A Critical Review for Proper Use of Water/Oil/Gas Transfer Functions in Dual-Porosity Naturally Fractured Reservoirs: Part II

Abstract

This paper continues the work presented in Ramirez et al. (2009). In Part I, we discussed the viability of the use of simple transfer functions to accurately account for fluid exchange as the result of capillary, gravity, and diffusion mass transfer for immiscible flow between fracture and matrix in dual-porosity numerical models.Here, we show additional information on several relevant topics, which include (1) flow of a low-concentration water-soluble surfactant in the fracture and the extent to which the surfactant is transported into the matrix; (2) an adjustment to the transfer function to account for the early slow mass transfer into the matrix before the invading fluid establishes full connectivity with the matrix; and (3) an analytical approximation to the differential equation of mass transfer from the fracture to the matrix and a method of solution to predict oil-drainage performance.Numerical experiments were performed involving singleporosity, fine-grid simulation of immiscible oil recovery from a typical matrix block by water, gas, or surfactant-augmented water in an adjacent fracture. Results emphasize the viability of the transfer-function formulations and their accuracy in quantifying the interaction of capillary and gravity forces to produce oil depending on the wettability of the matrix. For miscible flow, the fracture/matrix mass transfer is less complicated because the interfacial tension (IFT) between solvent and oil is zero; nevertheless, the gravity contrast between solvent in the fracture and oil in the matrix creates convective mass transfer and drainage of the oil.

Calibrated dual porosity, dual permeability modeling of fractured reservoirs

“…As previously mentioned, this type of model was first introduced in (Barenblatt et al, 1960;Warren & Root, 1963), and has continuously evolved since its initial introduction, see e.g. (Kazemi et al, 1976;Al-Kobaisi et al, 2009;Balogun et al, 2009;Ramirez et al, 2009). We begin by introducing the following dual porosity, dual permeability pressure equations…”

Application of the two-stage Markov chain Monte Carlo method for characterization of fractured reservoirs using a surrogate flow model

“…We employ the dual-porosity, dual-permeability model for single-phase flow through a fractured porous medium, denoted by . This type of model first appeared in the sixties (see, e.g., [5,29]) and has continuously evolved since its initial introduction [1,4,19,25].…”

“…Nevertheless, in the interest of focusing our effort on developing the general MCMC framework for fractured reservoirs we will use the more traditional models in [1,4,19,25]. We expect that as our level of understanding matures, exchange of these models in achievable.…”

“…We note that shape factors and applicable shape factor coefficients are a topic in the previous research, and we refer the interested reader to [1,4,19,25,29] for details of extensive discussion on the proper use of transfer terms. We remark that more sophisticated flow scenarios require increasingly difficult transfer functions.…”

“…Most notably, discrete-fracture models allow for easier implementation of more sophisticated multi-component and multi-phase flow scenarios. Dual models, such as those found in [1,4], require an explicit definition of the matrix-fracture exchange term, which becomes increasingly difficult when generalized flow scenarios are considered. However, it is important to note that more sophisticated dual models derived on the basis of mathematical homogenization theory provide a more convenient approach for treating increasingly complicated flow scenarios [3,6,10].…”