Bilevel Optimization of Enhanced Weathering Networks with P-graph

Carbon dioxide removal (CDR) will be needed to offset residual greenhouse gas (GHG) emissions and achieve carbon neutrality. Enhanced weathering (EW) is a promising CDR technique based on the acceleration of naturally occurring reactions between alkaline minerals with carbonic acid in rainwater. The reactive minerals are pulverized and then applied at a calibrated rate to terrestrial sites; the weathering reaction results in carbon sequestration as bicarbonate ions in the runoff water. EW can be deployed via carbon management networks (CMNs) of sources (mineral-crushing plants) and sinks (application sites). However, current CMN optimization models fail to account for the presence of multiple players (i.e., government and industry) with conflicting objectives. Bilevel optimization models can be used to account for these conflicts via leader-follower games. In this work, a P-graph approach to the optimization of EW-based CMNs is developed. The government is assumed to act as the leader seeking to minimize external costs to the public by specifying acceptable transport routes for mineral powder; the industry is assumed to act as the follower seeking to maximize its CDR earnings by minimizing its costs subject to the transport network topology constraints. Note that the government imposes the latter constraints in anticipation of the industry’s intent to maximize revenues. The model is implemented as a Python code and demonstrated with an illustrative case study. Results show that by following the Stackelberg solution, cost of transportation may be reduced by at least 5 % and the risk of death by 79 %.