This paper investigates a mean reaction rate closure for turbulent reacting flows called the Direct Quadrature Method of Moments using the Interaction by Exchange with the Mean micromixing model (DQMoM-IEM). The method is not new, but we present a systematic study that considers several important new aspects of the method. We present a rigourous numerical investigation of the behaviour and implementation of the method in a commercial computational fluid dynamics (CFD) package. The problems that arise are discussed in detail. We present practical hints and propose solutions to resolve these issues. In particular we demonstrate a new analytic expression for the DQMoM-IEM source terms. We extend the methodology to take advantage of this expression and show details of the implementation in the CFD code. We present an extensive set of numerical experiments and validation. The method is demonstrated to work for a problem known from the literature which includes an isothermal dimerisation process. Experimental and transported probability density function (PDF) data compare reasonably well. The method is discussed critically and areas for further research are suggested to make the method more practical.