Verification and Proper Use of Water/Oil Transfer Function for Dual-Porosity and Dual-Permeability Reservoirs

Abstract

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractAccurate calculation of multi-phase fluid transfer between the fracture and matrix in naturally fractured reservoirs is a very crucial issue. In this paper, we will present the viability of the use of a simple transfer function to accurately account for fluid exchange resulting from capillary and gravity forces between fracture and matrix in dual-porosity and dualpermeability numerical models. With this approach, fracture and matrix flow calculations can be decoupled and solved sequentially, improving the speed and ease of computation. In fact, the transfer function equations can be easily used to calculate the expected oil recovery from a matrix block of any dimension without the use of a simulator or oil recovery correlations.The study was accomplished by conducting fine-grid simulation of a typical matrix block and comparing the results with those obtained with the use of a simple transfer function for a water-oil system. This study was similar to a previous study (Alkandari, 2002) we had conducted for a gas-oil system.The transfer functions of this paper are specifically for the sugar-cube idealization of a matrix block, which can be extended to simulation of a match-stick idealization in reservoir modeling. The basic data required are: matrix capillary pressure curves, densities of the flowing fluids, and matrix block dimensions.

Deep Learning Applied to Computational Mechanics: A Comprehensive Review, State of the Art, and the Classics

“…Recall from Footnote 87 that [78] used an overhead "hat" (•) to indicate predicted value; see [78], p. 120, where θ is defined as the true parameters, and θ the predicted (or estimated) parameters. 92 See, e.g., [78], p. 128. 93 The normal (Gaussian) distribution of scalar random variable x, mean µ, and variance σ 2 is written as N (x; µ, σ 2 ) = (2πσ 2 ) −1/2 exp[−(x − µ) 2 /(2σ 2 )]; see, e.g., [130], p. 24.…”

“…which then agrees with the matrix dimension in the first expression for ∂J/∂θ ( ) in Eq. (92). For the last layer = L, all terms on the right-hand side of Eq.…”

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

“…The heart of the dual-porosity multiphase-flow modeling is the transfer function that accounts for the transfer of fluids between the fracture and the matrix (Barenblatt et al 1960;Warren and Root 1963;Kazemi et al 1976;Litvak 1985;Sonier et al 1988; Gilman and Kazemi 1988;Balogun et al 2007).…”

Gravity Drainage Mechanism in Naturally Fractured Carbonate Reservoirs; Review and Application

“…He concluded a hyperbolic decline of the oil recovery due to gravity drainage and he recommended construction of the transfer function using the oil recovery curves of the experimental results. Balogun [26] used several scenarios to demonstrate the effect of different recovery mechanisms and to improve the transfer function by matching the results of a fine-grid model. Abushaikha and Gosselin [21] studied the effect of the shape factor using different matrix shapes and they examined several sensitivity scenarios, in addition to comparing and evaluating different forms of shape factors and transfer functions including the gravity term.…”