Fast Objective Function Estimator Based on Parametric Dynamic Mode Decomposition for Wag-Co2 Injection in Carbonate Reservoirs

Objective/Scope

Fast-objective function estimators (FOFE) are often used to speed up reservoir management. This work presents a FOFE constructed with the parametric Dynamic Mode Decomposition (DMDp) method for a carbonate reservoir with WAG-CO2 injection. The FOFE results are then compared to simulation results to analyze the FOFE’s efficiency.

Method/Procedure/Process

We present an example of how changes in the production strategy can affect reservoir behavior. The FOFE utilizes snapshots of gas and water saturation of numerical simulation runs with different sizes of WAG-CO2 cycles to predict the snapshots and fluid rates of a production strategy with a desired WAG-CO2 cycle size. The FOFE utilizes the DMDp method to calculate the saturation snapshots and material balance equations to calculate oil, water, and gas rates. Unlike the standard where snapshots are stacked up for multiple parameters, leading to increased computational costs, here we perform interpolation directly on the reduced Koopman operator. This leads to enhanced performance as the time eigenvalues are no longer shared between all parameters. The case study is the public access benchmark UNΊSFM-ΓV-2022, a carbonate reservoir model with characteristics of the Brazilian pre-salt. This model represents a developed reservoir with a WAG-CO2 recovery method for a compositional simulator with historical data.

Results/Observations/Conclusions

For this work, the FOFE utilizes snapshots of two reservoir simulations, one with a WAG-CO2 cycle size of 6 months and the other with 18 months, to predict the states of a production strategy with 12 months of WAG-CO2 cycle. The FOFE results of gas, oil, and water are compared to a simulation result with the same production strategy. The comparisons for fluid dynamics are shown for reservoir conditions, and their curves with relative differences are provided. The FOFE can predict the states of a different field scenario, dispensing the necessity of extra numerical simulation runs. This result is promising for production optimization problems which require a significant amount of simulation runs to incorporate the many reservoir uncertainties, as it is observed in highly heterogeneous carbonate reservoirs.

Novel/Additive Information

The innovation of this work is the utilization of the DMDp in a highly heterogeneous reservoir with three-phase flow and WAG-CO2 injection utilizing commercial software. This FOFE can be utilized to reduce the time and computational effort necessary for the decision-making process involving the control variable of WAG-CO2 cycle size.

Incorporation of Conceptual Geological Model for Fracture Distribution in 3D Reservoir Modeling

Conceptual Geological Models (CGM) serve as a robust tool for 3D reservoir model building, since they allow the representation of geological knowledge in the subsurface, guiding the depiction of fault and fracture distribution, providing insights into their local occurrences, densities, orientations, and aperture. The Brazilian pre-salt carbonate reservoirs are characterized by complex fault systems and natural fractures, with variations related to structural geology, paleotopography, and stratigraphy. This study aims to integrate a CGM into 3D reservoir modeling, focusing on faults and fractures below seismic resolution for an area within an oilfield in the Santos Basin (Santos Outer High), centered on the Barra Velha Formation (BVE), where a PSDM seismic volume, wells (with conventional and special logs), and core samples and thin sections were available. Data analysis resulted in the interpretation of the main horizons in the area and the preferential distribution of fracture families (P10, P20, and P21). Findings from a CGM of fracture distribution were incorporated into reservoir modeling through the Discrete Fracture Network (DFN) methodology, in particular, that the fractures in the BVE are generally correlated with silica-rich zones of the formation. From this, maps of silica distribution were elaborated for the different stratigraphic units of the BVE and used as a constraint for the creation of the fracture networks and the DFN model. Preliminary results show that the use of a CGM proved to be advantageous in the DFN model creation process.

Estimating Rock Typing in Uncored Wells Using Machine Learning Techniques for Brazilian Pre-Salt Carbonate Reservoir

Accurate rock typing in uncored wells is essential for enhancing reservoir models, particularly in complex geological formations like the Brazilian pre-salt carbonate reservoirs. This study explores the application of machine learning (ML) techniques to estimate rock types in uncored wells. The research leveraged core data from 11 cored wells to calculate the Rock Quality Index (RQI) and Flow Zone Indicator (FZI), identifying 14 distinct rock types through the Discrete Rock Typing (DRT) method, along with well log data such as gamma ray, density, neutron, permeability, and porosity. Various machine learning models, including Support Vector Machine (SVM), K-Nearest Neighbors (KNN), Decision Tree, Gradient Boosting, Naive Bayes, XGBoost, and Random Forest were tested, where XGBoost achieved the highest accuracy of 73.3%. Applying XGBoost to all wells resulted in accuracy ranging from 0.6 to 0.91 and the model was subsequently used to estimate rock types in over 20 uncored wells to generate reservoir simulation models. This study highlights the efficacy of machine learning (particularly XGBoost) in addressing reservoir complexities and offering significant improvements in the understanding and development of carbonate reservoirs.

Integrated Multi-Scale Pore Characterization of Carbonate Rocks in the Barra Velha Formation, Santos Basin, Brazil

Carbonate rocks feature heterogeneous porous systems that span multiple scales, from pore level to the reservoir scale. The complexity and diversity of carbonate reservoirs demand a consistent approach to their characterization. The efficient integration of multiscale imaging data and petrophysical data is increasingly important to address the challenges associated with these complex carbonate reservoirs. A crucial step in overcoming these scale gaps in reservoir modeling and simulation involves enhancing the characterization of reservoir flow units and their associations with geological and petrophysical heterogeneities at varying scales. In this study, we focus on the classification of pore types using digital rock analysis and petrophysical evaluation of pre-salt lacustrine carbonates from the Barra Velha Formation (BVF) in the Santos Basin using computerized tomography (CT), core samples description, and petrography. Eight types of pores were identified at the core scale: interparticle, stratiform-vuggy, growth framework, vuggy, vuggy-fracture, fracture, interclast, and intraclast. The distribution and characteristics of these pore types were analyzed at different scales, including thin-sections and micro-CT, and nuclear magnetic resonance (NMR), which highlights the diversity in the porous system and the impact of different pore types on porosity and permeability. NMR analyses illustrated the pore size heterogeneity to provide distinction between tight and porous samples. Hydraulic rock units (HRUs) were defined based on flow zone indicator (FZI) using the probability plot approach. Seven HRUs were defined: HRU1 and HRU2 represent samples with the highest FZI and rock quality index (RQI) values, whereas HRU3 and HRU4 denote intermediate values. HRU5, HRU6, and HRU7 represent units with the lowest values. HRU1 and HRU2 were predominantly associated with vuggy, growth framework, and interparticle porosities, which are often enhanced by dissolution processes. Conversely, HRUs with reduced reservoir qualities (5, 6, and 7), characterized by the lowest permeability values, are more prevalent in intervals with higher silicification and silica and dolomite cementation, presenting a variety of pore types at a macroscale. The integration of multiscale imaging techniques and petrophysical data underscores the complexity of pore systems, providing crucial insights into their reservoir characteristics.

Numerical Study on the Impact of Advanced Phenomena in a Fractured Carbonate Reservoir Subjected to WAG-CO2 Injection

Advanced phenomena related to water-alternating-gas (WAG) injection are usually neglected in numerical simulations. This work evaluates the impact of different physical phenomena on field indicators, considering a typical pre-salt carbonate reservoir (UNISIM-II-D-CO, a dual-por dual-perm compositional case) subjected to WAG-CO2 injection. Additionally, the computational cost incurred by each of these phenomena is evaluated, since it represents a great challenge in optimization and probabilistic studies. The following phenomena are evaluated considering a nominal base case: (i) matrix-fracture transfer calculation, (ii) relative permeability hysteresis, (iii) CO2 and CH4 solubilities in aqueous phase, (iv) diffusion, (v) numerical dispersion control models, and (vi) velocity-dependent dispersion. CO2 and CH4 solubilities in the aqueous phase, as well as molecular diffusion, did not have a significant impact on field indicators, but they increased simulation runtime more than two times. Matrix-fracture transfer modeling was the most impactful factor, followed by hysteresis and velocity-dependent dispersion. Therefore, the impact of these phenomena was also investigated in a probabilistic approach, considering an ensemble of 197 geostatistical scenarios under uncertainty. Risk curves revealed that the advanced matrix-fracture transfer models improve sweep efficiency. This effect is mainly due to gravity force which acts as a driving mechanism for the oil moving from the matrix to fractures. The capillary effect, in turn, was small compared to gravity. The impact of dispersion and hysteresis on risk curves were smaller than the effect of matrix-fracture transfer modelling. However, these phenomena are particularly interesting in UNISIM-II-D-CO due to the presence of Super-K facies. Hysteresis, when applied to low and high permeability layers, reduced gas mobility and, consequently, the gas produced, contributing to the NPV for most models under uncertainty. On the other hand, the velocity-dependent dispersion mainly affected fluid flows in the regions adjacent to Super-K layers, promoting better oil recovery. The inclusion of advanced phenomena related to WAG-CO2 injection can hold importance when modeling fractured carbonate fields, like those found in the Pre-Salt in Brazil. Nevertheless, computational costs might make their inclusion impractical in full-field simulation models employed for optimization and probabilistic studies. In such cases, it is recommended to assess low-fidelity models or alternatives to accelerate simulations, focusing mainly on the most impactful phenomena related to WAG-CO2 injection.