kakaie, the query is short, and general. A considered answer would take pages. I'll try to give a short answer, not the overall picture; it would, by its nature, suffer from incompleteness.
An accepted definition of design is: the act of conceiving and planning the structure and parameter values of a system, device, process or even works of art. Normally, defining the scope (aka definition) of the project is a subject that the relevant authorities of a company must initiate.
Concerned with chemical process engineering as we are in this forum, basic design would mainly include gathering of sufficient information, and is a preliminary time-limited step in a project that generally ends with an economic feasibility analysis to show its relative advantage or disadvantage, be it research work for a new chemical, a new process, the study of erecting a new plant, a plant expansion, equipment replacement, etc. The amount of process engineering involved depends on the scope of the project.
Basic and detail design are separated by the important step of taking a decision (mainly by the board of directors, BOD) on whether to continue, expand, momentarily shelve, or altogether abandon a project.
The BOD may wish to consult with marketing and financial experts before reaching a decision. When discussing a multi-million dollar (preliminary) project they might have to consider the impact it will have on future company long-range policy and ask for a (present and future) market analysis for the products and raw materials. They may then decide to give it a temporary approval and ask for more basic work to be done as in a pilot plant. Or they may finally approve it. That's the moment detail engineering design starts.
The parameters involved in basic design are so many and varied, I'd recommend you read books on the subject. One that comes to mind is
Preliminary Chemical Engineering Design by William D. Baasel (Van Nostrand Reinhold).
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