Along-the-channel modeling and analysis of PEFCs at low stoichiometry: Development of a 1+2D model

Water management remains a key challenge in polymer-electrolyte fuel cells. In this work, a pseudo 3-D (1+2D) model is developed to account better for changes of water management along the channel, as well as verify the possibilities of using differential cells for data capture and translation to integral cell performance. An accurate 2-D membrane-electrode-assembly model is developed for differential cell modeling, which is combined with an along-the-channel stepping algorithm to account for down the channel changes in pressure, temperature, reactant concentration, and relative humidity. Variations in cell performance along the channel due to changes in operating conditions are characterized quantitatively and optimized, where drier feed conditions demonstratively require such an approach. Overall, the study identifies gaps between differential and integral cells including those related to flow velocity and highlights the need for better models to understand and link integral cell performance and water management

Applications of the DFLU flux to systems of conservation laws

The DFLU numerical flux was introduced in order to solve hyperbolic scalar conservation laws with a flux function discontinuous in space. We show how this flux can be used to solve systems of conservation laws. The obtained numerical flux is very close to a Godunov flux. As an example we consider a system modeling polymer flooding in oil reservoir engineering

Influence of the polymer properties and numerical schemes on tertiary oil recovery processes

Chemical Enhanced Oil Recovery (EOR) processes comprise a number of flooding techniques aimed at increasing the operational life of mature oilfields. Among these, polymer flooding is one of the most developed; its functionality is to increment the aqueous viscosity, avoiding the formation of viscous fingering. Reservoir simulators consider this influence as well as other physical properties (e.g., adsorption, permeability reduction). However, the polymer degradation is usually not considered even though it plays a critical role in the viscosity. In this paper this mechanism is analyzed and coupled with the previously mentioned physical phenomena in order to present a complete study of their influence in the EOR process. Moreover, since a fully second-order accuracy scheme is used along with a Total Variation Diminishing (TVD) flux-limiting function, the influence of the latter on the recovery factor is also discussed. Results showed that the negative effect of the polymer adsorption was the most relevant physical phenomenon in terms of the oil recovery. Furthermore, the analysis of the discretization of the differential equations showed that traditional, linear first-order schemes created numerical diffusion affecting negatively the macroscopic sweeping efficiency, which disappeared when TVD techniques were used. Reservoir simulators allow determining the desired designing properties for future polymers in relationship with the characteristics of the oilfield to be exploited

Influence of the polymer degradation on enhanced oil recovery processes

Polymer flooding is one of the most common and technically developed chemical Enhanced Oil Recovery (EOR) processes. Its main function is to increase the carrying phase's (i.e., water or brine) viscosity in order to mobilize the remaining trapped oil. Many numerical simulators have been developed during the last 30 years considering the influence of the polymer molecules on the viscosity as well as on other physical parameters (e.g., diffusion, adsorption). Nevertheless, there are certain phenomena which were not previously considered, for instance, the interfacial effects of hydrophobically modified polymers. Furthermore, the degradation of the polymer molecules in a harsh environment such as the one found in porous media is well known. This causes a deterioration on the viscosifying properties, diminishing the efficiency of the method. It is important also to consider the effect of the polymer viscoelasticity on the microscopic sweeping efficiency, lowering the residual oil saturation, which has not been properly addressed. A new compositional 2D numerical simulator is presented for polymer flooding in a two-phase, three-component configuration, considering all these physical effects present in porous media and using a fully second-order accurate scheme coupled with total variation diminishing (TVD) functions. Results demonstrated that degradation cannot be considered negligible in any polymer EOR process, since it affected the viscoelastic and viscosifying properties, decreasing the sweeping efficiency at both micro- and macroscopic scales. This simulator will allow setting the desired designing properties for future polymers in relationship with the characteristics of the oil field to be exploited

Surfactant–Polymer Flooding: Influence of the Injection Scheme

The use of standard enhanced oil recovery (EOR) techniques allows for the improvement of oilfield performance after waterflooding processes. Chemical EOR methods modify different properties of fluids and/or rock to mobilize the remaining oil. Moreover, combined techniques have been developed to maximize the performance by using the joint properties of the chemical slugs. A new simulator is presented to study a surfactant–polymer flooding, based on a two-phase, five-component system (aqueous and oleous phases with water, petroleum, polymer, surfactant, and salt) for a 2D reservoir model. The physical properties modified by these chemicals are considered as well as the synergy between them. The analysis of the chemical injection strategy is deemed vital for the success of the operations. This plays a major role in the efficiency of the recovery process, including the order and the time gap between each chemical slug injection. As the latter is increased, the flooding tends to behave as two separate processes. Best results are found when both slugs are injected overlapped, with the polymer in first place which improves the sweeping efficiency of the viscous oil. This simulator can be used to study different chemical combinations and their injection procedure to optimize the EOR process

Mathematical Models and Numerical Methods for Porous Media Flows Arising in Chemical Enhanced Oil Recovery

We study multiphase, multicomponent flow of incompressible fluids through porous media. Such flows are of vital interest in various applied science and engineering disciplines like geomechanics, groundwater flow and soil-remediation, construction engineering, hydrogeology, biology and biophysics, manufacturing of polymer composites, reservoir engineering, etc. In particular, we study chemical Enhanced Oil Recovery (EOR) techniques like polymer and surfactant-polymer (SP) flooding in two space dimensions. We develop a mathematical model for incompressible, immiscible, multicomponent, two-phase porous media flow by introducing a new global pressure function in the context of SP flooding. This model consists of a system of flow equations that incorporates the effect of capillary pressure and also the effect of polymer and surfactant on viscosity, interfacial tension and relative permeabilities of the two phases. We propose a hybrid method to solve the coupled system of equations for global pressure, water saturation, polymer concentration and surfactant concentration in which the elliptic global pressure equation is solved using a discontinuous finite element method and the transport equations for water saturation and concentrations of the components are solved by a Modified Method Of Characteristics (MMOC) in the multicomponent setting. We also prove convergence of the hybrid method by assuming an optimal O(h) order estimate for the gradient of the pressure obtained using the discontinuous finite element method and using this estimate to analyze the convergence of the MMOC method for the transport system. The novelty in this proof is the convergence analysis of the MMOC procedure for a nonlinear system of transport equations as opposed to previous results which have only considered a single transport equation. For this purpose, we consider an analogous single-component system of transport equations and discuss the possibility of extending the analysis to multicomponent systems. We obtain error estimates for the transport variables and these estimates are validated numerically in two ways. Firstly, we compare them with numerical error estimates obtained using an exact solution. Secondly, we also compare these estimates with results obtained from realistic numerical simulations of flows arising in enhanced oil recovery processes. This mathematical model and hybrid numerical procedure have been successfully applied to solve a variety of configurations representing different chemical flooding processes arising in EOR. We perform numerical simulations to validate the method and to demonstrate its robustness and efficiency in capturing the details of the various underlying physical and numerical phenomena. We introduce a new technique to test for the influence of grid alignment on the numerical results and apply this technique on the hybrid method to show that the grid orientation effect is negligible. We perform simulations using different types of heterogeneous permeability field data which include piecewise discontinuous fields, channel-like fractures, real world SPE10 models and multiscale fields generated using a stationary, isotropic, fractal Gaussian distribution. Finally, we also use the method to compare the relative performance of flooding schemes with different injection profiles both in a quarter five-spot as well as a rectangular reservoir geometry

The Application of Improved Numerical Techniques to 1-D Micellar/Polymer Flooding Simulation

Three examples of three phase flow models which have been developed are compared under various conditions. Although the dif-ference in oil recovery and surfactant trapping among the models was rather large with constant. salinity, a salinity gradient produced high oil recovery and low surfactant trapping with all three models. Since surfactant trapping is important and it is highly uncertain, this is another reason for designing a micellar flood with a salinity gradient, or something equivalent to a salinity gradient. The semi-discrete method was applied to a 1-D micellar/polymer flooding simulator. By using a semi-discrete method, the time step size can be controlled and varied to be as large as pos-sible without sacrificing accuracy. The stability limit can also be detected with this method. The method is tested and compared with the fully discrete method in various conditions such as differ-ent phase behavior environments and with or without adsorption. In the application of the semi-discrete method, four different ODE in-tegrators were used. Two of them are explicit methods while the other two are implicit methods. Although the implicit methods did not work as well as the explicit methods, there may be some improve-ment possible. With respect to the computation time, one of the explicit methods which is based on the· Runge-Kutta approximation worked best. Although the method can save 20 to 30% computation time under some conditions, compared with the fully-discrete method, the results are highly problem-dependent. To improve the computation time, two methods are suggested. One is to check the error only in the oil or water component rather than all components or any other one component such as surfactant. The other is to check absolute error instead of relative error and multiply by a small conservative factor to the calculated time step size. The stability was analyzed for the oil bank, and for the surfactant front. The former imposes a rather constant limitation on the time step size continuously until the plateau of the oil bank is completely produced: Although approximate, the stability analysis for the surfactant front suggests an unconditional local instability, which is caused by the change in the fractional flow curve due to the surfactant.Petroleum and Geosystems Engineerin