Phosphorus is a nutrient necessary for the development of crops and is thus
commonly applied as fertilizer to sustain agricultural production. It occurs
naturally, in indefinite quantities of uncertain quality in phosphate rock
formations, but also accumulates in urban and livestock wastewater wherefrom
it is often lost as a pollutant. Recovering phosphorus from wastewater,
however, is feasible through struvite crystallization technologies and has
the potential to reduce phosphorus pollution of the environment as well as
lower the agricultural demand for artificial P fertilizers. In this study, we
developed a model to assess the global potential of P fertilizer recovery
from wastewater and to visualize its trade at sub-national resolution.
Results show that humans discharge a maximum of 3.7 Mt P into wastewater,
thereby potentially satisfying 20 % of the global fertilizer demand.
Provided 2015 market dynamics, however, the model determines that only
4 % of this discharge is technologically and economically recoverable in
a market that offers cheap rock phosphate products also. The results of this
study demonstrate that in the current economic context, phosphorus recovery
from wastewater offers only a small contribution to resolving global
phosphorus issues. Nevertheless, this recovery offers many wastewater
treatment facilities the opportunity to contribute to creating sustainable
communities and protecting the environment locally, while reducing their own
operational costs.
Importance of phosphorus
Phosphorus (P) is an element necessary for the development of all living
beings as it forms an unsubstitutable, key structural component of DNA and
RNA. It is also a limiting nutrient, and therefore growth is often restricted
by the lack of naturally available P. While P-related malnutrition in humans
is uncommon, inhibited plant growth due to soil phosphorus deficiency is a
much more prevalent issue (MacDonald et al., 2011). For this reason, phosphorus is often applied to croplands in
the form of organic fertilizers or synthetically as single or triple
superphosphate, or mono-ammonium or di-ammonium phosphate (DAP). These
fertilizers are easy to transport and distribute over fields, while also
readily absorbed by plants. The most essential resource for the production of
artificial phosphorus fertilizers is phosphate rock.
The rates at which we exploit phosphate rock formations is out of proportion
to the rates at which they form – essentially classifying phosphate rock as
a non-renewable resource. Peak production of phosphate ore could occur as
early as 2030 (Cordell et al., 2009), with economically extractable P
resources becoming scarce or exhausted within the next 50 to 100 years (Smil,
2000; Steen, 1998; Van Vuuren et al., 2010). Other authors predict more
optimistically that reserves will last another 300–400 years (van
Kauwenbergh, 2010). After this depletion, it will likely be economically
infeasible to exploit the remaining ore as it will be too costly to process
due to its poor quality (i.e. low phosphorus and high heavy metal content).
Gradual depletion of economically extractable reserves will result in further
reduction in accessibility to fertilizer by smallholder and subsistence
farmers that comprise areas already struggling to cope with food shortages
(Pande and Savenije, 2016). Sub-Saharan Africa is one such region, as nearly
75 % of its agricultural soils are nutrient deficient, contributing
significantly to the crop yield gaps (Sanchez et al., 1997). The prospect of
phosphorus depletion ultimately threatens global food security, and regions
of poor soil nutrition levels are especially vulnerable to its effects.
The environment, humanity, and phosphorus
The introduction of intensified (P) fertilization during the Green Revolution
of the 1960s demonstrated P's significant potential to improve crop yields
but also the dangers it poses to the environment. Through seepage and runoff
processes (Bouwman et al., 2009), as well as the discharge of improperly
treated wastewater (Van Drecht et al., 2009; Morée et al., 2013),
phosphorus and other nutrient excesses come into contact with open surface
water. As a limiting nutrient, even the smallest quantity of P in water can
spark the growth of large algal blooms. These algal blooms have a detrimental
effect on aquatic ecosystems by causing the suffocation of aquatic life
through eutrophication, resulting in a loss of habitat and biodiversity (EPA,
2010). Such 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). If excess fertilization and water pollution 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 the environment while simultaneously
increasing phosphorus supply for food production.
There exist a broad range of sources that contribute the phosphorus loads in
wastewater. Excrements, detergents, care products, dishwashing liquids,
pharmaceuticals, and food preparation wastes are an example of some of the
most significant of these. Aside from this, there also exists a multitude of
technologically feasible phosphorus recovery options (Egle et al., 2016).
Unfortunately, these technologies are often deemed too costly to implement
and operate while their recovery efficiencies vary, among others, with local
wastewater composition and existing wastewater treatment infrastructure.
Adoption of these technologies is therefore often challenged by (perceived)
economic infeasibility or lacking economic incentives and social stigma. It
must be recognized, however, that 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) location-defined competitive advantage over the geographically
concentrated rock phosphate mines (Fig. 1), while temporally, the appeal for
recover will improve over time with the increasing price trends for
rock-based fertilizers (e.g. DAP) (Fig. 2)
Over the past 15 years
the phosphorus price of DAP has increased from 665 to 1552 USD t-1. In
that same period, the price has been as high as 5217 USD t-1 (2008)
and as low as 656 USD t-1 (2002) (IndexMundi, 2017).
.
Estimated global phosphorus reserve distribution. The vast majority
(73 %) of estimated natural reserves lie in Moroccan and west Saharan
territories (USGS, 2017).
Turning brown waste to green gold
To our knowledge, there exist no studies that evaluate the spatially dependent feasibility for
phosphorus recovery from wastewater, at sub-national resolution, in a global
and economically dynamic context. Insights provided by such a study,
however, could accelerate the efficient transitioning to a more sustainable
phosphorus fertilizer market by illustrating where recovery may economically
be most feasible. We therefore aim to determine the total phosphorus
recovery potential from wastewater, as well as the economic feasibility for
this recovery, in a global assessment. This is achieved by integrating
geospatial data, statistics, and findings from other studies into a model
that identifies and connects phosphorus recovery and demand sites based on
location, quantities, and prices.
Because of the wide array of pathways to phosphorus recovery, the subject of
this investigation is constrained to the recovery of phosphorus from urban
and livestock wastewater as a struvite and compost pellet fertilizer product
only. Phosphorus lost via other fluxes (e.g. municipal solid waste) are
therefore excluded from this assessment. The sole reason for focusing on
recovery through struvite crystallization is because of the fertilizer
potential of struvite as well as the current industrial-scale implementation
of the technology itself (Cornel and Schaum, 2009).
Nominal phosphate rock and DAP price trends (IndexMundi, 2017). The
rock phosphate and DAP price trend can be characterized as gradually
increasing and being vulnerable to market dynamics (i.e. the 2007 global
economic recession).
Materials and methods
The phosphorus cycle is delineated by a combination of both social and
physical attributes and as such demands a coupled human–water systems
perspective. A socio-hydrological approach is endeavoured as both these
attributes are here 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
wastewater at global scale is therefore interdisciplinary and extensive,
largely covering economics within a sciences context.
In general, the methodology can be summarized to consist of three phases,
which are also used to define the order of the materials and methods
section:
Identification of sites and quantities – identifying the locations of
wastewater accumulation sites and agricultural croplands and assessing the
potential associated phosphorus production and demand quantities;
Determination of node prices – approximating the minimum production costs of
recovering P fertilizers at the wastewater accumulation (recovery) sites, and
the maximum paying prices for P fertilizers at the agricultural (consumption)
sites;
Modelling international trade in phosphorus, involving
Determination of global market price, i.e. determining an
international, free-market price for phosphorus as a function of phosphorus
quantities and prices, as well as the distances between the different sites;
Visualizing trade flows, i.e. creating a realistic network of P-trade fluxes at subnational resolution.
The main tools employed in this investigation are Geographic Information
System (GIS) tools, used to prepare the spatial data (Q-GIS 2.14) (Quantum
GIS Development Team, 2017), and Python 3.6, used to build the trade network
model.
Identification of sites and quantities
Phosphorus trade occurs between production and demand sites, and therefore
two groups of actors are identified in the model: P producers and
P consumers. The first group, P producers, consists of three types of
actors:
Urban wastewater treatment facilities – nodes recovering P from domestic
wastewater (i.e. phosphorus excreted, used, and discharged by humans);
Livestock keepers – nodes recovering P from animal manure (i.e. manure and
liquid waste produced by farm cows, chicken, and swine, while stabled);
Phosphate mines – nodes extracting P from rock phosphate reserves.
The three actor types recover phosphorus in different forms, yet all act on
the same phosphorus market. The only objective characteristic that the model
will use to distinguish one type of product from another is the absolute
elemental P value of the product (i.e. US dollars per mass P;
USD mass-1 P). Since both mines and recovery sites have the same
purpose in the model (i.e. supplying phosphatic fertilizers), both node types
are grouped as “production nodes”.
Phosphorus production
The location and phosphorus production quantities of P-production nodes are
determined by integrating geospatial datasets with statistics and findings
from other studies. As phosphorus is not “produced” by organisms, but only
consumed and excreted, or used (i.e. detergents), we will refer to the annual
amount of phosphorus discharged in wastewater per individual as the
“phosphorus throughput rate” (kg head-1 a-1 P). Wastewater
phosphorus has variable sources ranging from human excrements to detergents,
toothpaste, dishwashing liquids, medicines, food preparation wastes, food
leftovers, etc. These sources are not considered individually. Instead we
assume that each individual person, globally, offers an equal contribution
to the phosphorus load in wastewater. We combine approximations for these
rates from different studies with population density maps for humans (CIESIN,
2016), cattle, swine, and poultry (Robinson et al., 2014), to determine the
spatial distribution of phosphorus excretion rates globally. This spatial
distribution of the mass phosphorus produced per unit area, per annum
(kg km-2 a-1) represents the phosphorus production density (a
map). Its determination per unit area on this map is summarized for as
follows (Eq. 1):
S=D⋅P⋅E,
where S is the maximum organic phosphorus production density
(kg km-2 a-1), D is the population density
(heads km-2), P is the phosphorus throughput rate
(kg head-1 a-1), and E is the estimated base recovery
efficiency (–). For humans, the phosphorus throughput rate (P) is assumed
to be globally homogeneous, fixed at 0.77 kg head-1 a-1. This is in
close relation to other published findings (0.77, Gilmour et al., 2008; 0.78,
CRC, 2005; 0.2–0.7, Mihelcic et al., 2011; 0.7, Smil, 2000). For livestock,
the throughput rate (P) is taken to be a function of slaughter weight
(FAOSTAT, 2018) following the methodology of Sheldrick et al. (2003). Manure recovery efficiencies (E) are taken as follows:
cattle (31 %), swine (80 %), poultry (77 %) (Sheldrick et al.,
2003). For humans, it is assumed that 100 % of the phosphorus discharged
as domestic wastewater reaches the treatment facility. The actual recovery
efficiencies will vary per recovery technology implemented at the wastewater
treatment plants (WWTPs) (Sect. 2.2.). The production density maps for
livestock and humans are presented in Fig. S1a and b in the Supplement. As a
final step, the phosphorus production densities per land area are converted
into point nodes using GIS tools (see Sect. 2.1.3). The spatial variation in
recovered P-production potential is therefore marked by global variation in
population and livestock densities.
The locations for the P-mining industry are, instead, geographically
concentrated. Data on P-production values and mine site locations are
acquired from a USGS (2002) dataset. This dataset is adjusted to match the
USGS-reported phosphate production estimates for different simulation years.
Phosphorus consumption
Similar to the phosphorus production density, the phosphorus demand density
map represents per unit area the yearly amount of phosphorus required by
agriculture (kg km-2 a-1). It is determined following a
comparable methodology to that of phosphorus production, where crop
densities, as approximated through crop harvested area maps (Monfreda et al.,
2008), are related to phosphorus-requirement rates (UNIDO and IFDC, 1998).
The crop phosphorus requirement rates (kg km-2 harvest-1) as
reported by UNIDO and IFDC (1998), however, are determined for optimal yield.
Provided that no farmer is going to fertilize for optimal yield when he or
she knows that these yields are unachievable provided persistent regional
water limitations, the actual P demand is proportionally reduced to the
potential water-constrained yield. This assessment is made for six
major crops: maize, wheat, rice, sorghum, soy bean, and potato. The
water-constrained yield is determined by adapting the
evaporation–transpiration deficit equation (Steduto et al., 2012) to the following (Eq. 2):
1-YaYm=Ky1-Ea⋅Tg365⋅AH⋅CEm,
where Ya is the actual yield (kg km-2 a-1), Ym
is the optimal yield (kg km-2 a-1), Ky is the crop
coefficient (–), Ea is the cumulative actual
evaporation–transpiration per year (mm a-1 Area-1),
Tg is the duration of the crop growing period
(days), AH is the fractional area
harvested (–), Em is the evaporation–transpiration for optimal yield
per harvest (mm a-1 km2), and C (–) is a correction factor. In
this investigation, Em is assumed to be equal to the crop water
requirement for optimal yield. Global approximations of Ky and Em
values were retrieved for different crops from FAO sources (2015), and
Ea was approximated from MODIS evapotranspiration products (NASA,
2005). A summary of the data used and their sources is presented in Table S2
of the Supplement.
Equation (2) is an adaptation of the original evaporation–transpiration
deficit equation. The original equation is designed for a single growing
period, yet much of the other input data is yearly. As the beginning and
ending of a crop's growing season will vary globally, it is not possible to
combine global yearly harvest area maps with monthly
evaporation data. Reformulation was therefore necessary to account for a
difference in temporal scales of the input data. For the adaptation, it is
assumed that of the yearly evaporation, an amount proportional to the
duration of a crops growing period is evaporated during the crop growing
season (Ea⋅Tg365). This value is then
further reduced by multiplication with the fractional crop harvested area
(AH) to account for evaporation from other land-cover types in the
area as well. Finally, as these simple manipulations introduce a significant
error, a correction factor (C) was added to globally scale potential yields
greater than optimum (i.e. > 1) back down to optimum (=1) and
to achieve a total, global phosphorus demand that approaches observed values
for these crops.
In this investigation, we assume no change in soil-stored phosphorus. The
yearly phosphorus demand per area therefore reflects only the crops' yearly
phosphorus uptake as a function of a crop's water-constrained yield and
harvested area. This phosphorus demand is described as a linear regression
between yield and P fertilizer requirement through Eq. (3):
DPT=YaYm⋅AH⋅Poptn,
where DPT is the calculated phosphorus demand density
(kg ha-1 a-1), Poptn is the crop specific (n) P
requirement for optimal yield (kg ha-1), and AH is the
crop harvested area (ha-1). The parameters per crop are again summarized
in Table S2. The six crops evaluated make up roughly 56 % of the global
demand (Heffer, 2009). To estimate the global demand quantity, inclusive of all crops, the value of each pixel on the map for the six crops is divided by 0.56 (56 %). Although this method introduces uncertainties to spatial demand distribution, it does allow for a more accurate estimate of the actual, total, global phosphorus demand quantities. The demand density maps for agriculture are presented in
Fig. S1c.
From raster to nodes
The areas of major production and consumption densities, determined in
Sects. 2.1.1 and 2.1.2, 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. Each node is systematically
positioned in the centre of a larger area of uninterrupted high phosphorus
production or demand density as determined by the raster map calculations
performed in steps 2.11 and 2.12. To avoid the aggregation of
administratively separate regions into a single node, the areas of continuous
high demand or production density
are separated by national boundaries for smaller countries, and first level
administrative borders (e.g. states and provinces) for large countries (e.g.
USA, India, Russia, Canada). Nodes with a production value of less than
3 kt yr-1 are considered insignificant in the global context and are
therefore excluded from further consideration in the economic analysis. This
constrains the total number of actors, reduces the complexity of the network,
decreases the processing time, and improves visualization of the results.
This preselection reduced the global P-recovery quantity by 15 %, while
reducing the number of actors by 76 %. The trade model thus only accounts
for trade from 24 % of all potential recovery sites, which, nevertheless,
represent 85 % of the global recovery potential.
Determination of node prices
Throughout this investigation, prices are presented as the price per tonne of phosphorus in each fertilizer product (USD t-1). This is because
struvite fertilizers (14 % P), conventional artificial fertilizers (DAP:
22 % P), and compost pellets (1 % P) are, although different in form
and P contents, acting on the same phosphorus market. In the model market,
they are discriminated only based on their total phosphorus content and, as
such, their values are determined based solely on the mass of P that they
contain.
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. Despite three
different producers having been identified (Sect. 2.1), each creating their own unique fertilizer
products, they are all subjected to the same economic constrictions. The
production cost of each producer is defined by (i) an investment cost for
infrastructure and (ii) a variable cost per mass P recovered. Additionally,
they are imposed with (iii) a transportation cost for selling. The sum of
these costs determines how attractive a producer is to the individual,
agricultural demand nodes.
Cost for recovery
The cost for recovery (i.e. production cost) varies depending on the
recovery technology, whose feasibility for implementation, in turn, depends
on wastewater composition and existing infrastructure. In this study,
municipal wastewater composition is assumed roughly globally homogenous.
The Sustainable Development Goals (SDG) dataset on percentage of urban population with access to sanitation is then used to
approximate how well developed the existing sanitary infrastructure is in
different parts of the world (WHO/UNICEF JMP, 2015). This estimation is then
used as an indicator for the feasibility to implement certain recovery
technologies. How the SDG dataset is used to interpret the feasibility for
implementation of specific recovery technologies is presented below.
A high national percentage of urban population with access to sanitation
(> 90 %) is likely to be indicative of highly developed
countries that observe stricter effluent standards and that therefore have,
or are working towards upgrading, conventional WWTPs for biological nutrient recovery (BNR) or chemical phosphorus removal.
The phosphorus recovery costs for these highly developed nodes are those
associated with the investment in a large
Ostara® Pearl Reactor for struvite
precipitation. The production cost for this highly developed group is reduced
by the savings in uncontrolled struvite scaling maintenance and sludge
handling costs that are associated with controlled struvite precipitation
(Shu et al., 2006). Although other struvite recovery technologies are
available, Ostara® Pearl Reactors were chosen
given their commercially effective implementation in various countries. There
exist other recovery technologies that allow for absolute greater recovery
amounts (see Egle et al., 2016), but few of these are potentially
economically competitive producers of pure P fertilizer products.
Most of the influent phosphorus at a WWTP accumulates at the centrifuge
(80 %–90 %), where it is separated into centrifuge cake (∼85 %) and liquor (∼15 %) (Jaffer et al., 2002). Struvite
crystallization from centrifuge liquor achieves efficiencies higher than
90 % (Jaffer et al., 2002; Münch and Barr, 2001). Therefore, assuming
some variability amongst WWTP, we make the optimistic estimate that
approximately 20 % of influent wastewater phosphorus may be recovered at
BNR WWTP through struvite precipitation.
Areas with intermediate urban access to sanitation (40 %–90 %) are
assumed to be serviced by simple, centralized wastewater treatment
facilities. The technology investment cost for these nodes are the same as
for the highly developed infrastructure group but excluding this time the
sludge handling cost savings. The recovery efficiency is again assumed to
equal 20 % of the influent P.
Low urban access to sanitation (< 40 %) is taken to be
indicative of low sanitary development and thus offers the flexibility to
adopt more novel, less water-dependent forms of sanitation. The technology
applied for these areas are source-separating and dry-composting toilets, where
urine and faecal compost are collected separately. The urine is collected by
40 000 L tank trucks and processed at a centralized struvite precipitation
facility. Faecal compost is collected, dried, and processed into compost
pellets, also at a central facility. A 90 % efficiency is easily achieved
when struvite is precipitated from source-separated urine (Wilsenach et al.,
2007). It is furthermore assumed that all of the faecal phosphorus is
retained in the composting, drying, and pelletization processes.
For livestock nodes the collected manure is
also composted, dried, and pelletized. As opposed to the source-separated faeces of dry composting toilets,
the pelletization of manure from livestock farms occurs not at a centralized
facility, but on-site. This is assumed feasible provided the high volumes of
manure produced by livestock in comparison to humans.
For all production nodes, a generalized phosphorus recovery cost can be
described as follows (Eq. 4):
fmini=R⋅SPT+BSPT-S+Tiρ
where fmini is the minimum price for phosphorus produced at
node i (USD t-1), R is the variable cost per tonne of P recovered
(i.e. the magnesium cost for struvite precipitation; the pelletization cost
for compost pelletization) (USD t-1 P), B fixed operational cost
(USD), and SPT is the total phosphorus recovery potential (t).
Furthermore, where relevant, S is the struvite scaling and sludge handling
cost savings per tonne of P recovered (USD t-1 P) (i.e. for BNR
plants), Ti is the intracity transport cost of collection
[USD t-1] (i.e. for urine and faeces from source-separating toilets),
and ρ is the proportion of phosphorus by weight of the transported
material (kg kg-1), which are 0.066 % and 0.46 % for urine and
dried, faecal, and toilet compost respectively (Vinnerås, 2001). The
annual fixed operational costs are taken as the annual costs minus the
resource costs as reported in the dissertation of Egle (2016), TU Wien. For
BNR plants, a struvite and sludge handling cost savings is included as 0.89 USD kg-1 of struvite removed (Shu et
al., 2006). This essentially allows BNR plants to supply struvite for free
(excluding transportation costs), which is a common occurrence for
struvite-precipitating BNR WWTPs in the Netherlands. The additional variable
cost for the dry-toilet solution is attributed to the collection of waste and
a pelletization cost of 30 USD t-1 compost (Hara, 2001). A
summary of these and other data values are presented in Tables S3, S4 and S5.
The intracity transport cost Ti is described as follows (Eq. 5):
Ti=DtaPd⋅ELt+LctV¯LtWLt,
where Dta is the average distance of a return journey for a
tanker truck in servicing the city per full load (km), Pd is the
price of diesel (USD L-1), ELt is the fuel efficiency of
the tanker truck (L km-1), Lct is the labour wage
(USD head-1), V‾Lt is the average velocity of the
truck in the city (km head-1), and WLt is the truck load weight
(t). The transportation cost from the processing facility to the consumer is
included in the final sale price (USD t-1) of the producer and is
therefore not accounted for yet at this stage.
Maximum buyer bid price
The maximum price that demand nodes are willing to purchase phosphorus at
depends on the marginal value of phosphorus. This varies per crop type and
can be described as follows (Eq. 6):
fmaxn=Yoptn⋅CanPoptn⋅Rn,
where fmaxn is the maximum price for phosphorus
(USD t-1), Yoptn is the optimal yield (t ha-1),
Can is the crop price in year a (USD t-1),
Poptn is the optimum fertilizer dosage rate (equal to total
P requirement for optimal, water constrained yield) (t ha-1), and
Rn is the ratio of fertilizer cost to total production costs (–), for
crop n.
Transportation cost
Lastly, the transportation costs between the production and demand sites are
determined with as-the-crow-flies distances and the parameters given
in Table S3 substituted into the following transport cost equation (Eq. 7):
Tci,n=Di,nFW⋅Pb⋅EW+CFV‾W⋅WW+FL⋅Pd⋅EL+LCV‾LWL,
where Tci,n is the transportation cost from node i to node n
(USD t-1), Di,n is the distance between node i and node n
(km), Pb is a bunker fuel price (shipping fuel) (USD t-1),
Pd is the price of diesel (USD L-1), EW is the fuel
efficiency of a container mainliner ship (t d-1), EL is the fuel
efficiency of a 2×30 tonne truck combination (L km-1),
CF is the fixed costs per ship (USD d-1), Lc is the
labour wage (USD head-1), V‾W is the average velocity of
the ship over water (km d-1), V‾L is the average
velocity of the truck over land (km head-1), WW is the full ship
weight (t), and WL is the full truck weight (t). FW and FL 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 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, FW (Eq. 8); and
over land, FL (Eq. 9). It is assumed that at least 15 % of the total
distance is always traversed over land.
8FW=851+e-D-μS,9FL=851+eD-μS+15,
where μ and S are function shape constants of 500 and 100 (–),
respectively.
Trade model
A model is constructed to determine (i) the market price for international
phosphorus trade and (ii) what amounts of phosphorus are being traded
between which nodes. Market prices emerge as a function of the individual
production–consumption prices and associated supply–demand quantities, which
will vary depending on which actors are included in the market scenario. The
phosphorus recovery potential is therefore assessed for three different
combinations of actors that represent, respectively, the current, potential
near-future, and potential far-future markets:
Current market – mine-supplied products only. The current phosphorus
market is strongly rock-phosphate oriented. When the model runs the data for
a “current market” scenario, only rock phosphate products are available on
the market. This scenario serves mostly a model validation purpose.
Future market – both mine and recovered products. Recovered phosphorus may
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.
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.
Determination of global market price
The global market price is determined as the price at which total quantity of
phosphorus demanded (sum of agricultural demand quantities) is equal to the
quantity supplied (sum of P-production quantities). It is approximated as the
point where global demand function (defined as cumulative phosphorus demand
vs. maximum buying price) intersects the global supply function (cumulative
phosphorus production vs. production price). 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 the minimum prices at which
supply nodes can sell certain amounts of phosphorus without going out of
business (i.e. without making a loss). Where the two curves intersect, the
market for P is cleared, providing a best approximation of the market price
(Arrow and Debreu, 1954). The Supplement text provides an illustration of
how market prices for the three scenarios are determined following this
principle, and how transportation costs complicate this method of price
determination.
Quantification of trade flows
The quantity of phosphorus traded for each scenario is determined following
a method of reduction and elimination. Firstly, a list of all possible
combinations of supply and demand nodes is created. Each combination of
supply and demand nodes is passed through two “filters” that removes some
pairs on the basis of simple conditional statements. This reduces the list down to
a selection of trading node pairs for each market scenario, for each year.
Before anything, the first filter in the model removes the pairs that can
never trade with each other based on their combination of the minimum
production costs, the maximum bidding price, and transportation costs
associated with the data of that year (e.g. fuel cost, wastewater flows). The second filter then removes node pairs which cannot trade with each
other at a given “hypothetical market” price imposed on the network. Either
the production cost may be above the imposed market price or the maximum bidding price may be below
it, implying that the nodes cannot trade. If both the
production cost is below the imposed market price and bidding price is above it, then the node pair is left in the list for that “theoretical” market
price. After these two filters, the list of potential trade partners is
reduced significantly and assessment may be made as to whether the saved
pairs actually trade and then with what quantities.
In the model, phosphorus consumers will look for the cheapest suppliers. The
matter becomes obscured here as, in reality, there are no cheaper or more
expensive suppliers for a single market price. Supply nodes that could,
however, supply at prices far lower than the set market price (due to lower
production costs) have a competitive advantage over those that cannot. At the
same time, agricultural demand nodes that are willing to pay much more than
the hypothetical market price have a greater financial capacity to outbid
those agricultural nodes whose maximum bid price is much closer to the
hypothetical market price. The difference between this market price and
(i) the production and transportation costs for production nodes and
(ii) maximum bid price for demand nodes shows how competitive a node pair
is. If a node is able to produce and transport at prices much lower
than market price, and if a demand node is able to pay much more
than the market price, then the model assumes that trade between these most
competitive nodes occurs first. Therefore, the list of remaining node pairs
is sorted according to the greatest difference between
production + transport cost, and maximum bid price, with market price.
For each of node pair lists for the different “hypothetical market” prices,
trade is executed and the list updated. After each trade, the list is updated
in terms of total phosphorus quantity (Q) demanded by demand node (D)
number n, or supplied by supply node (S) number i (DQn, and
SQi, for demand and supply respectively). The amount traded
(Q(i,n)) between each node pair is taken to be equal to the minimum of
supply or demand as formulated below (Eq. 10):
Q(i,n)=SQiifDQn>SQi;DQnifSQi>DQn.
The supply available and quantity demanded at each supply demand nodes are
updated as follows (Eq. 11),
SQi=0,DQ(new)n=DQ(original)n-Q(i,n)ifDQn>SQi;DQn=0,SQ(new)i=SQ(original)i-Q(i,n)ifSQi>DQn.
By Eq. (11), one of the nodes will have 0 production capacity or demand after
each trade, and so all possible trade combinations with that node are removed
from the list of possible trade partners remaining for that hypothetical
market price. The trade is recorded in a separate list of “successfully
executed trades”. This process is continued until the list is empty and thus
all feasible trade for that price has been conducted. Plotting the cumulative
phosphorus trade for each hypothetical market price simulated results in a
combined version of the supply and demand curves of Sect. 2.3.1, where the
apex coincides with the determined market price. The trade pairs saved in the
list of “successfully executed trades” are then connected through a series
of coloured vertices on maps to visualize the trade network.
Simulation years
The model is set up using human population density, livestock population
density, and croplands data for 2005. These data are adjusted using constant
growth rates when simulating other years. For example, in extrapolating the
human population density (CIESIN, 2016), and therefore phosphorus production
potential, from 2005 to another year, the models employs the following
equation:
Py=P2005(1+0.0122)y-2005,
where Py is the population density for an area in year y, P2005
is the population density for an area in 2005, and 0.0122 represents the 2005
to 2015 averaged, global human population growth rate of 1.22 % per year
(World Bank, 2017). The social phenomena of migration and urbanization are
not considered in the process. Also, contrasting growth rates of the
different areas of the world are lost, as by this definition the population
in each node, everywhere, grows equally. A summary of this yearly data and
its sources is presented in Table S4. This is followed up by Table S5, which
presents an overview of most fixed parameters.
The model script is accessible from the DANS data repository (Kok et al.,
2017).
Approximate continental phosphorus budgets
associated with maps. The “total” values represent an estimation of
recovering all phosphorus on the continent, while the “major nodes” values
represents that which can be recovered at sites of high potential only.
Livestock production Human production Agricultural demand TotalMajor nodesTotalMajor nodesTotalMajor nodes(Mt P)(Mt P)(Mt P)(Mt P)(Mt P)(Mt P)Asia5.85–2.29–9.49–North America3.10–0.31-3.30–Europe2.39–0.40–1.79–Africa1.72–0.53–2.51–South America3.89–0.22–2.17–Oceania0.05–0.00–0.00–Australia0.28–0.01–0.24–World17.1110.473.751.7319.5216.81ResultsPhosphorus recovery potentials excluding economic dynamics
The phosphorus recovery potential can be assessed in three different ways
depending on the constraints imposed. Firstly, and most simply, the sum of
all global production densities (Sect. 2.1.1) provides an indication of the
total potential of recovering all excreted phosphorus, everywhere,
without regard for any economic dynamics. For 2015, these are determined to
amount to 3.7 Mt P a-1 P for humans, and 17.39 Mt P a-1 for livestock.
Recovering all urban phosphorus discharged as wastewater can thus potentially
satisfy 20 % of the 19.1 Mt a-1 calculated agricultural demand.
Recovering all phosphorus in animal manure can potentially satisfy 90 %
of the total agricultural demand. The recycling of all animal manure and
human excreta confirms the large potential of recovery to substitute
phosphorus fertilizers (Bouwman et al., 2009).
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 efficient in areas of high population or
livestock density, while fertilization will mainly benefit areas of intensive
agriculture. By imposing a size constraint on the nodes determined from the
phosphorus density maps (Sect. 2.1.3), a more realistic assessment of the
contribution of recovered products to the global P demand can be made. For
2015, the phosphorus recovery potential from high density urban sites is
estimated at 1.73 Mt P a-1, which is 48 % of the original 3.7 Mt P a-1. This
percentage approaches the percentage of global
population urbanized (54 %; World Bank, 2018), partially confirming that
this constraint indeed excludes smaller rural areas, thereby limiting
recovery to the high-potential urban sites only. Recovery from livestock is
reduced from 17.39 to 8.8 Mt P a-1, now accounting only for the most
intensive animal husbandry sites in the world. With a demand of 16.81 Mt P a-1
from areas of intense agriculture, approximately 10 %
and 52 % of the demand may be satisfied by recovery from urban wastewater
and livestock, respectively (62 % total), while still excluding any
economic dimension.
The results of these optimistic recovery potentials are 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. The “virtual” phosphorus trade (e.g. soy bean
products) can play an important role in determining these continental budget
surpluses and deficits. In the end, however, the total phosphorus budget is
only slightly off balance at 109 % of the total production potential to
demand for the density maps. This global 9 % surplus suggests that there
is an inherent overestimation of the phosphorus production
(excretion) or underestimation of the demand (agriculture), 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
and IFA, 2000). Another explanation for this disproportionality is that
non-agricultural 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. The 9 % overestimation
could suggest a 9 % share of these actors in the global phosphorus
market. Including these actors would raise the demand and likely close the
deficit.
Minimum calculated production costs
per tonne of recycled P for supply nodes. Urb1-Str shows the prices for
struvite from WWTP in countries with highly developed sanitation systems
(BNR), where the struvite is offered for free (excluding transport costs)
because of the maintenance and sludge handling savings by controlled struvite
precipitation, Urb2-Str is from nations with slightly less developed
sanitation systems, Urb3-Str shows source-separated urine collection and
struvite precipitation in nations with underdeveloped sanitation systems,
Urb3-Pellets is the price per tonne of P (0.1 %) in urban compost
pellets, and Livestock shows the price per tonne of P in livestock pellets
(0.1 % P).
Phosphorus recovery potentials including economic dynamics
Phosphorus quantities, prices, and the distances between the nodes are used
to determine market prices at which phosphorus trade may occur globally.
This is used to assess the more realistic, spatially dependent, and
economically constrained phosphorus recovery potential. The production
costs for phosphorus for the different actors are summarized in Fig. 3.
In a 2015 market where sustainable products compete with rock-based
fertilizers (scenario 2), the model determines that approximately 0.15 Mt
can be economically recovered, thereby satisfying 0.8 % of total
agricultural demand. In a market without rock-based fertilizer products,
approximately 7.92 Mt can be economically recovered, satisfying 41 % of
the total agricultural demand. Due to differences in total supply and demand
amongst the scenarios, both the market prices and total quantities traded
will vary. Optimal trade in a near-future scenario of recovered and mined
phosphorus products (scenario 2) occurs at a market price of 2039 USD t-1. For a market of only recovered products (scenario 3), where
there exists a strong deficit in phosphorus supply for agriculture, optimal
trade occurs at much higher prices of 5700 USD t-1. The model price
and trade determinations for 2015 and other years are summarized in Table 2.
Price ranges and phosphorus quantities traded per scenario for all simulation years.
Scenario 1Scenario 2Scenario 3Units2005Maximum traded15.0115.015.59(Mt P)Sustainably traded00.125.59(Mt P)Percentage of total demand met10010037(–)Percentage of total demand met sustainably00.8037(–)Optimal price127611894000(USD t-1 P)Minimum price for 90 % of maximum trade100010003700(USD t-1 P)Maximum price for 90 % of maximum trade21 00021004000(USD t-1 P)2006Maximum traded15.4615.465.89(Mt P)Sustainably traded00.125.89(Mt P)Percentage of total demand met10010038(–)Percentage of total demand met sustainably00.7838(–)Optimal price155914604300(USD t-1 P)Minimum price for 90 % of maximum trade110011003800(USD t-1 P)Maximum price for 90 % of maximum trade230023004300(USD t-1 P)2007Maximum traded15.9115.916.59(Mt P)Sustainably traded00.126.59(Mt P)Percentage of total demand met10010041(–)Percentage of total demand met sustainably00.7541(–)Optimal price178016745500(USD t-1 P)Minimum price for 90 % of maximum trade150015004000(USD t-1 P)Maximum price for 90 % of maximum trade290029005500(USD t-1 P)2008Maximum traded10.0310.037.12(Mt P)Sustainably traded06.917.12(Mt P)Percentage of total demand met62.6962.6945(–)Percentage of total demand met sustainably043.1945(–)Optimal price455144456900(USD t-1 P)Minimum price for 90 % of maximum trade470035003500(USD t-1 P)Maximum price for 90 % of maximum trade690069006900(USD t-1 P)2009Maximum traded16.8116.816.82(Mt P)Sustainably traded00.166.82(Mt P)Percentage of total demand met100.00100.0041(–)Percentage of total demand met sustainably00.9541(–)Optimal price235522995500(USD t-1 P)Minimum price for 90 % of maximum trade210021004000(USD t-1 P)Maximum price for 90 % of maximum trade290029005500(USD t-1 P)2010Maximum traded17.2617.267.13(Mt P)Sustainably traded00.167.12(Mt P)Percentage of total demand met100.00100.0041(–)Percentage of total demand met sustainably00.9341(–)Optimal price253424446618(USD t-1 P)Minimum price for 90 % of maximum trade220022003400(USD t-1 P)Maximum price for 90 % of maximum trade340034006600(USD t-1 P)2011Maximum traded17.7117.718.16(Mt P)Sustainably traded00.68.16(Mt P)Percentage of total demand met100.00100.0046(–)Percentage of total demand met sustainably03.3946(–)Optimal price348133748000(USD t-1 P)Minimum price for 90 % of maximum trade310031003600(USD t-1 P)Maximum price for 90 % of maximum trade420042008000(USD t-1 P)
Continued.
Scenario 1Scenario 2Scenario 3Units2012Maximum traded18.1418.167.9(Mt P)Sustainably traded00.597.12(Mt P)Percentage of total demand met99.89100.0044(–)Percentage of total demand met sustainably03.2544(–)Optimal price348433487596(USD t-1 P)Minimum price for 90 % of maximum trade310030003500(USD t-1 P)Maximum price for 90 % of maximum trade390039007600(USD t-1 P)2013Maximum traded18.6118.618.01(Mt P)Sustainably traded00.28.01(Mt P)Percentage of total demand met100.00100.0043(–)Percentage of total demand met sustainably01.0743(–)Optimal price294328407389(USD t-1 P)Minimum price for 90 % of maximum trade250025003500(USD t-1 P)Maximum price for 90 % of maximum trade380038007400(USD t-1 P)2014Maximum traded19.0619.068(Mt P)Sustainably traded00.158(Mt P)Percentage of total demand met100.00100.0042(–)Percentage of total demand met sustainably00.7942(–)Optimal price246923657000(USD t-1 P)Minimum price for 90 % of maximum trade200020003500(USD t-1 P)Maximum price for 90 % of maximum trade370037007000(USD t-1 P)2015Maximum traded19.5119.517.92(Mt P)Sustainably traded00.157.92(Mt P)Percentage of total demand met100.00100.0041(–)Percentage of total demand met sustainably00.7741(–)Optimal price215520395700(USD t-1 P)Minimum price for 90 % of maximum trade190019004000(USD t-1 P)Maximum price for 90 % of maximum trade300030005700(USD t-1 P)
Associated with these quantities and prices are network trade maps. Although
easily created for every year and for every price, only those relating to
scenario two and three, for 2015, are presented in Figs. 5 and 6,
respectively. The high recovery potential and close proximity of recovery
nodes to agricultural demand nodes makes phosphorus recovery in Asia
particularly competitive in both scenarios. The struvite scaling maintenance
and sludge handling cost savings in developed areas (with BNR-equipped
WWTPs) also results in competitive trade in Europe and the United States.
Because compost pellets, which due to their low P density are far more
expensive per tonne of phosphorus than other products, the market prices for
phosphorus are driven upwards in the third 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 market – discriminated
only based on their phosphorus content. When struvite producers observe
consumers buying the relatively expensive (USD per amount of P) compost
pellets due to the depletion of struvite suppliers, the initial struvite
sellers will adjust their prices upwards, forcing consumers to pay more for
the same amount of P simply because they can (they are profit driven). 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, resulting in lower market prices.
Model validation and sensitivity assessment
Due to the hypothetical nature of global phosphorus recovery from wastewater,
model performance can only be assessed by comparing the quantities and prices
produced by the model for the “mines-only scenario” (scenario 1) with
observed and recorded DAP price statistics. These prices, along with the
results for the other two (more hypothetical) modelling scenarios, are
presented in Fig. 4. The graph of Fig. 4 shows that the model is able to
adequately reproduce DAP price trends. Only the price estimates of 2009,
2012, and 2013 are significantly different to those recorded, as they are 37 %,
29 %, and 31 % higher respectively. This may be a delayed response to
price stabilization after the inflations of 2008 and 2011. On average, over
all the years, the model predictions show a 17 % difference with the
observed prices, with a maximum difference of 37 % in 2009 and a minimum
difference of 3 % for 2008 and 2015.
Plausible phosphorus price ranges at which trade can occur at
global scale for different years: observed prices (grey) versus modelled
scenarios (Sc. 1, pink; Sc. 2, blue; Sc. 3, green). The ends of the whiskers
on the grey boxes for the observed prices represent the maximum and minimum
prices for DAP that year, the box itself shows the upper and lower quartiles
for that data, and the orange line indicates the median. For the modelled
scenario the whisker-ends show the maximum and minimum prices as
approximated by the model, the box indicates the most likely price range,
and the orange line marks the most probable price given supply–demand
ratios. Noticeable is that the model price determinations for the current
mines-only scenario are in close proximity with observed price ranges.
Scenario 2 and 3 are hypothetical scenarios and therefore do not have a
realistic counterpart dataset that can be used for comparison. Nevertheless,
they show predictable and realistic behaviour.
Phosphorus trade network for trade in
both conventional and recycled P (scenario 2) but showing only sustainable
trade flows. Optimal trade occurs at a phosphorus market price of
2039 USD t-1 with 16.81 Mt being traded in total, of which 0.15 Mt
is traded sustainably (0.8 % of total demand).
Phosphorus trade network for trade in recycled P only (scenario 3)
at determined phosphorus market prices of 5700 USD t-1 with 7.92 Mt
being traded. All of this trade is sustainable but is only able to
accommodate 41 % of demand.
Model sensitivity is determined through the one-at-a-time (OAT)
method. Following this technique, the value of one parameter is adjusted and
the model is re-run to evaluate how significant the change in model output is
as a result of the parameter change. For each of the individual 31 parameters
or input data, we assess how sensitive the model is to a -50 % to
+50 % change in original value. We assess the impact of this change for
the model-determined (i) total phosphorus trade, (ii) sustainable phosphorus
trade, and (iii) optimal market price, for a 2015 market of both recovered and
mined products.
The sensitivity analysis shows variable sensitivity to changes in parameter
(Table S7 and Fig. S3). Provided that each
different year has different input data, these sensitivities will likely
also vary depending on the simulation year. For example, in a year where
rock phosphate exploitation costs are high (e.g. 2008), the market may be
much more dependent on recovered products than in other years. The total
phosphorus trade will then likely fluctuate much more with the price of,
for example, magnesium chloride, than determined in the sensitivity analysis
conducted for 2005.
There is a high sensitivity of the optimal price and quantity of sustainable
trade with variations in transport parameters related to overseas transport
(Table S7). By far the most sensitive parameter is a ship's carry load. A
50 % decrease therein, for example, may result in up to 85 % increase
in phosphorus prices. The second most sensitive is a ships velocity, where a
50 % decrease results in 42 % higher prices. Unfortunately, there is
also high uncertainty around these parameters as there are
innumerable shipping options (ship loads, ship fuel efficiencies, costs, etc.) for
the transport of phosphorus overseas. Oppositely, the model results are shown to
be insensitive to changes in recovery parameters, suggesting that at global
scale the transportation cost of products have a much greater weight in
determining the feasibility for trade than the production costs do. Also, the
relatively small contribution of urban recovered P (maximum 10 % of
global P demand, Sect. 3.1) may be a reason why the global P market prices
are so insensitive to small changes in the parameters that determine the
P-recovery cost.
Discussion
Many generalizations, assumptions, and simplifications have been made in
this study. The lack of consideration for immediate on-site recycling,
transatlantic movement, assumptions of free trade, and other economic
simplifications are among those possibly contributing to errors in market
price determination and patterns of trade flow. Furthermore, external costs
such as those associated with environmental impacts (e.g. CO2 emissions
and energy requirements) for the various fertilizer production/recovery
chains has been neglected to keep the economic analysis simple. Including
these costs would likely significantly improve the favourability of
phosphorus recovery from wastewater considering the reduced transportation
distances and relatively CO2-neutral recovery technologies
(Molinos-Senante et al., 2011). Many of the assumptions of this
study are partially justified by the global and explorative nature of this
investigation on potentials. An overview of all significant assumptions and
their possible implications are presented in Table 3.
An overview of the assumptions made in this
study and their possible implications on the results.
MethodsAssumptionIn realityImplicationProduction and demand estimatesCrop phosphorus requirement only varies with crop type and water-constrained yield.A particular crop yield may be constrained by other factors than water availability (e.g. soil acidity levels, micronutrient levels, management practices, etc.), also influencing the actual phosphorus demand. Crop phosphorus requirements also depend on soil-dynamic processes determining leaching rates and sorption.The phosphorus demand quantities will be spatially more variable and are likely overestimated.Domestic wastewater composition is globally homogeneous, and its quantity only varies with population density.Wastewater composition and amount vary amongst different populations. Both quantity and quality factors of wastewater depend on the amount and nature of connected industries and lifestyle characteristics of the people connected (e.g. diets and detergents use), the regional climate, and whether or not the sewerage network is a combined or separate system, etc.Recovery efficiencies will likely be lower, provided the current assumption of western lifestyles, globally.We can approximate the type of wastewater treatment practiced in a country based on data that show the percentage of urban population that have access to sanitary facilities.The type of wastewater treatment at a node varies with many different socio-economic (and natural) parameters. It can hardly be approximated by using a single dataset.Even in the near future, few people in developing countries will have access to sanitation resulting in an even lower recovery efficiency of phosphorus from developing regions than is currently predicted.Phosphorus recovery efficiency is determined solely by the recovery technology.Phosphorus recovery efficiency varies not just per technology, but also with the wastewater composition.Node-specific phosphorus production potentials can potentially be higher or lower than is currently determined.Phosphorus throughput per individual is globally homogeneous.Phosphorus excretion rates vary enormously depending on age, diet, and gender of the individual. Phosphorus discharge relates also to population lifestyles which determine the diet (as described above) but also detergent use.Node-specific phosphorus production potential is lower in developing countries than is currently determined.Assume container ship as sea transport mode.Bulk trade occurs in bulk carriers. Depending on how finished the product is (e.g. bagged and sealed as a ready-to-apply fertilizer), it may also be transported by containerships.The sea transport cost of P can be highly variable.
Continued.
MethodsAssumptionIn realityImplicationProduction and demand estimatesFertilizer maximum bid price depends on crop.Farmers growing the same crop, requiring the same amount of fertilizer, may have different maximum prices for P fertilizers depending on other factors (e.g. experience, subsidies, crop quality, and client for which the crop is grown, hence different crop values).Recovery feasibility will be higher or lower depending on the profitability and experience in agriculture in an area.Modelling tradeAll phosphorus goes to the international fertilizer market.Most phosphorus is recycled locally, applied on nearby agricultural soils directly as manure or as treated wastewater sludge (ash). Some is distributed amongst pharmaceutical and detergent industries.Phosphorus recovery potentials are underestimated given the disregard for immediate local use. Phosphorus production from mines is overestimated, as not all is used for fertilizer production.Free tradeTrade does not stand separate from politics. Embargos, trade sanctions, or trade tariffs can influence the pattern and amount of global phosphorus trade.Trade patterns can look different depending on international politics.Non-preferential tradeTrade is not purely rational. Some countries or actors may be more or less likely to trade with each other depending on historical and current relations.Trade patterns can look different depending on international relations.Two actor tradesPhosphorus extraction from phosphate rock and its processing into artificial fertilizers may not occur at the same site, nor by the same actor. Often it involves many more parties. One for exploitation, for manufactory, for logistics, etc.Trade patterns are simplified, showing only the path from site of initial production to site of final demand.Transportation distances are calculated as straight lines as opposed to following existing infrastructure.Phosphorus transport in reality follows existing shipping routes and road infrastructure.The model likely underestimates the transportation cost of moving phosphorus from supply to demand areas. However, it does so consistently for both recovered as well as mined products. This nevertheless reduces recovery potential estimates.
Continued.
MethodsAssumptionIn RealityImplicationModelling tradeNo transatlantic trade due to planar projection of earth.International trade is not restricted by cartographic boundaries.Few implications for the simulated years as trade in phosphorus between the Americas and Asia is unlikely to occur due to the greater distances and relatively balanced continental phosphorus budget of North America.Near-future and far-future scenarios do not consider development of technology.Existing technologies are likely to become cheaper and more efficient in the future, while new technologies may also be developed.Recovery will rates will likely be higher in the future, thereby also reducing the price of phosphorus. However, provided the uncertainty around making technological development predictions, we decided to exclude this factor from our analysis.
The lack of studies on the global economic potentials for recovery
and phosphorus trade patterns at subnational resolution inhibits comparison
of this study's primary results. The model results on total potentials and struvite pricing, however, are well aligned to those of other
studies. Above we determined that in 2015, 3.7 Mt a-1 of phosphorus
is discharged into wastewater, satisfying 20 % of the reported 18.52 Mt a-1
agricultural demand (Heffer and Prud'homme, 2016) and
19 % of determined 19.51 Mt a-1 agricultural demand.
Smil (2000) found 3 Mt a-1 to be potentially
recoverable, which would account for 20 %–25 % of the global agricultural
demand. Extrapolating Smil's (2000) figure proportionally with a population
growth of 1.22 % per year would result in a potential urban production of
3.6 Mt a-1 in 2015, a less than 3 % difference from the model-determined potential.
Mihelcic et al. (2011), through a study on diets and phosphorus excretion,
concludes that the phosphorus excretion rates per individual can vary as much
as from 0.18 kg P a-1 in the Democratic People's Republic of Congo
to 0.73 kg P a-1 in Israel. This
confirms that our “Western” approximation for phosphorus excretion of
0.77 kg P a-1 is on the high end globally. For 2009, nonetheless,
Mihelcic et al. (2011) determines that 3.4 Mt P a-1 of human waste
produced could account for 22 % of the 15 Mt P a-1 of global
phosphorus demand.
Van Drecht et al. (2009) considers variability in
access to sanitation, livings standards, and other population-relevant
variables to determine a discharge of 1.3–3.1 Mt P a-1 to
wastewater systems in the period 2000 to 2050. Similarly,
Morée et al. (2013) determines a P discharge
of 0.2 to 1.0 Mt P a-1 from urban wastewater over the period 1950 to
2000. These are lower estimates than the ones produced in this study,
suggesting that our assumptions of (i) everyone being connected to some form
of sanitary infrastructure and (ii) everyone discharging phosphorus according
to western throughput figures is unrealistically optimistic even for near-future scenarios. However, Morée et al. (2013) also determines that, over that same period, 0.08 Mt P a-1
was recycled back to agriculture, which is lower, but in a similar range to our
estimated economic recovery potential of 0.13 Mt P a-1 for 2015.
Bouwman et al. (2013),
also using slaughter weights, determined that 17 Mt P a-1 is
produced by livestock in 2000, closely matching the model-determined 17.11 Mt a-1.
Bouwman et al. (2011) notes
the potential for recovery in industrialized countries, which is in line with
the general trade patterns presented in Fig. 5.
Koppelaar and Weikard (2013) estimate 4.2 Mt P a-1 domestic
discharge, which is 25 % of their 16.7 Mt P a-1 agricultural
demand. They also estimated total domestic animal manure production of
28.3 Mt P a-1. This is distinctly higher than this study's
17.11 Mt P a-1 from livestock. This is likely in part due to the
fact that they account for a much larger variety of livestock types than the
cattle, poultry, and swine considered in this study.
The model estimates struvite production costs ranging from 0 to 670 USD t-1, variable with the nature and location of the recovery site
(Fig. 3; converted prices
Prices in this study are mostly
represented as US dollars per tonne of phosphorus. For comparison purposes, we
can convert these to DAP prices through multiplication with DAP's P density
(24 %), or to struvite prices through multiplication with struvite's P
density (14 %).
). Phosphorus market prices for a market that
also offers rock phosphate products range from 273 to 391 USD t-1
over the different years (Fig. 4; converted prices). The supply deficit
resulting from a scenario without rock phosphate products, drives these sale
prices upwards to a range of 570 to 955 USD t-1. These costs and
prices, like the recovery potentials, are difficult to compare provided no
found study has evaluated the prices for economic recovery potential at
global scale. Instead, there exist case studies on the feasibility for
phosphorus recovery at specific sites.
Ueno and Fujii (2001) observed that struvite
obtained from wastewater in Japan is sold to fertilizer companies at rates of
300 USD t-1. A market study by Münch and Barr (2001)
revealed that struvite can be sold in Australia for between 220 and 370 USD t-1.
Shu et al. (2006), however, estimated that
the market price of struvite is around 550 USD t-1. Based on
fertilizer market estimation, Dockhorn (2009) estimated far
higher prices than those mentioned before, and values recovered struvite at
900 USD t-1. Dockhorn's high recovered product prices are approached
in the model by the 2015 struvite market price, 955 USD t-1, for a
market scenario with no rock phosphate competition and a severe P supply
deficit. It appears that the model-determined price range for global struvite
production covers the spectrum of different production costs, as determined in
various different other studies.
In this investigation we consider struvite precipitation as the primary means
to recover phosphorus from wastewater. In reality, there are many other
recovery technologies that also offer high recovery rates (Cordell et al.,
2011; Egle et al., 2016). It would be an interesting follow-up study to adapt
and run the model for different phosphorus recovery technologies and
visualize changes in trade patterns for the different phosphorus products.
Conclusion
Despite the simplifying assumptions, the model developed in this study
generates realistic trade networks for different phosphorus supply
scenarios, for different prices, at a subnational resolution. However, the
credibility of model outputs is only supported by an accurate simulation of
DAP prices because data and/or other studies on the purely hypothetical
nature of global trade in sustainably recovered P are lacking.
Nevertheless, the model sets a basis that provides some general indication
of the spatially dependent recovery feasibility of phosphorus from
wastewater. It is furthermore able to provide this indication for
potentially any recovery technology for which there exists adequate economic
data.
Model results reveal a relatively minor potential of economically
profitable struvite fertilizer production from wastewater. This recovery
thus appears to offer a limited contribution to resolving the global
phosphorus issues of the 21st century. Nevertheless, at a more local
scale , this recovery offers wastewater treatment plants the opportunity to
contribute to creating sustainable communities and protecting the
environment, while reducing their own operational cost. This potential
exists foremost in the highly populated cities of developed countries.
Although recognizing that there is no single solution to solving phosphorus
pollution and insecurity issues (Cordell and White, 2011),
recovering phosphorus from all waste sources may come to provide a greater
contribution as populations grow and urbanize, technologies develop, and the
economically extractable phosphorus reserves deplete. For this reason, it is
essential to determine how the widespread implementation of recovery
technologies impacts phosphorus market dynamics. Only then can we stimulate
and regulate its recovery in such a way that maximum benefits are achieved
for both the environment and the urban community, as well as the livestock
and agricultural sectors.
Data availability
The model script and a selection of the final results has
been made publically accessible in the DANS-Easy data repository under
10.17026/dans-286-6b5v (Kok, 2017).
The supplement related to this article is available online at: https://doi.org/10.5194/hess-22-5781-2018-supplement.
Author contributions
All of the authors helped to conceive
and design the analysis. DJDK and SP preformed the analysis and wrote the
paper. JBvL, ARCO, HS and SU contributed to the writing of the paper. JBvL
additionally contributed data and aided in the analysis.
Competing interests
The authors declare that they have no conflict of
interest. Edited by: Christian
Stamm Reviewed by: Mesfin Mergia Mekonnen, Kai Udert,
Zengwei Yuan, and Ivana Logar
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