Energy security concerns and an abundant supply of natural gas in the USA provide the impetus for engine designers to consider alternative gaseous fuels in the existing engines. The dual-fuel natural-gas diesel engine concept is attractive because of the minimal design changes, the ability to preserve a high compression ratio of the baseline diesel, and the lack of range anxiety. However, the increased complexity of a dual-fuel engine poses challenges, including the knock limit at a high load, the combustion instability at a low load, and the transient response of an engine with directly injected diesel fuel and port fuel injection of compressed natural gas upstream of the intake manifold. Predictive simulations of the complete engine system are an invaluable tool for investigations of these conditions and development of dual-fuel control strategies. This paper presents the development of a phenomenological combustion model of a heavy-duty dual-fuel engine, aided by insights from experimental data. Heat release analysis is carried out first, using the cylinder pressure data acquired with both diesel-only and dual-fuel (diesel and natural gas) combustion over a wide operating range. A diesel injection timing correlation based on the injector solenoid valve pulse widths is developed, enabling the diesel fuel start of injection to be detected without extra sensors on the fuel injection cam. The experimental heat release trends are obtained with a hybrid triple-Wiebe function for both diesel-only operation and dual-fuel operation. The ignition delay period of dual-fuel operation is examined and estimated with a predictive correlation using the concept of a pseudo-diesel equivalence ratio. A four-stage combustion mechanism is discussed, and it is shown that a triple-Wiebe function has the ability to represent all stages of dual-fuel combustion. This creates a critical building block for modeling a heavy-duty dual-fuel turbocharged engine system.