Lawrence Livermore National Laboratory

A. J. Simon


In this project, we assessed the feasibility of developing a stock and flow model of carbon for the United States economy and applying it to assess opportunities for the substitution of carbon dioxide (CO2) as a feedstock for industrial processes. Feasibility was assessed by integrating the results of the following three tasks: (1) taking a survey of data in existing government databases of commodity stocks and flows with the aim of identifying relevant data sources and data gaps and how they could be filled; (2) producing a quantitative top-down description of carbon stocks in and flows through the U.S. economy, in which we present the results in a Sankey diagram for carbon that will complement those prepared by Lawrence Livermore National Laboratory (LLNL) for the U.S. energy system; and (3) performing a quantitative case study of a selected material production pathway to assess the potential of assembling a national picture of carbon flows from the bottom up. We integrated results and identified a way to develop a refined national model of carbon stocks and flows to assess and compare CO2 utilization pathways.

Background and Research Objectives

The framework for assessing the stocks and flows of materials in the economy is called materials flow accounting (MFA) and has parallels to economic and energy accounting (Fischer-Kowalski et al. 2011). The concept of MFA was established in 1969 by Ayres and Kneese to frame the problem of pollution in terms of a materials-balance problem for the entire economy (Ayres and Kneese 1969). The framework proposed by Ayres and Kneese has evolved through application to other national economies and become a formalized discipline. Today, MFA databases are available for a handful of material categories (e.g., biomass, fossil fuels, metallic and non-metallic ores) for many regions and time periods. The flows in these databases are collected from many sources, which report data in both physical (e.g., volume, mass) and monetary units and may need to be converted into relevant flows through conversions such as metals prices. Few if any of these databases provide information sufficient to definitively close the mass balance for a national economy.

MFA has most commonly been applied retrospectively, to account for past flows, but may also be applied prospectively, for example, in scenario analysis. The study that most closely relates to the goals of this project (Ohno et al. 2018) presents the flow of fossil- and wood-derived carbon in petrochemicals and wood products supplied to the Japanese economy in 2011, from raw source to final products. Material flows in this work are derived primarily from national economic input–output tables showing economic flows between activities. These have been converted to physical units through prices and adjusted to include waste generation, that is, activity that is not captured as economic in nature (Nakamura et al. 2007). The study finds that nearly 45 million metric tons (Mt) of woody- and fossil-carbon were introduced into the Japanese economy in 2011, of which 14 Mt were consumed in the economy in a variety of forms. Ohno et al. do not determine the final disposition of the approximately 26 Mt of carbon exported or lost between raw material supply and final demand, nor do they comprehensively assess the final disposition of the 14 Mt of carbon consumed in final demand, e.g., added to long-lived stock in use, landfilled, or incinerated.

We present the results of our explorations in the form of a Sankey diagram that enforces material conservation and stimulates rigorous analysis of material flows. The preliminary Sankey diagram describing U.S. domestic carbon flows is shown in Figure 1.

Sankey diagram denoting flows of embedded carbon throughout the U.S. economy and environment circa 2015
Sankey diagram denoting flows of embedded carbon throughout the U.S. economy and environment circa 2015. Stocks of carbon are denoted by ovals, processes as squares, and the flows between them as arrows. The size of flows is proportional to the width of the arrow and listed next to each arrow in units of GtC per year. Estimated flows in black text are relatively well constrained by the available data, while those in red are poorly constrained. Flows in blue indicate emissions of carbon (principally as CO2) to the atmosphere; those in green denote carbon fixed by photosynthesis; those in black and grey denote flows of fossil carbon; and other colors denote flows of various commodities, goods, and wastes. Imports and exports were not included in the analysis.

Impact on Mission

This study resulted in a framework by which carbon flows throughout the U.S. economy can be quantified. This is a foundational advance for LLNL's carbon initiative, which seeks to enhance energy and climate security through technologies and strategies that remove greenhouse gases from the atmosphere. The conceptual framework and partial quantification of fossil, biological, and mineral carbon flows can help LLNL prioritize its negative carbon research and development and position sponsored research in that area for maximal impact. This research also strengthened collaborations with university partners. This study is the basis for a project funded by the Department of Energy’s Biomass Energy Technologies Office, a collaboration between LLNL and the University of California, Berkeley.


We conclude that it is feasible to map carbon flows through the U.S. economy. The preliminary map created in the feasibility study has shortcomings, both in structure and in the quantification of certain stocks and flows. Aggregating data and assembling a consistent framework is nontrivial; however, there is high confidence that further work could fill these gaps using the same techniques that were developed and applied during this study. Carbon MFA is an active topic of research and LLNL has the potential to lead in this area and seek broad collaborations to advance the state of the art.

The map provides insight into national carbon flows and can be used to identify technology gaps and compare carbon drawdown opportunities. Further research that results in a scenario analysis tool based on integrated carbon flow analysis could enhance the value of this research to LLNL in its mission to ensure energy and climate security.


Ayres, R. U. and A.V. Kneese. 1969. "Production, Consumption, and Externalities." The American Economic Review 59(3):282–297.

Fischer-Kowalski, M., et al. 2011. "Methodology and Indicators of Economy-wide Material Flow Accounting." Journal of Industrial Ecology 15(6):855–876.

Nakamura, S., et al. 2007. "The Waste Input-Output Approach to Materials Flow Analysis." Journal of Industrial Ecology 11(4):50–63.

Ohno, H., et al. 2018. "Configuration of Materially Retained Carbon in Our Society: A WIO-MFA-Based Approach for Japan." Environmental Science & Technology. doi:10.1021/acs.est.7b06412.

Publications and Presentations

Busse, G., et al. 2018. "Polylactic Acid: A Feasibility Test Case for Modeling Carbon Flows in the U.S. Economy." Lawrence Livermore National Laboratory Summer Student Poster Symposium, Livermore, CA, August 2018. LLNL-POST-756238.