Biochar application to soil is a potentially scalable carbon sequestration strategy. In practice, the amount of biochar that can be added to soil is constrained by the presence of contaminants such as salts, heavy metals, or dioxins. Process Systems Engineering (PSE) and Process Integration (PI) methods can be developed to optimize the reduction of greenhouse gas (GHG) emissions in such biochar-based Carbon Management Networks (CMNs). Previous works have proposed Mathematical Programming (MP) and Pinch Analysis (PA) approaches to the planning of these systems but are subject to the inherent methodological limitations. In this work, an alternative approach using Process Graph (P-graph) is developed, based on the source-sink matching problem being treated as a special Process Network Synthesis (PNS) problem. A case study is solved to illustrate the P-graph approach. In particular, optimal and near-optimal solutions are generated for the problem, which in real applications presents improved flexibility for purposes of practical decision support.