Improved Prediction of Oil Recovery from Waterflooded Fractured Reservoirs

Abstract

Simulations of waterflooding in fractured media are based on the Warren and Root (WR) approach, which uses an empirical transfer function between the fracture and matrix block. Arbogast used homogenization to formulate an improved flow model in fractured media, leading to an integro-differential equation; also called the boundary condition (BC) approach. A wellposed numerical 3D model for the BC approach has been formulated. This paper derives this numerical model to solve full 3D integro-differential equations. The results of this model are compared with the ECLIPSE results. For the interpretation it is useful to define three dimensionless parameters, which characterize the oil production in fractured media. The most important of these parameters is a Peclet number defined as the ratio between the time required to imbibe water into the matrix block and the travel-time of water in the fracture system. The results of the WR approach and the BC approach are in good agreement when the travel-time is longer than the imbibition time. However, for times with the same order of magnitude and for the travel time shorter than the imbibition time, the approaches give different results. The BC approach allows the use of transfer functions based on fundamental principles, e.g., the use of a rate dependent capillary pressure function. When implemented, it can be used to improve recovery predictions for waterflooded fractured reservoirs. Introduction Naturally fractured petroleum reservoirs (NFR's) represent over 20% of the world's oil and gas reserves (Saidi 1983), but are among the most complicated class of reservoirs to produce efficiently. NFR's comprise an interconnected fracture system that provides the main flow paths and the reservoir rock or matrix that acts as the main source of hydrocarbons. From the geological point of view it is possible to distinguish between various types of fractured reservoirs (Nelson 1985; Stearns 1969; Stearns 1972). The most important aspect is whether the fracture network provides a continuous flow path (Saidi 1983) or whether it has regions with different fracture geometries or systems consisting of a hierarchy of fracture systems at different scales (multi-scale fractures) (Yu-Shu Wu 2004). When the fracture network is not continuous, the reservoir can be split up in fractured and non-fractured domains. Also in the fractured domains the reservoir is heterogeneous, with different fracture densities, fracture apertures, anisotropies etcetera. In some approximate sense the fractured reservoirs shows some repetition of fractured sub-domains. This aspect will be used for obtaining averaged properties of the subdomains. The same idea can also be used as a first guess to obtain the global flow field. Alternatively it is possible to use the global flow field to obtain boundary conditions at the local scale and repeat this procedure until convergence has been obtained. Flow modeling in fractured reservoirs was greatly advanced by Barenblatt et al. (1960) who introduced the concept of dual porosity. In addition, he introduced the transfer function and shape factor. From the geometrical point of view, Barenblatt assumed that the fracture system is regular "to some extent". Warren and Root (1963) used the double porosity model and applied it to a well test analysis. They also introduced the sugar cube model, which has been the basis of many of the fractured reservoir simulators since that time. The double porosity model of Warren and Root for examining pressure drawdown and buildup phenomena in naturally fractured reservoirs was extended by Kazemi et al. (1969, 1992) to interpret interference test results. These ideas were extended with the introduction to the so-called dual permeability model, where the matrix blocks can also contribute to the global flow depending on the permeability ratio of fractures and matrix blocks.

Upscaling of fractured oil reservoirs using homogenization including non-equilibrium capillary pressure and relative permeability

“…The numerical procedure described below is an extension of the method used by Arbogast [5] and Salimi and Bruining [42,44] for the sugar-cube model. The difficulty arises due to the coupling of flow in the vertical direction, which is important in the upscaled-VFR model.…”

“…Virtually, all reservoirs contain at least some natural fractures [1,32]. However, from the point of view of reservoir modeling, a fractured reservoir is defined as a reservoir in which naturally occurring fractures have a significant effect on fluid flow [42][43][44][45][46]. We only consider reservoirs where fluid flow occurs predominantly in a connected-fracture network and do not consider the case of limited connectivity and cases in which fractures act as a barrier to fluid flow.…”

Experimental Study of Controlled Gravity Drainage in Fractured Porous Media

“…Most fractured reservoirs having a primary or secondary gas cap are produced by gas injection or gravity drainage processes (Saidi et al 1979;Paul and Zoback 2007;Quintard and Whittaker 1996a, b;Rossen and Shen 1989;Salimi and Bruining 2008). Production from fractured reservoirs under a gravity drainage mechanism is dominated by two major interacting forces, namely capillary and gravity forces, though viscous force may play an important role in forced gravity drainage processes (Saidi et al 1979;Saidi 1983Saidi , 1974Ahmadi et al 1996;Aziz and Settari 1979;Warren and Root 1963).…”

“…Essentially, the oil content of fractures, which is not a considerable volume as a result of their low storativity values, would be drained first because of the associated high values of inherent permeability. The resulting void space would then be occupied by the invading gas phase, which originally comes from either the associated gas cap or from the source of gas injection (Saidi et al 1979;Saidi 1983Saidi , 1974Ahmadi et al 1996;Aziz and Settari 1979;Da Sle and Guo 1990;Dean and Lo 1988;Paul and Zoback 2007;Quintard and Whittaker 1996a, b;Rossen and Shen 1989;Salimi and Bruining 2008). It is believed that the original oil held in place through the matrix, which contains the major portion of ultimate recovery as a result of considerable storativity of matrix, needs more time to be transmitted toward fractures compared to the time associated with fractures drainage (Tan and Firoozabadi 1995;Chatzis and Ayatollahi 1995;Dullien et al 1990;Kantzas et al 1988;Da Sle and Guo 1990;Zendehboudi et al 2008).…”

The Influence of Wettability on Oil Recovery From Naturally Fractured Oil Reservoirs Including Non-Equilibrium Effects

“…Virtually, all reservoirs contain at least some natural fractures (Aguilera 1998;Nelson 2001). However, from the reservoir modeling point of view, a fractured reservoir is defined as a reservoir in which naturally occurring fractures have a significant effect on fluid flow (Salimi and Bruining 2008, 2010a, 2010b. We only consider reservoirs where fluid flow occurs predominantly in a connected fracture network and do not consider the case of limited connectivity and for the case that fractures act as a barrier for fluid flow.…”