# DETERMINATION OF RELATIVE PERMEABILITY CURVES IN DIGITAL ROCKS AS FUNCTION OF INITIAL SATURATION USING LATTICE-BOLTZMANN METHOD

## Palavras-chave:

Relative permeability, Initial Saturation, LBM, Spencer’s Model, Sandrock, X-ray computed microtomography, Digital petrophysics## Resumo

The characterization of fluids in a porous media has attracted interest both academic research

and in engineering. Particularly, the comprehension of fluid displacement in a two-phase system affects

areas as, enhanced oil recovery, geological carbon dioxide sequestration and contaminated groundwater

remediation. To properly characterize multiphase fluid transport in porous media it is necessary to con-

sider a set of properties that exerts influence in the subsurface flow like wettabillity, capillary pressure,

viscosity and initial saturation. In this work, we aim to establish a correlation between initial saturation

and relative permeability. The later is a key to estimate two-phase flow in petroleum reservoirs because

it represents the mobility of one phase in a multiphase saturated porous media. There are many ways to

distribute the initial saturation in a porous media. The most common is to randomly allocate the fluids

in porous space. Although easily computational implementation, it has no relation with initial distribu-

tion expected both from experiments and from natural migration inside reservoirs rocks. To solve this

inconsistency, some approaches can be applied: (i) Using gravitational and oscillatory forces to induce

separation in an initially random saturated media; (ii) performing forced-drainage and forced-imbibition

processes; (iii) allocating the wetting phase next to the solid walls and (iv) filling the smaller pores with

wetting phase. In this work we quantify how relative permeability curves respond to the initial condition

(i) e (iii) using the color gradient Lattice-Boltzmann Model to simulate relative permeability curves in

a two-dimensional porous medium image obtained previously by Sheppard et al. [1]. It was possible to

see that random saturation implied in relative permeability deviations due the lack of control in filling

porous medium. To EDT, it was also observed some deviations because the nature of algorithm that used

random saturation to avoid tendentiousness in filling some porous. The deviations were less apparent in

wetting phase than in non-wetting phase. Also, it was observed increase in relative permeability to lower

contact angles due the lubrication effect, both, to random and EDT cases.