An Experimental and Numerical Study of Relative Permeability Estimates Using Spatially Resolved $$T_1$$-z NMR

Machine Learning Assisted Prediction of Porosity and Related Properties Using Digital Rock Images

Accurately estimating reservoir rock properties is paramount for modeling the storage and flow of fluids (hydrocarbon, carbon dioxide, and groundwater) in porous media. However, existing laboratory techniques to measure rock properties are usually time-consuming, expensive, and computationally intensive. This work proposes an efficient workflow that uses the machine learning algorithm, based on the convolutional neural network (CNN) framework, to predict rock properties from microcomputed tomography (micro-CT) X-ray images. The workflow involves data preprocessing, label extraction, training, and prediction using the segmented images of the rock to predict porosity, throat area, and pore surface area, which are essential for pore-scale modeling. The model was trained and validated on the Bentheimer sandstone, which was then used to predict properties of other sandstones (Castlegate and Leopard) with different pore structures and flow properties. The model yielded a good prediction for the throat and pore surface area but a significant error for porosity. Subsequently, a new complex model was trained and validated using diverse images from Bentheimer and an additional rock Castlegate, which was then used to predict the properties of Leopard sandstone. The new model improved the prediction of each property, resulting in mean absolute percentage error (MAPE) values of 2.19%, 3.04%, and 6.08% for porosity, pore surface area, and throat area with the binary images, respectively. In addition, we present a novel data-driven method using a simple regression model to predict the absolute permeability of a digital rock sample using the pore network parameters as predictors. The extreme gradient boost (XGBoost), which performed the best among several machine algorithms, was trained and validated using digital rock images from Bentheimer and Castlegate sandstone. The generated model was then used to predict the absolute permeability of the Leopard sandstone with an R 2 of 0.813, which was a significant improvement over the model generated solely by using either the Bentheimer or the Castlegate sandstone images. Furthermore, our analysis showed that the tortuosity had the most significant effect on the absolute permeability prediction of the rock sample. This study showed that we can reliably predict the morphological properties of porous media using computationally efficient models generated from digital rock images, which can be used to build a regression model to predict the crucial petrophysical properties needed to model the flow of fluids in porous media.

Introduction of a novel mathematical model for the prediction of the preformed particle gel's swelling in the presence of monovalent and divalent ions

Excess water production is one of the challenges that can cause several operational and economic problems. In this work, a comprehensive study of the PPG swelling in the presence of monovalent and divalent ions was conducted. Then, a comprehensive and practical mathematical modified fractal grow (MFG) model that can calculate the amount of PPG swelling in different salinities overtime was introduced. The output of the model was compared with the experimental data and showed a matching of about 80%. The viscosity of the PPGs at various shear rates was studied and matched with the cross-viscosity model. To assess the thermal stability of the particle gels. The TGA result represented the 10% of weight loss up to the reservoir temperature. In the following, core flooding tests with different injection scenarios were conducted. The oil recovery for the water and water/PPG/water scenarios were 39.5% and 71.5%, respectively. Eventually, the relative permeability curves were plotted using the Corey approach, and the effect of the PPG injection on the relative permeability curves was shown. The PPG injection increased oil production and reduced the excess water production by reducing water mobility.

NMR Relaxation Modelling in Porous Media with Dual-Scale-Resolved Internal Magnetic Fields

A pore-scale forward modelling approach for NMR relaxation responses of sandstones incorporating their dual-scale nature is presented. The approach utilises X-ray micro-CT images to capture inter-granular porosity and scanning electron microscopy images to reconstruct clay regions via a resolved clay micro-structure model. A key to calculating the NMR response with resolved clay micro-structure is the development of a dual-scale internal magnetic field calculation. This is achieved by a separation of near- and far-field effects in a dipole approximation of the internal field with periodic clay micro-structures, the latter of which take local clay pocket porosity into account. Tri-linear interpolation of the micro-CT image before calculation of the internal magnetic field further reduces errors in the transition regions between coarse- and fine-scale structure, with final discretisation level matching the fine-scale clay micro-structure model across the whole domain. The method is validated against direct calculations of model media at full resolution and applied to Bentheimer sandstone. Measured and simulated NMR $$T_2$$ T 2 relaxation responses, including relaxation time distribution shape, are in excellent agreement and distributions of internal magnetic field gradients at the highest spatial resolution as well as diffusion-averaged effective gradients are reported.

Application of low-field, 1H/13C high-field solution and solid state NMR for characterisation of oil fractions responsible for wettability change in sandstones

Asphaltene adsorption on solid surfaces is a standing problem in petroleum industry. It has an adverse effect on reservoir production and development by changing rock wettability, plugging pore throats, and affects oil transport through pipelines. Asphaltene chemistry constitutes important part of the ageing process as part of petrophysical studies and core analysis. The mechanisms and contribution of various oil components to adsorption processes is not fully understood. To investigate the kinetics of the ageing process and address the relative contribution of different oil components, we prepared three sets of sandstone core plugs aged in different oil mixtures over various time intervals. Cores were then re-saturated with decane to evaluate their wetting state using low-field NMR relaxometry by monitoring a change of surface relaxivity. Adsorbed deposits were then extracted from cores for solution-state NMR analysis. Their ¹H and ¹H-¹³C correlation spectra obtained using heteronuclear single quantum coherence (HSQC) technique were matched to spectra of four SARA (saturates, aromatics, resins and asphaltenes) components of oil mixtures to deduce components of deposits and inter-component interactions. We notice that wettability reversal of rock is inversely proportional to initial asphaltene concentration. Analysis of deposits reveals an increase in their aliphatic content over ageing time, which is accompanied by a change of the morphology of the pore space due to cluster aggregates forming a network. Results suggest that the ageing process in respect to the wetting state of rock samples consists of three distinctive stages: (i) an early-time period, when the fraction of most polar asphaltenes creates a discontinuous layer corresponding to mixed-wet state; (ii) an intermediate-time interval, at which the full grain coverage may be achieved (at favourable chemical environment) corresponding to strong oil-wetting; (iii) a late-time stage, where intense macro-aggregates accumulation occurs, changing the pore space integrity. It is likely asphaltene-aliphatic interactions leading to growth of sub-micron size macro-aggregates.

About the connectivity of dual-scale media based on micro-structure based regional analysis of NMR flow propagators

The characterisation of heterogeneous porous media at multiple length scales typically requires the classification of structure at some scale to allow the calculation of effective transport properties at a scale relevant for macroscopic description. While such a classification may be derived from various imaging methods, a shortcoming is often the simultaneous characterisation of the connectivity between regions representing different micro-structure. In this work we combine NMR based flow propagators with the simulations performed on corresponding reconstructed structure, and relate the NMR measurements to their simulated global and local representations to study fluid transport locally and the exchange between micro- and macro-porous regions. This is achieved by carrying out detailed lattice Boltzmann simulations and random walk method to track the displacements of tracers in each kind of region. Using Euclidean distance maps (EDT) we analyse the fluid invasion to regions of different scale and relate it to the connectivity of the system. We demonstrate that numerical simulation has great flexibility in providing additional sensitivity to the inference of region-region connectivity.