A Comparison between Klinkenberg and Maxwell-Stefan Formulations to Model Tight Condensate Formations

Abstract

Summary Cyclic solvent (gas) injection is an efficient recovery method for condensate reservoirs. However, in tight, unconventional formations, the added complexity of low permeability results in more physics at play, beyond the widely used Darcy model for conventional reservoirs. In this work, a rigorous mass transfer model is implemented considering the real gas version of the Maxwell-Stefan formulation to evaluate cyclic injection schemes in tight condensate reservoirs. This model is then compared to the more widespread used Klinkenberg formulation, which does not include molecular diffusion. An evaluation is performed to check if a simplified formulation can be used to provide reasonable results in modeling production and enhanced recovery in tight condensate formations. Verification of the implemented equations is performed using experiments (Maxwell-Stefan model) and a commercial reservoir simulator (Klinkenberg model). Furthermore, the cell length used for the numerical studies is selected based on a sensitivity study to evaluate how numerical dispersion impacts recovery factor and liquid saturation for different cell sizes. By comparing the Klinkenberg model with different tangential momentum accommodation coefficient (TMAC) values to the Maxwell-Stefan model during primary production, it is possible to select a value of TMAC that can match closely the recovery values of lighter components when using the Maxwell-Stefan equations. However, for heavier hydrocarbon fractions, difference in recovery is more accentuated owing to increased molecule size (more molecular friction). This results in differences in condensate yield during primary production that may be relevant in a field scale. In the cyclic injection scheme, the importance of accounting for frictional effects between molecules is demonstrated using the Maxwell-Stefan formulation. In this case, molecular diffusion fluxes are influenced by high composition gradients. This results in differences between the Maxwell-Stefan and Klinkenberg models in terms of gas stored and hydrocarbon produced during cyclic injection simulations. Furthermore, a sensitivity study on operational parameters in the cyclic injection stage demonstrated that increasing the length of production cycles may be more beneficial than increasing the length of injection or soaking cycles. For the simulations in this study, the gas is injected above the dewpoint and pressure diffusivity is at least one order of magnitude higher than the other physics present in the process. Therefore, increasing the length of production cycles allows for recovery of heavier hydrocarbon fractions that remain in the gas phase. In this work, it is demonstrated that using a rigorous mass transfer formulation, such as the Maxwell-Stefan equations, can provide more information on a per component basis when evaluating cyclic injection schemes in tight condensate reservoirs.