A boundary element method to estimate the interfacial boundary of two immiscible stratified liquids using electrical resistance tomography

• BEM is applied to ERT for estimating the boundary of two immiscible liquids.
• Front point method is used to represent the complex shape of interface.
• BEM is formulated for open boundary problem with analytic boundary integration.
• Unknown front point position is estimated using with LM method.
• The number of front points on the boundary determines the estimation performance.

Flow of two immiscible stratified liquids in a pipe is observed in many industrial applications. Estimating the interfacial boundary between the immiscible liquids inside the pipeline can provide valuable information about volume fraction therefore can aid in monitoring the flow process. Several methods are proposed to represent the shape of an open boundary using linear combination of known functions. In this paper, the open boundary is characterized by discrete front points from the reference horizontal line at the center. The boundary parameterization with front points eliminates the fixed end problem that is caused while using Fourier series or a polynomial like a Bezier curve. Therefore, it can be more suitable to practical conditions and can be used to represent any complex shape with fewer unknowns. The forward problem is solved using boundary element method (BEM) with the integral equations solved analytically. The proposed BEM formulation is computationally efficient due to less number of system equations to solve. The unknown front points locations that describe the boundary surface are estimated using Levenberg–Marquardt method. Numerical and phantom experiments are performed to validate the performance of the proposed computational method.