A major part of the world's remaining oil reserves is in fractured carbonate reservoirs, which are dual-porosity (fracture-matrix) or multiporosity (fracture/vug/matrix) in nature. Fractured reservoirs suffer from poor recovery, high water cut, and generally low performance. They are modeled commonly by use of a dual-porosity approach, which assumes that the high-permeability fractures are mobile and low-permeability matrix is immobile. A single transfer function models the rate at which hydrocarbons migrate from the matrix into the fractures. As shown in many numerical, laboratory, and field experiments, a wide range of transfer rates occurs between the immobile matrix and mobile fractures. These arise, for example, from the different sizes of matrix blocks (yielding a distribution of shape factors), different porosity types, or the inhomogeneous distribution of saturations in the matrix blocks. Thus, accurate models are needed that capture all the transfer rates between immobile matrix and mobile fracture domains, particularly to predict late-time recovery more reliably when the water cut is already high. In this work, we propose a novel multi-rate mass-transfer (MRMT) model for two-phase flow, which accounts for viscous-dominated flow in the fracture domain and capillary flow in the matrix domain. It extends the classical (i.e., singlerate) dual-porosity model to allow us to simulate the wide range of transfer rates occurring in naturally fractured multiporosity rocks. We demonstrate, by use of numerical simulations of waterflooding in naturally fractured rock masses at the gridblock scale, that our MRMT model matches the observed recovery curves more accurately compared with the classical dual-porosity model. We further discuss how our multi-rate dual-porosity model can be parameterized in a predictive manner and how the model could be used to complement traditional commercial reservoir-simulation workflows.

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In this paper, we present an upscaled model for horizontal immiscible displacement in highly heterogeneous media. This type of heterogeneity can be found, for instance, in fractured rock, which consists of two flow domains, a mobile fracture and a virtually immobile matrix. We derive an upscaled double-continuum model capable of predicting flow in mobile-immobile domains using homogenization theory. The model consists of a flow equation for the saturation of displacing fluid in the fracture domain, and a capillary flow equation for saturation in the matrix, which are coupled via a source term. By linearizing capillary counter current flow in the matrix domain, we combine this system of equations into a non-local single-equation model for the fracture saturation, which can be interpreted as a multi-rate mass-transfer (MRMT) model for immiscible displacement. We discuss this simplification and the parametrization of the upscaled model equation from local hydraulic parameters obtained from rock samples and from knowledge of the average flow properties of the fracture network. We demonstrate its performance for predicting two-phase flow by considering a single fracture with imbibition into a rectangular matrix domain. The upscaled model is parameterized directly from geometry and hydraulic parameters of matrix and fracture of the reference model, which means that no parameters need to be fitted. We compare the detailed and upscaled models in terms of breakthrough curves for the displaced fluid at a control plane within the medium. Both the detailed numerical simulations and the upscaled model show a preasymptotic ^{t - 1 / 2} scaling and a breakoff at the characteristic time scale for filling the matrix by counter current flow.

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A major part of the world's remaining oil reserves is located in fractured carbonate reservoirs, which are dual-porosity (fracture-matrix) or multi-porosity (fracture-vug-matrix) in nature. Fractured reservoirs suffer from poor recovery, high water cut, and generally low performance. They are modelled using a dual-porosity approach, which assumes that the high-permeability fractures are mobile and low-permeability matrix is immobile. A single transfer function models the rate at which hydrocarbons migrate from the matrix into the fractures. As shown in many numerical, laboratory, and field experiments, a wide range of transfer rates occurs between the immobile matrix and mobile fractures. These arise, for example, from the different size of matrix blocks (yielding a distribution of shape factors), different porosity types, or the inhomogeneous distribution of saturations in the matrix blocks. Accurate models are hence needed that capture all the transfer rates between immobile matrix and mobile fracture domains, particularly to predict late-time recovery more reliably when the water cut is already high. In this work we propose a novel multi-rate mass transfer model for two-phase flow, which accounts for viscous dominated flow in the fracture domain and capillary flow in the matrix domain. It extends the classical (i.e., single-rate) dual-porosity model in that it allows us to simulate the wide range of transfer rates occurring in naturally fractured multi-porosity rocks. Using numerical simulations of water-flooding in naturally fractured rock masses at the grid-block scale we demonstrate that our multi-rate mass-transfer model matches the observed recovery curves more accurately compared to the classical dual-porosity model. We further discuss how tracer tests can be used to calibrate our multi-rate dual-porosity model before the water-flood commences and how our model could be employed in commercial reservoir simulation workflows.@en