Global Phosphorus Recovery for Agricultural Reuse

Phosphorus is is an element necessary for the development of crops and is thus commonly applied as fertilizer to 5 sustain agricultural production. It occurs naturally at indefinite quantities, of uncertain quality, in phosphate rock formations, but also concentrates itself in urban and livestock wastewater wherefrom it is often lost as a pollutant. Recovering phosphorus from wastewater to partially meet agricultural demand can contribute to tackling both phosphorus pollution as well natural resource depletion. Here we show that humans discharge a maximum of 3.7 Mt P into wastewater thereby potentially satisfying 22% of the global fertilizer demand. Provided 2015 market dynamics, however, we conclude that only 10 4% of this throughput is technologically and economically recoverable while rock phosphate products exist. Nonetheless, through this recovery, many wastewater treatment facilities can contribute to creating sustainable communities as well as protecting the environment while reducing their own operational cost.


Turning brown waste to green gold
The introduction of intensified (P) fertilization during the Green Revolution of the 1960's demonstrated P's significant potential to improve crop yields, but also the dangers it poses to the environment. Through seepage and runoff processes, as well as the discharge of improperly treated wastewater, phosphorus and other nutrient excesses come into contact with open surface waters, cause pollution, and lead to a loss in aquatic biodiversity (Sims et al., 2000). 4 As a limiting nutrient, the 5 smallest quantity of phosphorus in water can spark the growth of disproportionately large algal blooms. These have a detrimental effect on water based ecosystems in suffocating aquatic life through eutrophication (EPA, 2010). 5 If excess fertilization is a major threat to water quality around the world, then why not extract this excess from the water system and put it back in the food chain? Proper nutrient management practice in tandem with nutrient recovery from rural and urban water systems may potentially be an important strategy to reduce phosphorus pollution by reducing phosphorus discharge to 10 the environment while simultaneously increasing phosphorus supply for food production.
Numerous phosphorus recovery technologies are available; their effectiveness varying, among others, with local wastewater composition and existing wastewater treatment infrastructure. While there exist numerous studies on the efficiency of specific recovery technologies, on the potential recovery from wastewater, and on the duration of the rock phosphate 15 reserves, there are few studies that evaluate recovery in a global and economic context. As such, the adoption of phosphorus recovery technologies is often challenged by (perceived) economic infeasibility or lack of economic incentives and social stigma. Hypothetically, however, the economic feasibility of recovery is not globally homogeneous but varies in space and time. Spatially, the global accretion of phosphorus in wastewater provides recovered products with a (diffused) locationdefined competitive advantage over the geographically concentrated rock phosphate mines ( fig. 1). Temporally, the gradual 20 depletion of rock phosphate reserves, and the unstable but increasing price trends for non-sustainable phosphatic fertilizers (IndexMundi, 2017), will improve the economic appeal for recovery over time ( fig. 2). 6

Motivation
Though various factors such as the political will, technology and knowledge are already there to facilitate the transitioning of the phosphorus market, the economic appeal for recovery still lags behind. Favourable economic prospectives, however, are 25 spatially diverse and will strengthen over time. Global studies that identify locations and conditions for competitive phosphorus recovery at subnational scale could accelerate this transition but are currently inexistent. This study aims to fill that gap by identifying and connecting those areas where there exist high potentials for phosphorus production, to those areas of high agricultural demand. Revealing where recovery may be economically feasible may then stimulate the implementation of recovery technologies, or at least promote further investigation in those areas that show a high potential for recovery.

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The phosphorus cycle is delineated by combination of both social and physical attributes and as such demands a coupled 4 In 1990 about 43% of the grassland and 82% of the maize land in the Netherlands was approximated to be saturated in nutrients due to over fertilisation (Breeuwsma and Silva, 1992). As a result, the nutrient concentrations in surface waters in The Netherlands still consistently exceed water quality standards (Oenema et al., 2007;Oenema and Roest, 1998). 5 These deoxygenated "dead zones" can be found in both lakes and seas, and affect an estimated 245,000 km2 of marine ecosystems (Corcoran et al., 2010). 6 Over the past 15 years the phosphorus price of DAP has increased from 665 [$ t -1 ] to 1,552 [$ t -1 ]. In that same period, the price has been as high as 5,217 [$ t -1  human water systems perspective. A socio-hydrological approach is endeavored as here both these attributes are expressively and emphatically accounted for (Sivapalan et al., 2012). The social component, however, of this coupled human-phosphorus system is confined to the characteristics of a distinct economic nature. The materials and methods employed in assessing the recovery potential of P from waste water at global scale is therefore interdisciplinary and extensive, and covers largely economics within a sciences context.

2 Materials and Methods
An integrated approach is required to identify locations and conditions for competitive phosphorus recovery at global scale. This comprises of: 1. Identification of sites and quantities: Identifying where in the world phosphorus-laden wastewaters and agricultural areas concentrate themselves, and assessing the associated, approximate phosphorus production and 10 demand quantities.
2. Determination of node prices: Approximating the minimum production costs of different production sites, and maximum paying prices of varying crop sites respectively.
3. Modelling international trade in phosphorus, which involves: a. Determination of global market price: Determining an international, free-market price for 15 phosphorus as a function of P-quantities, prices, and distances between the different sites.
b. Trade flows corresponding to the market price: Visualizing a realistic network of phosphorus trade fluxes for different market prices.
Geographic Information System (GIS) tools (Q-GIS 2.14) (Quantum GIS Development Team, 2017) are used to pre-process spatial data for utilization by the trade network model built in Python 3.6. 20

Identification of Sites and Quantities
Using population density maps (Robinson et al., 2014), globally generalized phosphorus excretion rates (Barker, Hodges, & Walls, 2001;CBS, 2014;Gilmour, Blackwood, Comber, & Thornell, 2008), and phosphate mine production rates (USGS, 2002(USGS, , 2007, a crude, global mapping of phosphorus production sites is achieved. The sustainable phosphorus production potential is roughly approximated through globally generalized, maximum phosphorus throughput figures and population 25 density maps for humans, cows, pigs and chicken (see Table S1 in supplementary materials), which are related through the following formulation: constrained yield. These yields are determined through the evaporation-transpiration deficit approach (Steduto et al., 2012).
The adapted equation is described as followed (eq. 2): is a correction factor that accounts for the induced error by the 'annual approach' to the evapotranspiration-deficit equationscaling the maximum yield ratio globally to be no greater than 1. B is the evaporation-transpiration for optimal yield [mm a -1 km 2 ], which is assumed equal to the crop water requirement for optimal yield. The associated phosphorus requirement for 10 this yield is determined through a linear regression between yield and P-fertilizer application as described in eq. 3.
where D HI is the total P-demand [t ha -1 a -1 ]; MNO P is the crop specific P-demand for optimal yield [t ha

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The areas of major production and consumption densities are aggregated into nodes that are described by a coordinate position, a class (group: urban or livestock, or crop type), and a quantity of yearly phosphorus supply or demand. Nodes with a production of less than one kilo tonne per year for livestock, and less than 400 tonnes demand per year for urban/rural sites, are considered insignificant in the global context and are therefore excluded from further consideration. This constrains the total number of actors, reduces the complexity of the network, reduces the processing time required, and improves 25 visualization of the results. In the visualizations, the remaining nodes will be stylized to vary in size according to their annual P production and demand potentials [kt a -1 ] to make the significant actors more easily identifiable.

Determination of Node Prices
Whether trade is possible between a demand and a production node depends on the transportation and production costs of the production node and the maximum bid price of the demand node. The production cost varies depending on the recovery 30 technology, whose feasibility for implementation depends on wastewater composition and existing infrastructure.  (Schoumans et al., 2015). Although other struvite recovery technologies are available, this one was chosen given its commercially effective implementation in various different countries. The production cost for the highly developed group is reduced due to savings in uncontrolled struvite scaling 5 maintenance and sludge handling. Areas with intermediate urban access (40-90%) are assumed to be serviced by a simple, centralised wastewater treatment facility. The technology investment cost for these nodes are the same as for the the highly developed infrastructure group but excluding this time the sludge handling cost savings. Lastly, low urban access (<40%) is assumed to be indicative of low sanitary development and thus offers the flexibility to adopt more novel, less water dependant forms of sanitation. The technology applied for these areas are source separating-, dry composting toilets, where 10 urine and fecal compost are collected separately. The urine is collected by 40,000 litre tank trucks and processed at a centralized struvite precipitation facility. Fecal compost is collected, dried and processed into compost pellets at a central facility. For livestock farms this compost pelleting technology is also applied, but occurs on-site.
The recovery efficiency factors ( ,# ) in eq. 1 depend on the recovery technology applied for each organism group O 15 (humans, pigs, poultry, cows). A phosphorus recovery efficiency of 20% of the influent is taken for struvite crystallization in wastewater (Schoumans et al., 2015); while a 90% efficiency can easily be achieved when struvite precipitation is applied on source-separated urine (Wilsenach et al., 2007). An efficiency of 85% and 75% for cattle and swine, and poultry respectively is assumed for pelletization of composted livestock waste.

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For production nodes, a generalized struvite precipitation cost is determined by the following (eq. 4):

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The maximum price that demand nodes are willing to pay depends on the marginal value of phosphorus. This varies per crop type and can be described as followed (eq. 6): MNO P is the optimum fertilizer dosage rate (equal to total P-requirement for optimal, water constrained yield) [t ha -1 ]; and P is the ratio of fertilizer cost to total production costs [-], for crop n.
Lastly, the transportation costs are determined with as-the-crow-flies distances with the parameters given in Table S3 (see   15 Supplementary Materials) substituted into the following transport cost equation (eq. 7): where m T,P is the transportation cost from node i to node n [$ t -1 ]; T,P is the distance between node i and node n . i and k are the fractions of the total distance that is travelled over land and over sea. The model at present does not distinguish between the transportation over land and over 25 sea based on observed geography. Instead the model employs a cumulative probability curve that approximates the proportion of the total distance likely to have been traversed over water, i (eq. 8); and over land, k (eq. 9), where it is assumed that at least 15% of the total distance is always transversed over land.

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where µ and S are function shape constants of 500 and 100 [-], respectively.

Trade model
First, the model determines the optimal price for international phosphorus trade. Then, a trade network is created that identifies the nodes involved in trade and quantifies the amounts they exchange at the determined price. These two steps are taken for three different market scenarios: 1) Current market -mine supplied products only: The current phosphorus market is strongly rock-phosphate oriented.

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When the model runs the data for a 'current market' scenario, only rock phosphate products are available on the market.
2) Future market -both mine and recovered products: Recovered phosphorus is likely to become a more important product in the future market. When the model runs the data for a 'future market' scenario, it is assumed that both rock phosphate as well as recovered phosphorus products partake.
10 3) Far-Future market -only recovered products: In the far future market, most rock phosphate reserves will have been depleted. When the model runs the data for a 'far-future' scenario, it is assumed that rock phosphates no longer take part in the market which is then solely dominated by sustainable, recovered products.

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The global market price is determined as the price at which total quantity of phosphorus demanded is equal to the quantity supplied (i.e. the market for P is cleared; (Arrow and Debreu, 1954)). This is approximated as the point where global demand function for phosphorus intersects the global supply function. The demand function is the locus of the maximum prices at which demand nodes are willing and able to purchase phosphorus, and the supply function is the locus of minimum prices at which supply nodes can sell certain amounts of phosphorus without going out of business (i.e. without making a loss). The

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Supplementary Text provides an illustration of how market prices for the three scenarios are determined and how transportation costs complicate the determination of supply function and hence the determination of global market price for phosphorus.

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The following steps are taken in order to identify trade flows. Firstly, a list of all possible combinations of supply and demand nodes is created, which is passed through two 'filters' for a given 'hypothetical market' price. The first filter removes the pairs that can never trade with each other based on their combination of the minimum production costs, the maximum price boundary and transportation costs (which happens when productions costs are higher than the revenues that a supply node can generate by selling to a demand node). The second filter removes node pairs which cannot trade with each 30 other at a given 'hypothetical market' price imposed on the network. This occurs when the production cost is above the imposed market price.
In the model, phosphorus consumers will look for the cheapest suppliers. The matter becomes obscure here as, in reality, there are no cheaper or more expensive suppliers when there is a single, set market price (note that single set market price is different from the 'hypothetical market' price mentioned above). However, supply nodes that could supply at prices far 35 lower than the set market price (due to lower production costs) have a competitive advantage over those that cannot. The difference between these 'hypothetical market'-and actual market price shows how competitive a node is. If a node pair is able to trade at a much lower price than market price, then the model assumes that this trade occurs first. These nodes have the power to undercut their (more expensive) competitors and safeguard their own favourable trading position. This concept (i.e. the notion of hypothetical markets) is essentially used to identify most likely trade partners so that in the end a global trade network can be created that trades at one global price of recycled P.

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For different 'hypothetical market' prices, a list of trade partners is obtained by executing the trade at each price, and updating the list in terms of total phosphorus quantity (Q) demanded by demand node (D) number n, or supplied by supply node (S) number i ( Š P , and Š T , for demand and supply respectively). The amount traded ( (T,P) ) between each node pair is taken to be equal to the minimum of supply or demand as formulated below (eq. 10): The supply available and quantity demanded at each supply demand nodes are updated as follows (eq. 11),  also suits a validation purpose. When the model run for a mines-only (current market) scenario, it produces prices for mined P that may be validated against the currently recorded prices for mined P.

Identification of Sites and Quantities
The spatial distribution of phosphorus recovery potential [t km -2 a -1 ] from livestock and humans, as well the global 5 agricultural phosphorus demand, are presented in the Supplementary Figures (S1) at a resolution of 0.08 decimal degree in WGS84 projection. The associated data is summarized per continent in Table 1.
Some continents (i.e. South and North America) show significant disproportionalities in recoverable P from waste vs.
phosphorus demand for crop production (Table 1). (Virtual) phosphorus trade (e.g. soy bean products) can play an important 10 role in determining these continental budget surpluses and deficits. In the end, however, the global recovered phosphorus budget is only slightly off balance at 109% total production potential to demand. This global (9%) surplus suggests that there is an inherent overestimation of the phosphorus excretion rates or underestimation of the agricultural phosphorus demand, or that some degree of soil nutrient mining by the crops is considered in the phosphorus requirement values presented in 'Fertilizers and Their Use' (FAO & IFA, 2000). Another explanation for the this disproportion is that non-agricultural 15 consumers of phosphorus (e.g. medicine and detergents industries) are not considered as actors even though their consumed products are included in the wastewater discharge figures.
Unfortunately, however, it is not feasible to recover every ounce of phosphorus excreted, or to fertilize every crop patch everywhere. More realistically, recovery will be economically efficient in areas of high population or livestock density while 20 fertilisation will benefit mainly areas of intensive agriculture. A more realistic assessment of the contribution of recovered products to the global P demand can be made by disregarding production and demand areas of low P density, and selecting only for major production and demand nodes. The results below are discussed following this second more refined and conservative definition of production potential.

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The minimum production costs for the production nodes has been determined ( fig. 3). The low density of phosphorus (1% phosphorus by weight) results in relatively high production and transportation costs of compost pellets per tonne of phosphorus content. The added value that is not considered in the model is that compost pellets also upgrade the soil in providing substantial amounts of nitrogen and organic matter as well. The significant, general difference in the production cost of P from recycled sources with that of mines means that transportation costs, i.e. distance between trading nodes and 30 fuel costs, will have to play a critical role if sustainable trade in recycled P is to be feasible.

Trade model results
Based on the methodology presented in section 2, phosphorus quantities, costs, and the distances between the nodes are used to determine market prices at which trade may occur globally to evaluate the economically constrained recovery potential.   . 4). In addition to this, the model results for the other two (more hypothetical) modelling scenarios are included as well.

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The boxplots of calculated prices in fig. 4 show plausible ranges for P prices at which trade can occur at global scale. The whiskers on the grey boxes for the observed prices (grey) represent the range within which the price fluctuated during that year, the box itself shows the upper and lower quartiles for that data and the orange line indicates the median. Note that the price range estimated by the model closely follows the range of observed prices within that year for all the simulation years 10 (i.e. 2005, 2006, 2011 and 2015). The price ranges for simulation year 2015 specifically are presented in Table 2, where the minimum price represents the model determined lower boundary of the range, the maximum its upper boundary, and the optimum represents the most realistic price approximation as determined by the model.

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The network maps for the 'optimum' market prices from Table 2  Recovered phosphorus is considered as the only source in the third scenario and with this only 38% of the global agricultural 25 demand can be met. Because compost pellets, which due to their low P-density are far more expensive per tonne phosphorus than other products, the market prices for phosphorus are driven upwards in this scenario. This is a result of the model economics, where the different commodities (struvite vs. compost pellets) are treated as products acting on the same marketdiscriminated only based on their phosphorus content. When struvite producers observe consumers buying expensive compost pellets due to the depletion of struvite suppliers, the intial struvite sellers will adjust their prices upwards forcing 30 consumers to pay pay more for the same amount for P. The inverse would be true also if agricultural consumers observed cheaper trades occurring among other actors. They would then demand lower prices from their producer or switch producer all together, both resulting in lower market prices. the results may be directed to assumptions on technological potential of recovery. The technological potential is assessed through the dataset on urban population with access to improved sanitary facilities -where improved facilities are defined as those designed to hygienically separate excreta from human contact. These may include anything ranging from pit latrines to flushed piped systems. A country's scoring in this dataset is then used as an indicator for the state of sanitary development in that country. Struvite precipitation from digestor liquor is assumed to be the technology appropriate for the highest scoring 5 countries (>90% access). However, there is no guarantee that struvite precipitation from anaerobic digestor liquor is possible for nodes in these countries, seeing as by definition improved sanitary facilities 100% access may indicate that 100% of the urban population has access to a pit latrine. Even if information on the wastewater treatemeant infrastructure was known at all locations, then the phosphorus recovery efficiency from these rich sidestreams is still likely vary due to differences in phosphorus concentration of the influent. In summary, large uncertainties in the feasability to recover arise from the 10 generalised technological assessment carried out. The assumptions are partially justified by the global and explorative nature of this study on potentials.
Despite the lack of studies on the global economic potential for recovery to compare results with, the results on total potentials and struvite pricing are well aligned to those of other studies.    100% 100% 38% Table 2. Price ranges and amounts traded per scenario for 2015. The minimum price represents the lower boundary of the 10 determined market price range, the maximum its upper boundary, and the optimum represents the model approximated economic-optimal, most realistic, actual price. The 'maximum amount traded' shows how much percent of the total agricultural demand is accommodated in each supply scenario.