (PRT) and permeability prediction are of great significance for various disciplines of oil and gas industry. This study offers a novel, explainable data-driven approach to enhance the accuracy of petrophysical rock typing via a combination of supervised and unsupervised machine learning methods. 128 core data, including porosity, permeability, connate water saturation (S_wc), and radius of pore throats at 35% mercury injection (R₃₅) were obtained from a heterogeneous carbonate reservoir in Iran and used to train a supervised machine learning algorithm called Extreme Gradient Boosting (XGB). The algorithm output was a modified formation zone index (FZIM*), which was used to accurately estimate permeability (R² = 0.97) and R₃₅ (R² = 0.95). Moreover, FZIM* was combined with an unsupervised machine learning algorithm (K-means clustering) to find the optimum number of PRTs. 4 petrophysical rock types (PRTs) were identified via this method, and the range of their properties was discussed. Lastly, shapely values and parameter importance analysis were conducted to explain the correlation between each input parameter and the output and the contribution of each parameter on the value of FZIM*. Permeability and R₃₅ were found to be most influential parameters, where S_wc had the lowest impact on FZIM*.

A Probabilistic Formulation of the Diffusion Coefficient in Porous Media as Function of Porosity

We investigate the upscaling of diffusive transport parameters using a stochastic framework. At sub-REV (representative elementary volume) scale, the complexity of the pore space geometry leads to a significant scatter of the observed diffusive transport. We study a large set of volumes reconstructed from focused ion beam-scanning electron microscopy data. Each individual volume provides us sub-REV measurements on porosity and the so-called transport-ability, being a dimensionless parameter representing the ratio of diffusive flux through the porous volume to that through an empty volume. The detected scatter of the transport-ability is mathematically characterized through a probability distribution function (PDF) with a mean and variance as function of porosity, which includes implicitly the effect of pore structure differences among sub-REV volumes. We then investigate domain size effects and predict when REV scale is reached. While the scatter in porosity observations decreases linearly with increasing sample size as expected, the observed scatter in transport-ability does not converge to zero. Our results confirm that differences in pore structure impact transport parameters at all scales. Consequently, the use of PDFs to describe the relationship of effective transport coefficients to porosity is advantageous to deterministic semiempirical functions. We discuss the consequences and advocate the use of PDFs for effective parameters in both continuum equations and data interpretation of experimental or computational work. The presented statistics-based upscaling technique of sub-REV microscopy data provides a new tool in understanding, describing and predicting macroscopic transport behavior of microporous media.

Benchmarking the Viability of 3D Printed Micromodels for Single Phase Flow Using Particle Image Velocimetry and Direct Numerical Simulations

Holistic understanding of multiphase reactive flow mechanisms such as CO2 dissolution, multiphase displacement, and snap-off events is vital for optimisation of large-scale industrial operations like CO2 sequestration, enhanced oil recovery, and geothermal energy. Recent advances in three-dimensional (3D) printing allow for cheap and fast manufacturing of complex porosity models, which enable investigation of specific flow processes in a repeatable manner as well as sensitivity analysis for small geometry alterations. However, there are concerns regarding dimensional fidelity, shape conformity and surface quality, and therefore, the printing quality and printer limitations must be benchmarked. We present an experimental investigation into the ability of 3D printing to generate custom-designed micromodels accurately and repeatably down to a minimum pore-throat size of 140 μm, which is representative of the average pore-throat size in coarse sandstones. Homogeneous and heterogeneous micromodel geometries are designed, then the 3D printing process is optimised to achieve repeatable experiments with single-phase fluid flow. Finally, Particle Image Velocimetry is used to compare the velocity map obtained from flow experiments in 3D printed micromodels with the map generated with direct numerical simulation (OpenFOAM software) and an accurate match is obtained. This work indicates that 3D printed micromodels can be used to accurately investigate pore-scale processes present in CO2 sequestration, enhanced oil recovery and geothermal energy applications more cheaply than traditional micromodel methods.

GeoChemFoam: Direct Modelling of Multiphase Reactive Transport in Real Pore Geometries with Equilibrium Reactions

GeoChemFoam is an open-source OpenFOAM-based toolbox that includes a range of additional packages that solve various flow processes from multiphase transport with interface transfer, to single-phase flow in multiscale porous media, to reactive transport with mineral dissolution. In this paper, we present a novel multiphase reactive transport solver for simulations on complex pore geometries, including microfluidic devices and micro-CT images, and its implementation in GeoChemFoam. The geochemical model includes bulk and surface equilibrium reactions. Multiphase flow is solved using the Volume-Of-Fluid method, and the transport of species is solved using the continuous species transfer method. The reactive transport equations are solved using a sequential operator splitting method, with the transport step solved using GeoChemFoam, and the reaction step solved using Phreeqc, the US geological survey’s geochemical software. The model and its implementation are validated by comparison with analytical solutions in 1D and 2D geometries. We then simulate multiphase reactive transport in two test pore geometries: a 3D pore cavity and a 3D micro-CT image of Bentheimer sandstone. In each case, we show the pore-scale simulation results can be used to develop upscaled models that are significantly more accurate than standard macro-scale equilibrium models.