Channel geometry is represented by a signed distance function, and boundaries are then updated gradually by solving level set equation and matching of production historical data using two-stage Markov chain Monte Carlo (MCMC) method. In the first stage, streamline-derived sensitivities are employed to approximate a likelihood function, and instrumental proposal distribution of MCMC is modified by the approximation. In the second stage, proposals that pass the first stage are further assessed by running full numerical simulations, and a precise likelihood function is acquired. The models are checked for acceptance with modified acceptance probability. Finally, a 2D example demonstrates effectiveness of the method.