Review articleReview of the effect of temperature on oil-water relative permeability in porous rocks of oil reservoirs
Introduction
Thermal recovery of heavy oil and bitumen involves two-phase and three-phase flow of oil, water and gas at high temperatures in oil bearing porous formations. Modeling of such processes requires accounting for changes in the multiphase flow properties of reservoir rocks resulting from the increase in temperature. Heating the rock from original reservoir temperature to the high temperatures, which can exceed 300 °C in steam injection and much higher in in-situ combustion processes [1], brings about changes in rock-fluid properties that can have a large impact on the flow behavior. The viscosity of heavy oil decreases by several orders of magnitude [2], [3], [4], [5], [6], [7] and this by itself can significantly change the flow characteristics [8], [9], [10], [11]. Furthermore, such large increase in temperature can also change other rock-fluid properties, including wettability [4], [12], [13], [14], [15], [16], [17], [18], [19], [20], interfacial tension [7], [14], [16], [21], [22], [23], [24], [25] and pore geometry.
Multiphase flow in porous media is complicated due to contributions of many factors, such as, complex pore geometry, the rock wettability, properties of different phases, capillary pressure, pore and throat size distributions and compressibility of the porous medium. The commonly used mathematical description of multiphase flow in porous media is based on the extension of the Darcy’s equation to multiphase flow [26] by introducing the concept of effective permeability for each phase that varies with saturations of different phases. Under two-phase flow conditions, the effective permeability for each fluid phase becomes a function of its own saturation [27], [28], [29]. This dependence of effective permeability on saturation is usually described by defining a relative permeability, which represents the ratio of the effective permeability to a base permeability, which is often the absolute permeability of the medium [28], [29], [30]. The advantage of using relative permeability to describe the variation with saturation is that it separates the changes in absolute permeability from the effects of fluid saturation. It allows one to account for the effect of permeability heterogeneity in the reservoir by assuming that the same relative permeability curve applies at different values of the absolute permeability. In most reservoir engineering flow studies, the relative permeability is one of the most crucial parameters [31].
The knowledge of two-phase water/oil relative permeability is needed to predict the production rate, breakthrough time and the ultimate oil recovery in processes involving displacement of oil by water [32], [33]. The relative permeability also affects the pressure response and velocity profile of fluids flowing through the porous rock in such displacements. The relative permeability varies from one oil reservoir to another and it may even be different for two core plugs with the same geometry, geology, lithology, composition, and physical properties (porosity and permeability) but with different pore size distributions [29], [34]. In the same rock, the relative permeability can change with the type of fluids saturating the pores [29], [32]. Accordingly, there is always some uncertainty when a given set of relative permeability data, which was measured using the best available technique on a core sample from a specific reservoir using native fluids, is used for analysis of other similar reservoirs [29], [30]. Actually, uncertainty remains, to some extent, even in the analysis of the reservoir from which the core sample was obtained, due to the possibility of changes in the behavior in different parts of the formation.
Numerous studies have been reported in the petroleum literature on relative permeability properties of different types of porous media and on the effects of rock-fluid characteristics that affect the flow behavior [29], [35], [36]. The effect of temperature on relative permeability curves has received significant attention since 1950’s [6]. There are published reports that contradict each other on the temperature impact on two-phase relative permeability for various systems [2], [3], [4], [6], [7], [12], [25]. In addition, numerous studies have attempted over the years to present the effect of temperature on relative permeability by proposing some useful relative permeability models even for a particular system [5], [25], [37], [38], [39], [40], [41], [42]. The objective of this study is to critically review such published articles [2], [3], [4], [6], [7], [8], [12], [13], [15], [16], [17], [19], [21], [24], [25], [38], [40], [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53] on the effect of temperature on two-phase relative permeability and distill useful information and insights into the changes in behavior that occur as a function of the temperature. This involves careful examination of the effect of temperature on characteristics of relative permeability curves for different porous media types and various fluid types in a wide range of temperature and pressure. This extensive survey endeavors to clarify how the contribution of various variables including wettability alteration, viscosity ratio, capillary end effect, saturation history, data interpretation method, type of oil and porous medium, and the employed experimental procedure, as well as human errors and experimental artifacts could have led to contradictory findings. In this review, the most cited publications since 1956 are examined and the effect of temperature on different attributes of the relative permeability curves are extracted and analyzed.
Section snippets
Relative permeability concept
When two immiscible fluids flow simultaneously through a reservoir rock, the conductivity of the rock to each fluid depends not only on the permeability of the rock but also on the relative amount of each fluid present in the pore space. In other words, the effective permeability to each fluid depends on the absolute permeability of the rock and the fraction of the pore space occupied by that fluid, which is called the fluid saturation. The relative permeability is defined as the effective
Methods for determination of relative permeability curves
The two-phase relative permeability of a porous medium can be evaluated using several techniques, including different experimental measurement techniques, methods based on mathematical modeling of two-phase flow, empirical correlations, and by the analogy method [27], [29], [30]. The laboratory methods include the steady-state and unsteady-state flow tests, the centrifuge method and the use of capillary pressure measurements to estimate relative permeability [27], [29], [30]. The focus in this
Impact of experimental conditions on observed effect of temperature on relative permeability
One of the important factors controlling the relative permeability is the wettability state of porous medium [29], [56]. The properties of the two fluid phases used will affect the contact angle, wettability, interfacial tension, and capillary pressure. Many other factors can also affect the relative permeability to varying degrees. Some researchers [2], [15], [17], [20], [22], [25], [42], [45], [50] used preserved core plug samples to closely simulate the reservoir conditions while others [3],
Effect of temperature on fluid and rock properties
As the system temperature is increased, the properties of both fluids and the rock can change significantly. In this section, we examine the impact of temperature on properties that can have substantial effect on measured relative permeability.
The effect of temperature on relative permeability curves
As discussed above, several rock-fluid properties that can affect the relative permeability might change with increasing temperature. These include the surface energies of rock-fluid and fluid-fluid interfaces (which determine the wettability and affect the dominance of surface forces in controlling fluid distribution) and the viscosity of each fluid. The effect of temperature on relative permeability will therefore depend on whether or not changes in these properties in a specific system are
Conclusions
The preceding review of previous studies shows that in spite of numerous investigations spanning over half a century, the issue of temperature’s impact on oil-water relative permeability is still not fully resolved. New findings are still being reported on this topic [117]. There appear to be three reasons for the lack of consensus in experimentally observed results:
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The measurements of relative permeability at high temperature are complex and often the reported results include experimental
Acknowledgements
The financial support for this work was provided by NSERC/Nexen and CNOOC Industrial Research Chair in Advanced In-Situ Recovery Processes for Oil Sands program and University of Calgary’s Global Research Initiative in Sustainable Low Carbon Unconventional Resources, funded from the Canada First Research Excellence Fund.
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