Analytical study of constant gas/oil-ratio behavior as an infinite-acting effect in unconventional multiphase reservoir systems

In multifractured horizontal wells producing from unconventional reservoirs, linear flow is commonly observed to be the dominant flow regime during early production. This linear flow regime may remain infinite-acting for a long stretch of time because of the ultralow permeability character of these formations. In this study, we first analytically corroborate that constant gas/oil ratio (GOR) should be expected in unconventional multiphase reservoirs (gas condensates and volatile oils below saturation conditions) exhibiting linear flow under constant-bottomhole-pressure (BHP) production constraint during infinite-acting periods (i.e., before pressure transient reaching the reservoir boundary). We propose a semianalytical solution to the multiphase governing partial-differential equations (PDEs) by applying the similarity method-also referred to as the Boltzmann transformation-to transform the system of PDEs to ordinary-differential-equation (ODE) form. The transformed system of ODEs and boundary conditions are solved by means of Runge-Kutta integration. By solving the equations for pressure and saturation, the GOR trend and value can be fully predicted before availability of production data. The results show that a constant GOR effect could be maintained as long as the flow regime remains infinite-acting and its value varies with BHP specifications for a given reservoir and fluid system.