Hamidreza Salimi

Improved Prediction of Oil Recovery From Waterflooded Fractured Reservoirs Using Homogenization

Summary Most 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. We use homogenization to obtain an improved flow model in fractured media, leading to an integro-differential equation; also called the boundary-condition (BC) approach. We formulate a well-posed numerical 3D model for the BC approach. This paper derives this numerical model to solve full 3D integro-differential equations in a field reservoir simulation. We compare the results of the upscaled model with ECLIPSE TM results. For the interpretation, it is useful to define three dimensionless parameters that 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 of the same order of magnitude as the imbibition time. However, if the travel time is shorter or longer 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.

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

In the laboratory, partially water-wet systems are often mistaken for completely oil-wet systems, because imbibition only starts after removal of the oil layer, which originally covers the grains. The (long) time required to remove the oil film will be referred to as delay time. Incorporation of delay time in a more general description of capillary pressure and relative permeability functions is called the non-equilibrium effect. No attempt has yet been made to model non-equilibrium effects in fractured reservoirs for a field-scale problem and this is the main innovative aspect of this paper. We apply homogenization to derive an upscaled model for fractured reservoirs and include delay time effects. Furthermore, we develop a computationally efficient numerical approach to solve the upscaled model. The upscaled model overcomes limitations of the dual-porosity model including the use of a transfer function and shape factor. This paper examines various aspects of wettability behavior in fractured reservoirs, viz., the contact angle, mixed wetting, and non-equilibrium effects in capillary pressure. The main characteristic that determines reservoir behavior is the Peclet number that expresses the ratio of the average imbibition time divided by the residence time of the fluids in the fractures. At low Peclet numbers and thus high gravity numbers, under-riding is aggravated by large contact angles and longer delay times. However, for low Peclet and low gravity numbers, the effect of contact angle and delay time for the non-equilibrium effects can be ignored without appreciable loss of accuracy. For low Peclet numbers, the recovery for the mixed-wet fracture/ mixed-wet matrix case is more than for the water-wet fracture/mixed-wet matrix case because a combination of capillary imbibition and gravity drainage occurs in the former case. For low Peclet numbers, the ultimate oil recovery for the water-wet fracture/mixed-wet matrix case is about the matrix Amott index times the recovery obtained for completely water-wet reservoirs. For residence times of water in the fractured reservoir much longer than the delay time, the delay time (nonequilibrium effect) does not influence the oil recovery qualitatively. Conversely, for high Peclet numbers, the residence time of water in the fractures is short and the relatively longer delay times reduce the cumulative oil production considerably as expected. Furthermore, at high Peclet numbers, after water breakthrough, the oil recovery appears to be approximately proportional to the cosine of the contact angle. It is important to distinguish between truly oil-wet systems and systems that are water-wet with long delay times. The efficiency of waterflooding in naturally fractured oil reservoirs decreases in the sequence of completely water-wet, mixed-wet fracture/mixed-wet matrix, water-wet fracture/mixed-wet matrix, and completely oil-wet, respectively. For the same amount of injected water, the recovery at low Peclet numbers is larger than the recovery at high Peclet numbers. Introduction Fractured hydrocarbon reservoirs provide over 20% of the world’s oil reserves and production (Saidi 1983; Firoozabadi 2000). 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. Fractured-reservoir simulations completely differ from conventional-reservoir simulations. The challenge of upscaling is to give an accurate representation of the interaction between fractures and matrix blocks. This is because the fracture-matrix interaction leads to a delayed response that distinguishes the flow through fractured reservoirs from the flow through heterogeneous single-porosity reservoirs (Wu et al. 2004; Salimi and Bruining 2009, 2010a). Many geological situations lead to some type of fractured reservoirs (Aguilera 1998; Nelson 2001). From the geological point of view, fractured reservoirs can exhibit a number of topologically different configurations. These are reservoirs built

Numerical Simulation of Density-Driven Natural Convection in Porous Media with Application for CO2 Injection Projects

In this paper we investigate the mass transfer of CO2 injected into a homogenous (sub)-surface porous formation saturated with a liquid. In almost all cases of practical interest CO2 is present on top of the liquid. Therefore, we perform our analysis to a porous medium that is impermeable from sides and that is exposed to CO2 at the top. For this configuration density-driven natural convection enhances the mass transfer rate of CO2 into the initially stagnant liquid. The analysis is done numerically using mass and momentum conservation laws and diffusion of CO2 into the liquid. The effects of aspect ratio and the Rayleigh number, which is dependent on the characteristics of the porous medium and fluid properties, are studied. This configuration leads to an unstable flow process. Numerical computations do not show natural convection effects for homogeneous initial conditions. Therefore a sinusoidal perturbation is added for the initial top boundary condition. It is found that the mass transfer increases and concentration front moves faster with increasing Rayleigh number. The results of this paper have implications in enhanced oil recovery and CO2 sequestration in aquifers. 2007 Elsevier Ltd. All rights reserved.

Negative-saturation approach for (non)-isothermal compositional three-phase flow simulations in porous media

This article describes the extension of the two-phase (non)-isothermal negative-saturation solution approach to the three-phase (non)-isothermal negative-saturation (NegSat3) solution approach. The NegSat3 solution approach solves efficiently any (non)-isothermal compositional flow problem in porous media that involves phase transitions between different phase states when the maximum number of phases is less than four. The solution approach circumvents using different equations and primary variables for single-phase, two-phase, and three-phase regions in porous media. Consequently, the NegSat3 solution approach avoids switches or variable substitutions at phase transitions where the convergence of the Newton-Raphson procedure is hampered by oscillations between m-phase and n-phase states. The NegSat3 solution approach can be implemented efficiently in numerical simulators to deal with modeling issues for thermal recovery processes, CO2 sequestration, and for multicontact miscible gas injection in oil reservoirs if the number of phases is less than four. We illustrate the NegSat3 solution approach by way of example to steam injection in a 1D heavy-oil reservoir. However, the NegSat3 solution approach can be used for any n ≤ 3-dimensional, multicomponent three-phase problems. The example solution is compared with a standard numerical solution that is analytically verified by the method of characteristics and shows excellent agreement. The results show that the oil recovery depends critically on whether the boiling temperature of the volatile oil is around the water boiling temperature, or much below or above it. These boiling-temperature ranges give rise to three different types of wave structures. When the boiling temperature of the volatile oil is near the boiling temperature of water, the striking result is that the speed of the evaporation front is equal or somewhat larger than the speed of the steam-condensation front. Thus, the volatile oil condenses at the location where the steam condenses too, yielding virtually complete oil recovery. Conversely, if the boiling temperature is too high or too low, there is incomplete recovery.