Process integration is a term in chemical engineering which has two possible meanings.
# A holistic approach to process design which emphasizes the unity of the process and considers the interactions between different unit operations from the outset, rather than optimising them separately.  This can also be called integrated process design or process synthesis.  El-Halwagi (1997 and 2006) and Smith (2005) describe the approach well.  An important first step is often product design (Cussler and Moggridge 2003) which develops the specification for the product to fulfil its required purpose. 
# Pinch analysis, a technique for designing a process to minimise energy consumption and maximise heat recovery, also known as heat integration, energy integration or pinch technology.  The technique calculates thermodynamically attainable energy targets for a given process and identifies how to achieve them. A key insight is the pinch temperature, which is the most constrained point in the process. The most detailed explanation of the techniques is by Linnhoff et al. (1982), Shenoy (1995), Kemp (2006) and Kemp and Lim (2020), and it also features strongly in Smith (2005). This definition reflects the fact that the first major success for process integration was the thermal pinch analysis addressing energy problems and pioneered by Linnhoff and co-workers. Later, other pinch analyses were developed for several applications such as mass-exchange networks (El-Halwagi and Manousiouthakis, 1989), water minimization (Wang and Smith, 1994), and material recycle (El-Halwagi et al., 2003). A very successful extension was "Hydrogen Pinch", which was applied to refinery hydrogen management (Nick Hallale et al., 2002 and 2003). This allowed refiners to minimise the capital and operating costs of hydrogen supply to meet ever stricter environmental regulations and also increase hydrotreater yields.