Efficient numerical methods for simulating surface tension of multi-component mixtures with the gradient theory of fluid interfaces

• Proposed schemes overcome challenges of the infinite domain and matrix singularity.
• Efficient methods are formulated for surface tension of multi-component mixtures.
• Proposed algorithms are based on a linear transformation and a path function.
• Proposed algorithms are successfully tested using extensive hydrocarbon examples.

Surface tension significantly impacts subsurface flow and transport, and it is the main cause of capillary effect, a major immiscible two-phase flow mechanism for systems with a strong wettability preference. In this paper, we consider the numerical simulation of the surface tension of multi-component mixtures with the gradient theory of fluid interfaces. Major numerical challenges include that the system of the Euler–Lagrange equations is solved on the infinite interval and the coefficient matrix is not positive definite. We construct a linear transformation to reduce the Euler–Lagrange equations, and naturally introduce a path function, which is proven to be a monotonic function of the spatial coordinate variable. By using the linear transformation and the path function, we overcome the above difficulties and develop the efficient methods for calculating the interface and its interior compositions. Moreover, the computation of the surface tension is also simplified. The proposed methods do not need to solve the differential equation system, and they are easy to be implemented in practical applications. Numerical examples are tested to verify the efficiency of the proposed methods.