The effect of saturation path on three‐phase relative permeability

Abstract

Simulation and fluid flow prediction of many petroleum‐enhanced oil recovery methods as well as environmental processes such as carbon dioxide (CO2) geological storage or underground water resources remediation requires accurate modeling and determination of relative permeability under different saturation histories. Based on this critical need, several three‐phase relative permeability models were developed to predict relative permeability; however, for practical purposes most of them require a variety of parameters introducing undesired complexity to the models. In this work, we attempt to find out if there is a simpler way to express this functionality. To do so, we experimentally measure three‐phase, water/oil/gas, relative permeability in a 1 m long water‐wet sand pack, under several saturation flow paths to cover the entire three‐phase saturation space. We obtain the in situ saturations along the sand pack using a CT scanner and then determine the relative permeabilities of liquid phases directly from the measured in situ saturations using an unsteady state method. The measured data show that at a specific saturation, the oil relative permeability varies significantly (up to two orders of magnitude), depending on the path through saturation space. The three‐phase relative permeability data are modeled using standard relative permeability models, Corey‐type, and Saturation Weighted Interpolation (SWI). Our measured data suggest that three‐phase oil relative permeability in water‐wet media is only a function of its own saturation if the residual oil saturation is treated as a function of two saturations. We determine that residual saturation is the key parameter in modeling three‐phase relative permeability (effect of saturation history).

Modeling Relative Permeability Variations in Three-Phase Space

“…It has been previously shown (Kianinejad et al, 2015a;2015b) that by simply only changing residual oil saturation, the simple Corey model fits our experimental data well, in both sandpack and Berea sandstone. However, in the petroleum industry, it is common practice to estimate three-phase relative permeabilities from the two-phase relative permeability curves.…”

“…The calculated fluid fluxes were then used to calculate relative permeabilities at each time and position through the Darcy's equation, where k is absolute permeability, k r is relative permeability, is viscosity, P is pressure, is density, and g is gravity. More details regarding the derivation of the equations above, relative permeability calculation procedure, assumptions and criteria, and the saturation profiles measured during the experiments are given in (Kianinejad et al, 2015a;2015b).…”

“…The sandpack column had a porosity of 0.365 and permeability of 13 darcy, while the Berea sandstone used in these experiments had a porosity and permeability of 0.21 and 300 md, respectively. More details regarding the experiments can be found in (Kianinejad et al, 2015a;2015b). Table 1 lists the details of the experiments.…”

“…In addition, Figure 2 shows that the relative permeability data of each experiment extrapolate to a different residual oil saturation, indicating that residual oil saturation depends on water saturation. More details on the data shown in Figure 2 are discussed in (Kianinejad et al, 2015a). Figure 3 shows the three-phase oil relative permeability data measured in our Berea sandstone during Test 8-11.…”

Predicting relative permeability from experimental capillary pressure porous plate test for two phase flow

“…The commonly used techniques for measurement relative permeability can be sub-divided as direct laboratory methods and indirect predictive methods. Direct laboratory data from steady-state or unsteady-state techniques [2,6,[9][10][11]13] are not always available [8]. Through years some indirect predictive models were developed and are used widely.…”