Cubic Law Evaluation Using Well Test Analysis for Fractured Reservoir Characterization

Abstract

Abstract In fractured reservoir, the use of the so-called cubic law represents a method to describe fluid flow through fractures and to estimate effective fracture porosity from effective fracture permeability and matrix block size. The method supposes perfect fracture connectivity. In practice, however, it often underestimates field fracture porosity. This paper explores the relation between fracture porosity, fracture permeability and matrix block size using field, and in particular well test, data. We used field data coming from four naturally fractured sand-stone reservoirs in foothills. Values of storativity ratio (ω) and inter-porosity flow coefficient (λ) coming from thirty-three pressure buildup derivatives interpretations are listed and used to estimate fracture porosity and matrix block size. The effective permeability associated to each well test, which is obtained from the stabilization of the pressure derivative, was also recorded. A non-linear regression was put in place in order to correlate fracture porosity, matrix block size and effective permeability. Obtained fracture porosities and block sizes are similar to values from other sources, such as thin section analysis and image log data. The most significant finding is that field data can be correlated by introducing in the cubic law a correction parameter that increases fracture porosity by about two orders of magnitude. The reason for deviation from the theoretical cubic law can be threefold: first, the cubic law considers the entire hydraulic aperture of the fracture as contributing to the fluid flow, while in reality the flow may be hindered by presence of cement in-filling the fracture (thin section data supports this assumption); secondly, the cubic law assumes a perfectly connected fracture network, while in real cases some fractures may die out without intersecting any other fracture; thirdly, transient flow effects and distribution of block sizes may lead to a less well pronounced dip in the derivative, which may be interpreted as a larger fracture porosity when using a pseudo steady-state model for analysis. The correction parameter is likely not universal, and will depend on the degree of fracture in-fill and connectivity in a given field. The work presented in this paper provides fracture permeability, fracture porosity, and block size estimates for the given type of environment. It issues a strong warning with respect to the application of the cubic law to estimate fracture porosity, and proposes a corrected cubic law expression that gives more accurate results. The methodology is useful for characterizing fracture porosity, a parameter that is notoriously difficult to measure.