Unified viscoelastic injectivity model: Analytical solutions predicting polymer excess pressure and fracture initiation

Abstract

The most pressing question to embark on polymer flood projects is whether a polymer can be injected at economic rates while below reservoir parting pressure. There are several published examples of field polymer floods with unexpected injectivity and/or fracture initiation/propagation. Current commercial reservoir simulators lack the capability to model viscoelastic polymer rheology and fracture initiation and often lead to misleading expectations. The laboratory tests to select a polymer are performed without considering fracture or shear-thickening behavior near wellbores. This paper presents a physical-mathematical model to estimate excess pressure due to viscoelastic polymers and assist field operators in better polymer selection and injection design. One of the primary purposes of this paper is to develop predictive analytical tools based on the well-known Unified Viscoelastic Model (UVM), capable of estimating excess pressure and fracture initiation, independent of numerical solutions and reservoir simulators. Asymptotic techniques and special functions theory are utilized to construct a set of general closed-form analytical solutions. It is found that viscoelastic pressure drop can be determined by merely knowing the polymer rheology and slug radius from the wellbore. The derived viscoelastic pressure drop solutions can be easily implemented in MS Excel, which is convenient for engineers participating in the design and execution of polymer flooding projects. Analytical solutions are compared with numerical solutions, laboratory experiments, and field data, and excellent agreement is found.