Gaussian Inversion-Assisted Automated History-Matching Workflows for 3D Reservoir Models with Multiple Geological Boundaries
Authors: Rajput Saunil , Kumar Vishal , Lopes Velerian Sanjao , Sharma Abhijeet , Kumar Arvind , Wydiabhakti Tety Benedicta 
Published: November 2024

Abstract
Single-well reservoir modeling (SWRM) has traditionally been used during the early stages of exploration primarily to estimate reservoir productivity and to fine-tune completion strategies. Despite its utility, the effectiveness of SWRM is often limited by the availability of petrophysical and dynamic pressure data, which are typically gathered from only a single well or a few wells within the reservoir block. This scarcity of data constrains the model's accuracy and reliability. Over time, various methods have been developed to enhance the robustness and predictive accuracy of SWRMs. In this context, the research introduces a groundbreaking technique designed to address these limitations by simultaneous inversion of crucial reservoir parameters—namely horizontal permeability, vertical permeability, skin effect, and boundary distances—within the grid cells of a 3D SWRM. This novel approach aims to make use of data obtained from standard pressure transient analysis of well test pressures and rates. By employing these data as foundational a priori information, the method seeks to address the complex challenges inherent in the inversion problem. The primary goal of this technique is to significantly reduce the time and effort associated with manual history-matching processes, which have traditionally been time consuming and labour intensive. Additionally, it aims to facilitate the creation of more intricate and accurate reservoir boundaries within a sector model. By integrating these advanced methods, the technique promises to enhance the overall efficiency and precision of SWRM, offering a more reliable basis for making informed decisions about reservoir management and development.
The methodology initiates with the development of a layer-cake geological model, which is constructed based on the a priori information obtained from pressure transient analysis. This model serves as the foundation for the subsequent steps in our approach. Following the creation of this geological model, we perform a systematic flow simulation of field well test operations. This simulation process yields pressure data relative to flow rates within the model. A critical aspect involves addressing the discrepancy between the pressure data predicted by the model and the actual measured pressure data. To manage this discrepancy and ensure the convergence of our model, we establish a cost function that integrates both the well test pressure data and the pressure data derived from the model. This cost function is essential for guiding the inversion process and ensuring that the model accurately reflects the observed data. A crucial feature of our inversion methodology is its oversight by an advanced multiphase fluid flow simulation tool. This simulator continuously solves the implicit black oil fluid-flow diffusivity equations at each iteration, thereby updating the distribution of reservoir parameters in response to new data. This iterative process ensures that the reservoir parameter distribution is refined progressively. Another notable aspect of this approach is the management of parameter nonuniqueness within the grid cells of the model. This is achieved by defining minimum and maximum value ranges for each reservoir parameter. These defined ranges help to constrain the possible values of the parameters and are incorporated into an error scheme that is guided by the cost function. To facilitate the inversion across the grid cells of the geomodel, we use a Gauss-Newton (GN) inversion method, which is enhanced by a regularization technique. This combination allows for the joint inversion of parameters, improving the accuracy and stability of the inversion process. To further refine the results and enhance the fidelity of the inversion outcomes, the a priori parameters provided to the solver are thoroughly evaluated and, if necessary, adjusted through the uncertainty parameter optimization (UPO). This rigorous assessment and adjustment process ensures that the final model is both accurate and reliable, offering a robust framework for reservoir analysis and decision making.
The proposed technique provides a more rapid and reliable approach for redistributing reservoir parameters within a homogeneous layer-cake geological model, effectively introducing the essential heterogeneity that such models typically lack. This systematic redistribution of parameters not only enhances the overall reliability and credibility of the geological model, but also establishes it as a robust and reliable foundation for a wide range of production forecasting strategies. By automating this process, our approach significantly reduces the time and effort previously required for manual history matching and boundary modeling tasks. In practical terms, for a well situated in a region characterized by channel sandstone and a nearby single fault, the inversion workflow facilitated by this method resulted in a reduction of approximately 60% in modeling time compared to traditional methods. This substantial decrease in time expenditure underscores the efficiency and effectiveness of this technique. What sets the method apart is its sophisticated integration of simultaneous inversion processes with established reservoir parameters, all within a comprehensive 3D framework. By using a blend of simulations, inversion algorithms, and optimization techniques, we have developed a methodology that markedly improves the precision and applicability of geological models. This approach not only refines reservoir parameter estimation and distribution, but also establishes a new standard for accuracy and reliability in the field of reservoir modeling.