Practical Mathematical Model for the Evaluation of Main Parameters in Polymer Flooding: Rheology, Adsorption, Permeability Reduction, and Effective Salinity

Abstract

Polymer flooding is one of the most used chemical enhanced oil recovery (CEOR) technologies worldwide. Because of its commercial success at the field scale, there has been an increasing interest to expand its applicability to more unfavorable mobility ratio conditions, such as more viscous oil. Therefore, an important requirement of success is to find a set of design parameters that balance material requirements and petroleum recovery benefits in a cost-effective manner. Then, prediction of oil recovery turns out to handle more detailed information and time-consuming field reservoir simulation. Thus, for an effective enhanced oil recovery project management, a quick and feasible tool is needed to identify projects for polymer flooding applications, without giving up key physical and chemical phenomena related to the recovery process and avoiding activities or projects that have no hope of achieving adequate profitability. A detailed one-dimensional mathematical model for multiphase compositional polymer flooding is presented. The mathematical formulation is based on fractional flow theory, and as a function of fluid saturation and chemical compositions, it considers phenomena such as rheology behavior (shear thinning and shear thickening), salinity variations, permeability reduction, and polymer adsorption. Moreover, by setting proper boundary and initial conditions, the formulation can model different polymer injection strategies such as slug or continuous injection. A numerical model based on finite-difference formulation with a fully implicit scheme was derived to solve the system of nonlinear equations. The validation of the numerical algorithm is verified through analytical solutions, coreflood laboratory experiments, and a CMG-STARS numerical model for waterflooding and polymer flooding. In this work, key aspects to be considered for optimum strategies that would help increase polymer flooding effectiveness are also investigated. For that purpose, the simulation tool developed is used to analyze the effects of polymer and salinity concentrations, the dependence of apparent aqueous viscosity on the shear rate, permeability reduction, reversible–irreversible polymer adsorption, polymer injection strategies on petroleum recovery, and the flow dynamics along porous media. The practical tool and analysis help connect math with physics, facilitating the upscaling from laboratory observations to field application with a better-fitted numerical simulation model, that contributes to determine favorable scenarios, and thus, it could assist engineers to understand how key parameters affect oil recovery without performing time-consuming CEOR simulations.

Compositional Streamline-Based Modeling of Polymer Flooding Including Rheology, Retention, and Salinity Variation

“…Now, applying the SL coordinate transformation technique to the 1D model for polymer flooding developed in our previous publication, we can establish the following system of nonlinear differential equations for water, polymer, and salt, i.e., components 1, 4, and 5, respectively ∂ ∂ t [ S 1 ] + ∂ ∂ τ [ f 1 ] = 0 ∂ ∂ t [ C 41 S 1 + Ĉ 4 ] + ∂ ∂ τ [ f 1 C 41 ] = 0 ∂ ∂ t [ C 51 S 1 ] + ∂ ∂ τ [ f 1 C 51 ] = 0 with S 1 (τ, t ), C 41 (τ, t ), and C 51 (τ, t ) as unknowns. Initial and boundary conditions, that complete the definition of the problem, can be adequate to any condition state of the previous production, polymer injection strategies, and other operational conditions.…”

“…In eqs –, fractional flow, f 1 , is a function of saturation and concentrations, and relative permeabilities (given by Corey-type equations ,,, ) and polymer rheology properties are considered. Although a detailed description of the 1D polymer flooding model is thoroughly discussed in our previous paper, a brief review of the equations for the key phenomena is included as follows (model parameters’ details are in the nomenclature section). Polymer adsorption with salinity variation is represented by a Langmuir-type model in the numerical simulation. , Ĉ 4 = min [ C̃ 4 , a 4 false( C̃ 4 − Ĉ 4 false) 1 + b 4 false( C̃ 4 − Ĉ 4 false) ] Viscosity at zero shear rate with salinity variation is modeled with the modified Flory–Huggins equation. , μ 1 normalo = μ 1 [ 1 + ( a p 1 C 41 + a p 2 C 41 2 + a p 3 C …”

“…The compositional description considered an adaptation of the equation presented by Pope et al and the aqueous transport equation for compositional-multiphase flow previously derived to establish the 2D flow as follows ϕ ∂ ∂ t false[ C i 1 S 1 + Ĉ i false] + ∂ ∂ x false[ u x 1 C i 1 false] + ∂ ∂ y false[ u y 1 C i 1 false] = 0 ⁣ i = 1 , 2 , · · · , N C …”

“…The 1D flow model used in this work to describe polymer flooding along the SL was previously presented. 32 It is based on the fractional flow theory, two-phase and compositional, and considers in an integrated way the key phenomena controlling the polymer flooding process, such as rheology behavior (shear thinning and shear thickening), salinity variations, permeability reduction, and reversible−irreversible polymer adsorption. The common notation for chemical flooding 14,47 is adopted, so that the four components are water (1), oil (2), polymer (4), and salinity or total monovalent anions (5).…”

Study on Micro-Displacement Mechanism and Reservoir Compatibility of Soft Dispersed Microgel

“…In order to solve the limitation that polymer flooding can only be used in the near-well area. Many scholars try to conduct “high-dose profile control”, also known as “deep profile control” [ 19 , 20 , 21 , 22 , 23 ], but the treatment radius is often no more than 10–20 m and the treatment cost is high. In addition, with the increase of water-cut in oilfields, the water-flooding contradiction changes from the shallow reservoir to the deep reservoir, or even the entire reservoir flow field.…”