Reaction rates are usually identified at laboratory scale, by comparing measured concentrations with those of the corresponding mathematical models. However, laboratory-scale reaction rates may not necessarily reflect the reactive transport scenarios at the field scale. Thus, a major challenge for field-scale modeling is the determination of reaction kinetics and rates. The conventional inversion of reaction rates relies on optimization approaches that require expensive computation to obtain the gradient of objective functions. In this manuscript, we present a combined simulation-emulation approach for calibrating the first-order reaction rates at the field scale. A number of sample points are adaptively selected to represent the high-dimensional parametric space including dimensions of reaction rates. Correspondingly, reactive transport models are generated and executed for constructing response surfaces of objective functions. Taking the advantage of smooth response surfaces, optimization of reaction rates is efficiently performed. For several benchmark cases, the advantage of using global sensitivity analysis and uncertainty quantification of the objective functions in terms of uncertain reaction rates is demonstrated.