Coal gasification yields synthesis gas, an important intermediate in chemical manufacturing. It is also vital to the production of liquid fuels through the Fischer-Tropsch process and electricity in Integrated Gasification Combined Cycle power generation. Minerals naturally present in coal become molten in entrained-flow slagging gasifiers. Molten coal ash slag penetrates and dissolves refractory bricks, leading to costly plant shutdowns. The extent of coal ash slag penetration and refractory brick dissolution depends on the slag viscosity, the gasification temperature, and the composition of slag and bricks. We measured the viscosity of several synthetic coal ash slags with a high-temperature rotary viscometer and their ash fusion temperatures through optical image analysis. All measurements were made in a carbon monoxide-carbon dioxide reducing atmosphere that approximates coal gasification conditions. Empirical correlation models based on ash fusion temperatures were used to calculate critical viscosity temperatures based on the coal ash compositions. These values were then compared with those obtained from thermodynamic phase-transition models. An understanding of slag viscosity as a function of ash composition is important to reducing refractory wear in slagging coal gasifiers, which would help to reduce the cost and environmental impact of coal for chemical and electricity production.