Analysis of inter-well connectivity in underground geological reservoirs via percolation theory

During subsurface storage in geological underground reservoirs, operators implement various well configurations, also known as injection patterns, to inject target invading fluids into a reservoir. Each pattern consists of several injection and production wells arranged uniquely. Therefore, reservoir connectivity plays a key role in determining the optimal well location for each pattern. In this study, we apply concepts of percolation theory to investigate the impact of well locations on overall reservoir connectivity within injection patterns. We generate 10⁴ reservoir realizations using Monte Carlo simulations. We then examine reservoir connectivity for two well-configuration scenarios and compare the results with the literature values of the conventional line-to-line (L2L) percolation connectivity model. In the first scenario, we investigate reservoir percolation properties and connectivity by fixing one well at the corner of the reservoir and placing the second well at the opposite side representing the boundary connectivity model. In the second scenario, we examine reservoir connectivity for wells located within the reservoir boundaries, known as the off-boundary connectivity model. To verify the algorithm, we compute the infinite percolation thresholds and compare them with values reported in the literature. Our results indicate that the most challenging connectivity occurs when wells are located at the corners of the reservoir, as in the boundary connectivity model. Comparing the mean connectivity curves and the connectivity exponent values of the boundary, off-boundary, and L2L connectivity models reveals that the off-boundary connectivity model has characteristics between the other two models. The results demonstrate that connectivity in underground storage systems is highly dependent on well placement, permeability heterogeneity, and reservoir boundaries. By comparing various connectivity models, we establish a relationship between injection well locations and reservoir fluid migration pathways, providing insights into optimizing storage and retrieval efficiency.