Simulation of Naturally Fractured Reservoirs
Authors: Saidi A.M. 
Published: December 2007

Member SPE-AIME

Abstract
A three-dimensional, three-phase reservoir simulator was developed to study the behavior of fully or partially fractured reservoirs. partially fractured reservoirs. It is also demonstrated, that when a fractured reservoir is subject to a relatively large rate of pressure drop and/or it composed of relatively large blocks, the pseudo steady-state pressure concept gives large errors as compared with transient fromulation. In addition, when gravity drainage and imbibitum processes, which is the most important mechanism in the Fractured reservoirs, are represented by a "lumped parameter" even larger errors can be produced in exchange flow between matrix and fractures. For these reasons, the matrix blocks are gridded and the transfer between matrix and fractures are calculated using pressure and diffusion transient concept. In this way the gravity drainage is also calculated accurately. As the matrix-fracture exchange flow depends on the location of each matrix grid relative to the GOC and/or WOC in fracture, the exchange flow equation are derived and given for each possible case. The differential equation describing the flow of water, oil, and gas within the matrix and fracture system, each of which may contain six unknowns, are presented. The two sets of equations are solved implicitly for pressure water, and gas stauration in both matrix and pressure water, and gas stauration in both matrix and fractures. The first twenty two years of the history of Haft Kel field was successfully matched with this model and the results are included.

Introduction
The presence of a wide variety of fractured reservoirs, in Iran, with varied natural forces and rock properties some having over 60 years of documented history and more than 20 years of laboratory and fiels research, plus a continuous analysis of their past histories using different simulation techniques and different recovery mechanisms, offers a unique experience to the rest of the Petroleum Industry. Petroleum Industry. The statement made by REISS(1) in his book which reads "No book on fractured reservoirs could be complete without reference to the Iranian experience", is a statement of fact rather than intuition or exaggeration. It is with the above background, opportunity and rich experience that the following analysis on the existing fractured reservoirs is based and a proper approach for developing a simulator for fractured reservoir is proposed. A brief review of the mechanisms that are taking place in fractured reservoirs are discussed by SAIDI. Similarly, matrix geometry is one of the main factors in estimating recovery from a fractured reservoir and it is therefore very important to evaluate the block size distribution throughout a given reservoir, or at least, to have the average block size versus depth. Several methods can be used to determine this important parameter. Some of these methods are discussed by SAIDI. parameter. Some of these methods are discussed by SAIDI. In the past, a fairly complete history of gas-oil, water-oil contacts, minimum closing well head pressure and oil and gas production measurements were provided in the Iranian and Irakian fractured reservoirs with documents dating back to 1915. By plotting the gas-oil and water-oil contacts of each field versus the cumulative production, and by extrapolating the two contacts until they come within 50 feet, the reserves of each field were estimated. It was not until the end of the fifties that the need for a mathematical model became apparent and the first simulation model was developed for Iranian fracuted limestone reservoirs by Iranian Oil Operating Companies. In this model, the matrix blocks were considered as pots surrounded by fractures. The reservoir was divided into, several columns of different rock types so that the sum of each horizontal layer of the columns represented oil-inplace versus depth. Solution gas drive and fluid expansion were calculated theoretically and gravity drainage from each block (pot) was calculated using a single block concept. Production from each block was calculated by the Production from each block was calculated by the previously derived simple equations mentioned above. Core previously derived simple equations mentioned above. Core Lab. was involved in the operation of this model. It was after several years of experience in working with different version of the above model that YAMAMOTO, published the first single block compositional model in 1971. In 1972, a new fully compositional simulator was developed. In this model, matrix blocks were gridded to with a felexibility to have as large an area open to the fracture as desired, and all the newly discovered mechanisms were incorporated. The fracture was not grid ded, although its volume versus depth was needed in the model.