Sequential Fully Implicit Formulation for Compositional Simulation using Natural Variables

The Sequential Fully Implicit (SFI) method was proposed (Jenny et al., JCP 2006), in the context of a Multiscale Finite Volume (MSFV) formulation, to simulate coupled immiscible multiphase fluid flow in porous media. Later, Lee et al. (Comp. Geosci. 2008) extended the SFI formulation to the black-oil model, whereby the gas component is allowed to dissolve in the oil phase. Most recently, the SFI approach was extended to fully compositional isothermal displacements by Moncorgé et al., (JCP 2017). SFI schemes solve the fully coupled system in two steps: (1) Construct and solve the pressure equation (flow problem). (2) Solve the coupled species transport equations for the phase saturations and phase compositions. In SFI, each outer iteration involves this two-step sequence. Experience indicates that complex interphase mass transfer behaviors often lead to large numbers of SFI outer iterations compared with the Fully Implicit (FI) method. Here, we demonstrate that the convergence difficulties are directly related to the treatment of the coupling between the flow and transport problems, and we propose a new SFI variant based on a nonlinear overall-volume balance equation. The first step consists of forming and solving a nonlinear pressure equation, which is a weighted sum of all the component mass conservation equations. A Newton-based scheme is used to iterate out all the pressure dependent nonlinearities in both the accumulation and flux terms of the overall-volume balance equation. The resulting pressure field is used to compute the Darcy phase velocities and the total-velocity. The second step of the new SFI scheme entails introducing the overall-mass density as a degree-of-freedom, and solving the full set of component conservation equations cast in the natural-variables form (i.e., saturations and phase compositions). During the second step, the pressure and the total-velocity fields are fixed. The SFI scheme with a nonlinear pressure extends the SFI approach of Jenny et al. (JCP 2006) to multi-component compositional processes with interphase mass transfer. The proposed compositional SFI approach employs an overall balance for the pressure equation; however, unlike existing volume-balance Sequential Implicit (SI) schemes (Acs et al. and Doster et al., CRC 2014), which use overall compositions, this SFI formulation is well suited for the natural variables (saturations and phase compositions). We analyze the 'splitting errors' associated with the compositional SFI scheme, and we show how to control these errors in order to converge to the same solution as the Fully Implicit (FI) method. We then demonstrate that the compositional SFI has convergence properties that are very comparable to those of the FI approach. This robust sequential-implicit solution scheme allows for designing numerical methods and linear solvers that are optimized for the sub-problems of flow and transport. The SFI scheme with a nonlinear pressure formulation is well suited for multiscale formulations, and it promises to replace the widely used FI approach for compositional reservoir simulation

The stochastic counterpart of conservation laws with heterogeneous conductivity fields: application to deterministic problems and uncertainty quantification

Conservation laws in the form of elliptic and parabolic partial differential equations (PDEs) are fundamental to the modeling of many problems such as heat transfer and flow in porous media. Many of such PDEs are stochastic due to the presence of uncertainty in the conductivity field. Based on the relation between stochastic diffusion processes and PDEs, Monte Carlo (MC) methods are available to solve these PDEs. These methods are especially relevant for cases where we are interested in the solution in a small subset of the domain. The existing MC methods based on the stochastic formulation require restrictively small time steps for high variance conductivity fields. Moreover, in many applications the conductivity is piecewise constant and the existing methods are not readily applicable in these cases. Here we provide an algorithm to solve one-dimensional elliptic problems that bypasses these two limitations. The methodology is demonstrated using problems governed by deterministic and stochastic PDEs. It is shown that the method provides an efficient alternative to compute the statistical moments of the solution to a stochastic PDE at any point in the domain. A variance reduction scheme is proposed for applying the method for efficient mean calculations

Universal and Non-Universal First-Passage Properties of Planar Multipole Flows

The dynamics of passive Brownian tracer particles in steady two-dimensional potential flows between sources and sinks is investigated. The first-passage probability, $p(t)$, exhibits power-law decay with a velocity-dependent exponent in radial flow and an order-dependent exponent in multipolar flows. For the latter, there also occur diffusive ``echo'' shoulders and exponential decays associated with stagnation points in the flow. For spatially extended dipole sinks, the spatial distribution of the collected tracer is independent of the overall magnitude of the flow field.Comment: 7 pages, LaTe

Convective dissolution of carbon dioxide in saline aquifers

Geological carbon dioxide (CO2) storage is a means of reducing anthropogenic emissions. Dissolution of CO2 into the brine, resulting in stable stratification, increases storage security. The dissolution rate is determined by convection in the brine driven by the increase of brine density with CO2 saturation. We present a new analogue fluid system that reproduces the convective behaviour of CO2‐enriched brine. Laboratory experiments and high‐resolution numerical simulations show that the convective flux scales with the Rayleigh number to the 4/5 power, in contrast with a classical linear relationship. A scaling argument for the convective flux incorporating lateral diffusion from downwelling plumes explains this nonlinear relationship for the convective flux, provides a physical picture of high Rayleigh number convection in a porous medium, and predicts the CO2 dissolution rates in CO2 accumulations. These estimates of the dissolution rate show that convective dissolution can play an important role in enhancing storage security

Association between Hepatic Steatosis and Entecavir Treatment Failure in Chinese Patients with Chronic Hepatitis B

Background: The coexistence of HBV infection and nonalcoholic fatty liver disease (NAFLD) becomes characteristic of liver disease in China, with unknown bilateral influence. We aimed to investigate the effect of hepatic steatosis, a common hepatocyte change in NAFLD, on antiviral therapy in patients with chronic hepatitis B (CHB). Methods and Findings: We carried out a prospective nested case control study in CHB patients receiving Entecavir for initial antiviral therapy, by recording demographic, anthropometric and clinical data at baseline, 24 wk,48 wk and 96 wk. Univariate analysis and multivariate logistic regression were applied to find out independent factors of hepatic steatosis and Entecavir treatment failure. The rates of HBV-DNA clearance, HBeAg seroconversion and ALT normalization were compared between CHB patients with and without steatosis by post hoc analysis. A total of 267 Chinese patients with CHB entered final analysis, with overall percentages of hepatic steatosis and HBeAg positive as 30.5 % and 62.4%. Multivariate analysis showed waist circumference, serum TG and uric acid levels were independent factors of hepatic steatosis. The response rates to Entecavir were 54.9%, 63.8%, 74.2 % at 24 wk,48 wk and 96 wk. Hepatic steatosis was revealed as an independent factor of Entecavir treatment failure by multivariate logistic regression at 24 wk,48 wk and 96 wk. In CHB patients with hepatic steatosis, HBV-DNA clearance and HBeAg seroconversion were both lower throughout the follow-up, but only the former reached statistical significance. Besides, ALT normalization was also significantly lower at 24 wk and 48 wk

Imaging and quantification of spreading and trapping of carbon dioxide in saline aquifers using meter-scale laboratory experiments

The role of capillary forces during buoyant migrati on of CO2 is critical towards plume immobilization within the post-injection phase of a geological carbon sequestration operation. However, the inherent heterogeneity of the subsurface makes it very challenging to evaluate the effects of capillary forces on the storage capacity of these formations and to assess in-situ plume evolution. To overcome the lack of accurate and continuous observations at the field scale and to mimic vertical migration and entrapment of realistic CO2 plumes in the presence of a background hydraulic gradient, we conducted two unique long-te rm experiments in a 2.44 m × 0.5 m tank. X-ray attenuation allowed measuring the evolution of a CO2-surrogate fluid saturation, thus providing direct insight into capillarity- and buoyancy-domin ated flow processes occurring under successive drainage and imbibition conditions. The comparison of saturation distributions between two experimental campaigns suggests that layered-type h eterogeneity plays an important role on non- wetting phase (NWP) migration and trapping, because it leads to (i) longer displacement times (3.6 months vs. 24 days) to reach stable trapping c onditions, (ii) limited vertical migration of the plume (with center of mass at 39% vs. 55% of aquife r thickness), and (iii) immobilization of a larger fraction of injected NWP mass (67.2% vs. 51. 5% of injected volume) as compared to the homogenous scenario. While these observations confirm once more the role of geological heterogeneity in controlling buoyant flows in the s ubsurface, they also highlight the importance of characterizing it at scales that are below seismic resolution (1-10 m)