An algebraic reaction rate closure involving filtered scalar dissipation rate of reaction progress variable is studied. The filtered scalar dissipation rate closure requires a model for sub-grid scale velocity, u′, which is estimated using four algebraic models and transported sub-grid scale kinetic energy. A priori analyses using DNS data show that the filtered dissipation rate, and thus the reaction rate closure, has some sensitivity to the u′ model. The sensitivity of various statistics obtained from LES of three piloted Bunsen flames of stoichiometric methane-air mixture to the modelling of u′ is observed to be weaker compared to that for the DNS analysis. Moreover, analysis using transported sub-grid scale kinetic energy does not indicate a necessity to include flame-generated turbulence in the modelling of u′ for the Bunsen flames in the thin reaction zones regime. The measured and computed flame brush structures are compared and studied and the algebraic closure for the filtered reaction rate is found to be quite good.