Abstract
Previous 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 finite-skin 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 rock-fluid 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 long-time 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 straight-line plotting schemes are presented for effective interpretation of experimental data.
The present model can accurately represent the matrix-fracture 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.
