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

摘要

Previous matrix-fracture transfer models overlooked thehinderence effect of the fracture surface conditions onpetroleum recovery from naturally fractured reservoirs. Thesemodels are simplistic and do not represent the matrix-fracturetransfer with sufficient accuracy.This paper presents improved matrix-fracture-transfermodels and approximate analytical solutions for petroleumrecovery from naturally fractured reservoirs. The restrictedand hindered matrix-fracture interface fluid transferphenomenon is considered in order to account for the finiteskineffect of the matrix block surfaces by various processes,including the formation of a stationary fluid film or an actualskin because of formation damage by various processes, suchas deposition of minerals and other debris, and adverse rockfluidinteractions. The slab, matchstick, parallelepiped,cylindrical, and spherical type simpler shapes are consideredto represent the matrix blocks formed by intersecting fracturesin petroleum reservoirs. Then, full scale, and short- and longtimeanalytical solutions are presented. The analyticalsolutions are derived also for special boundary conditionsinvolving the rectangular and cylindrical shape rock samplesused in typical laboratory tests to represent the matrix blocks.The functional behavior of the transfer functions isdemonstrated using various charts and the practical straightlineplotting schemes are presented for effective interpretationof experimental data.The present model can accurately represent the matrixfractureinterface fluid transfer over the full range of the fluidrecovery period, while the previous models can only representeither the early- or the late-time behavior with limitedaccuracy. The present analytical solutions can be instrumentalin developing effective and accurate simulation of oil and gasproductions from naturally fractured reservoirs. The newmodels provide alternative matrix block shapes, skin effect of the matrix block surface, and variable shape factors. Whereasthe previous models primarily assumed constant shape factors,ignored the skin effect, and considered a few simple blockshapes. The new improved transfer functions are advantageousbecause these consider variable shape factors and areapplicable for primary recovery of gas or oil reservoirsinvolving single-phase flow and waterflooding or secondaryrecovery of oil reservoirs involving two-phase flow. Thespecial analytical solutions developed for laboratory coresamples can be used for interpretation and evaluation of theresults of laboratory core tests.