The so-called allocation or partitioning problem which is still indeterminable in life cycle assessment (LCA) has been studied. The phi balance defined in this study is used to describe the relations of inputs and outputs in each subsystem consisting of the whole environment system. In doing so, the mass balance of pollutant materials in environment system under consideration is expressed in much smaller dimension compared to the case where the conventional mass balance is employed and thus the mathematical procedure is highly simplified in establishing a computer program for calculating the cumulative CO2 emission unit which is equivalent to the total quantity of CO2 emitted to the atmosphere to produce the present material or energy from raw fossil resources. The cumulative CO2 emission unit which is an indicative value of CO2 pollution used in this study of LCA are calculated for some petrochemical materials for plastics depending on several kinds of partitionings.