Examine the principles of process economics in chemical engineering, including cost estimation, profitability analysis, and economic optimization. Discuss the factors influencing the economics of chemical processes, such as capital costs, operating costs, and market demand, and explain the methodologies used to assess the economic feasibility of chemical projects, such as net present value $($NPV$),$ internal rate of return $($IRR$),$ and payback period. Analyze the role of process economics in decision$-$making, project evaluation, and investment planning in the chemical industry.