Full, Short-, and Long-Time Analytical Solutions for Hindered Matrix-Fracture Transfer Models of Naturally Fractured Petroleum Reservoirs

Abstract

TX 75083-3836 U.S.A., fax 01-972-952-9435. AbstractPrevious matrix-fracture transfer models overlooked the hinderence effect of the fracture surface conditions on petroleum recovery from naturally fractured reservoirs. These models are simplistic and do not represent the matrix-fracture transfer with sufficient accuracy. This paper presents improved matrix-fracture-transfer models and approximate analytical solutions for petroleum recovery from naturally fractured reservoirs. The restricted and hindered matrix-fracture interface fluid transfer phenomenon is considered in order to account for the finiteskin effect of the matrix block surfaces by various processes, including the formation of a stationary fluid film or an actual skin because of formation damage by various processes, such as deposition of minerals and other debris, and adverse rockfluid interactions. The slab, matchstick, parallelepiped, cylindrical, and spherical type simpler shapes are considered to represent the matrix blocks formed by intersecting fractures in petroleum reservoirs. Then, full scale, and short-and longtime analytical solutions are presented. The analytical solutions are derived also for special boundary conditions involving the rectangular and cylindrical shape rock samples used in typical laboratory tests to represent the matrix blocks. The functional behavior of the transfer functions is demonstrated using various charts and the practical straightline plotting schemes are presented for effective interpretation of experimental data.The present model can accurately represent the matrixfracture interface fluid transfer over the full range of the fluid recovery period, while the previous models can only represent either the early-or the late-time behavior with limited accuracy. The present analytical solutions can be instrumental in developing effective and accurate simulation of oil and gas productions from naturally fractured reservoirs. The new models provide alternative matrix block shapes, skin effect of the matrix block surface, and variable shape factors. Whereas the previous models primarily assumed constant shape factors, ignored the skin effect, and considered a few simple block shapes. The new improved transfer functions are advantageous because these consider variable shape factors and are applicable for primary recovery of gas or oil reservoirs involving single-phase flow and waterflooding or secondary recovery of oil reservoirs involving two-phase flow. The special analytical solutions developed for laboratory core samples can be used for interpretation and evaluation of the results of laboratory core tests.

Dual permeability flow behavior for modeling horizontal well production in fractured-vuggy carbonate reservoirs

“…(1) Sugar cube fractures as seen in classical multiple porosity media models are used (Rasmussen and Civan, 2003;Warren and Root, 1963;Wu et al, 2004); the shape of matrix blocks and vugs varied with different shape with different geometric shape factor a m and a v (Al- Ghamdi and Ershaghi, 1996;Camacho-Velázquez et al, 2005;Corbett et al, 2010).…”

A Multicomponent Dual-Porosity Model for Gas Reservoir Flow With Adsorption Behaviour

“…To deal with a flow problem in such porous media which have two greatly different spatial scales, dual-porosity models (also called matrix-fracture transfer functions) have been developed following the concept proposed by Barenblatt and Zheltov 4 (Warren and Root 5 , De Swann 7 , Najuriteta 8 , Dykhuizen 9 , Zimmerman and Bodvarson 10 , Zimmerma 11 , et al, Lim and Aziz 12 , Civan and Rasmussen 13 , Babadagli, and Zeidain 14 , Rasmussen and Civan 15 , Civan and Rasmussen 16 , etc.). Of these the Warren-Root 5 model is a popular approach and is incorporated into a variety of commercial gas-reservoir simulation codes.…”

Modeling and Validation of Hindered-Matrix-Fracture Transfer For Naturally Fractured Petroleum Reservoirs

“…In return, this approach requires the derivation of suitable matrix-fracture flow interaction models, often referred to as transfer functions. Warren and Root 2 , de Swaan 12,13 , Kazemi et al 14,15 , Moench 7 , Zimmerman et al 8 , Civan 16 , Gupta and Civan 17 , Lim and Aziz 4 , Cil and Reis 6 , Rasmussen and Civan 18 , Civan and Rasmussen 19,20 have derived theoretical models. Zhang et al 21 , Ma et al 22 , Xia and Morrow 23 , Guo et al 24 , and Matejka et al 25 have developed empirical correlations.…”