Using the local bijectivity of Keller maps, we give a proof of two-dimensional Jacobian conjecture.

Polymer flooding is an established enhanced oil recovery (EOR) method, still many aspects of polymer flooding are not well understood. This study investigates the influence of mechanical degradation on flow properties of polymers in porous media. Mechanical degradation due to high shear forces may occur in the injection well and at the entrance to the porous media. The polymers that give high viscosity yields at a sustainable economic cost are typically large, MW > 10 MDa, and have wide molecular weight distributions. Both MW and the distributions are altered by mechanical degradation, leading to changes in the flow rheology of the polymer. The polymer solutions were subjected to different degrees of pre-shearing and pre-filtering before injected into Bentheimer outcrop sandstone cores. Rheology studies of injected and produced polymer solutions were performed and interpreted together with in-situ rheology data. The core floods showed a predominant shear thickening behavior at high flow velocities which is due to successive contraction/expansion flow in pores. When pre-sheared, shear thickening was reduced but with no significant reduction in in-situ viscosity at lower flow rates. This may be explained by reduction in the extensional viscosity. Furthermore, the results show that successive degradation occurred which suggests that the assumption of the highest point of shear which determines mechanical degradation in a porous media does not hold for all field relevant conditions.

Leak of carbon dioxide (CO2) from conventional underground carbon storage reservoirs is an increasing concern. It is highly desirable to inject CO2 into low-temperature reservoirs so that CO2 can be locked inside the reservoir in solid state as CO2-hydrates. Marine gas hydrate reservoirs and surrounding water aquifers are attractive candidates for this purpose. However, the nature of low-permeability of these marine sediments hinders injection of CO2 in commercial scale due to the low-injectivity of wells with conventional completions. This study investigates injection of CO2 into the low-permeability marine reservoirs using a new type of well namely radial-lateral wells (RLW). An analytical model was developed for predicting CO2 injectivity of the RLW to assess well injectivity improvement. A case study and sensitivity analysis were performed with field data from the South China Sea. Result of analysis reveals that the injectivity of the RLW is nearly proportional to reservoir permeability, lateral wellbore length, and number of laterals. CO2 injection rate is predicted to be 19 tons/day to 250 tons/day, which is 3 to 15 times higher than the injectivity of frac-packed wells. It is feasible to inject CO2 into the low-permeability-low-temperature marine reservoirs at commercial flow rates. This work provides an analytical tool to predict CO2-injectivity of RLW in low-temperature marine reservoirs for leak-free CO2 storage.

Water soluble polymers have gained an increasing interest in enhanced oil recovery (EOR) processes, especially as polymer flooding. Despite the fact that the flow of polymer in porous medium has been a research subject for many decades with numerous publications, there are still some research areas that need progress. The prediction of polymer injectivity remains elusive. Polymers with similar shear viscosity might have different in-situ rheological behaviors and may be exposed to different extent of mechanical degradation. Hence, determining polymer in-situ rheological behavior is of great significance for defining its utility. In this study, an investigation of rheological properties and mechanical degradation of different HPAM (partially hydrolyzed polyacrylamide) polymers was performed using Bentheimer sandstone outcrop cores. Results show that, HPAM in-situ rheology is different from bulk rheology measured in rheometer. Specifically, shear thickening behavior occurs at high rates, and near-Newtonian behavior is measured at low rates in porous media. This deviates strongly from measurements in the rheometer. Polymer molecular weight and concentration influence its viscoelasticity and subsequently its flow characteristics in porous media. Exposure to mechanical degradation by flow at high rate through porous media leads to significant reduction in shear thickening and thereby improved injectivity. More importantly, the degraded polymer maintained in-situ viscosity at low flow rates indicating that improved injectivity can be achieved without compromising viscosity at reservoir flow rates. This is explained by reduction in viscoelasticity. Mechanical degradation also leads to reduced residual resistance factor (RRF), especially for high polymer concentrations. For some of the polymer injections, successive degradation (increased degradation with transport length in porous media) was observed. The results presented here may be used to optimize polymer injectivity.