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In most process control systems nowadays, process measurements are periodically collected and archived in historians. Analytics applications process the data, and provide results offline or in a time period that is considerably slow in comparison to the performance of many manufacturing processes. Along with the proliferation of Internet-of-Things (IoT) and the introduction of "pervasive sensors" technology in process industries, increasing number of sensors and actuators are installed in process plants for pervasive sensing and control, and the volume of produced process data is growing exponentially. To digest these data and meet the ever-growing requirements to increase production efficiency and improve product quality, there needs a way to both improve the performance of the analytic system and scale the system to closely monitor a much larger set of plant resources. In this paper, we present a real-time data analytics platform, referred to as RT-DAP, to support large-scale continuous data analytics in process industries. RT-DAP is designed to be able to stream, store, process and visualize a large volume of real-time data flows collected from heterogeneous plant resources, and feedback to the control system and operators in a real-time manner. A prototype of the platform is implemented on Microsoft Azure. Our extensive experiments validate the design methodologies of RT-DAP and demonstrate its efficiency in both component and system levels.