## 3 Methods
### Life Cycle Inventory Development
#### 3.2.3 MICP Process Emissions  
MICP has direct and indirect process emissions associated with its application to soils and produced byproducts, including aqueous NH\({}_{4}\)\({}^{+}\), unhydrolyzed urea, and sorbed NH\({}_{4}\)\({}^{+}\). MICP byproducts and associated process emissions were estimated from the obtained experimental data (see \"Estimating MICP By-products\" section in the Supplementary Materials) [19; 24] and following the recommendations of the other published literature [42; 43]. Estimates of in situ MICP byproduct masses as a function of injected rinse solution volumes and rinsing time (rinse injection flow rate = 0.75 L/min) are provided in Figure 3 and tabulated in Supplementary Table S3.  
Following MICP treatments, generated in situ nitrogen (N) remaining within soils (in the form of aqueous NH\({}_{4}\)\({}^{+}\), unhydrolyzed urea, and sorbed NH\({}_{4}\)\({}^{+}\)) may contribute to air and water pollution through various environmental mechanisms or impact pathways. These include the potential for (1) the volatilization of produced nitrogen species as ammonia gas (NH\({}_{3}\)), (2) the generation of nitrous oxide (N\({}_{2}\)O), nitric oxide (NO), and nitrogen gas (N\({}_{2}\)) emissions resulting from the potential aerobic oxidization of NH\({}_{4}\)\({}^{+}\) to nitrate (NO\({}_{3}\)\({}^{-}\)) and subsequent anaerobic reduction of NO\({}_{3}\)\({}^{-}\), and (3) aqueous transport and runoff/leaching of N, mainly as NH\({}_{4}\)\({}^{+}\) and NO\({}_{3}\)\({}^{-}\)[43]. Although the fate and transport of NH\({}_{4}\)\({}^{+}\) byproducts following MICP remain uncertain and are likely site-specific, assumptions were made to approximate these emissions and their environmental impacts. For conservatism, it was assumed that the mass of total MICP byproducts (Figure 3b) would eventually become available as aqueous NH\({}_{4}\)\({}^{+}\). Thus, it was assumed that all remaining urea (when present) would eventually be hydrolyzed to form NH\({}_{4}\)\({}^{+}\) and all sorbed NH\({}_{4}\)\({}^{+}\) would desorb and  
Figure 3: (a) Reductions in post-treatment MICP byproduct masses (as nitrogen) during rinse injections in Column 1, including reductions in column aqueous NH\({}_{4}\)\({}^{+}\), NH\({}_{4}\)\({}^{+}\) from unhydrolyzed urea, sorbed NH\({}_{4}\)\({}^{+}\), and total NH\({}_{4}\)\({}^{+}\) masses. (b) Comparison of reductions in total MICP nitrogen byproduct masses for Columns 1, 2, and 3 during rinse injections.  
exist in free soil solution. Thirty percent of this aqueous NH4\({}^{+}\) was assumed to nitrify to produce NO3\({}^{-}\)[43]. Direct N2O and NO emissions due to the denitrification of this NO3\({}^{-}\) were assumed to be 1.1% and 0.7% of in situ N, respectively [42]. Direct N2 emissions were assumed to be 8.9% of in situ N, following studies which found that the N2O:N2 production ratio during denitrification in natural soils is approximately 0.12 [44]. The remaining NO3\({}^{-}\) that was not denitrified was assumed to leach into groundwater. All remaining NH4\({}^{+}\) (approximately 59.3% of in situ N) was assumed to remain in the soil pore space or leach into groundwater. Indirect N2O emissions from N losses through leaching and/or runoff were assumed to be 0.75% of leached NO3\({}^{-}\) and NH4\({}^{+}\)[43]. It was assumed that no emissions were released via NH3 volatilization as MICP was applied to saturated subsurface soils and post-treatment pH values were near 7.5, resulting in a minimal speciation of total NH4\({}^{+}\) as NH3. These allocations are best estimate values based upon current knowledge, but the assumed fate of generated N species may be further refined following future chemical measurements during and after MICP treatments.