The most efficient and cost-effective process for producing high-density polyethylene HDPE polymer is the gas-phase polymerization process, specifically using the Ziegler-Natta catalyst.Optimal conditions for the gas-phase polymerization process are as follows:1. Temperature: The optimal temperature range for the gas-phase polymerization process is between 50C and 100C. Higher temperatures can lead to the formation of low-density polyethylene LDPE instead of HDPE.2. Pressure: The optimal pressure for the gas-phase polymerization process is between 10 and 40 bar. Higher pressures can lead to the formation of LDPE, while lower pressures can result in lower polymerization rates.3. Catalyst type: The most effective catalyst for producing HDPE is the Ziegler-Natta catalyst, which is a combination of a transition metal compound usually titanium and an organometallic compound usually an aluminum alkyl . This catalyst system provides high activity, stereospecificity, and a broad molecular weight distribution, which are essential for producing high-quality HDPE.In summary, the gas-phase polymerization process using the Ziegler-Natta catalyst is the most efficient and cost-effective method for producing HDPE. The optimal conditions for this process are temperatures between 50C and 100C, pressures between 10 and 40 bar, and the use of a Ziegler-Natta catalyst system.