Post-Vehicle-Application Lithium – Ion Battery Remanufacturing , Repurposing and Recycling Capacity : Modeling and Analysis

Purpose: A mathematical model is used to help determine the manufacturing capacity needed to support post-vehicle-application remanufacturing, repurposing, and recycling of lithium-ion batteries over time. Simulation is used in solving the model to estimate capacity in kWh. Lithium-ion batteries that are commonly used in the electrification of vehicles cannot be simply discarded post-vehicle-application due to the materials of which they are composed. Eventually, each will fail to hold a charge and will need to be recycled. Remanufacturing, allowing a battery to return to a vehicle application, and repurposing, transforming a battery for use in a nonvehicle application, postpone recycling and increase value. The mathematical model and its solution using simulation test the hypothesis that the capacity needed for remanufacturing, repurposing, and recycling as well as new battery production is a function of a single parameter: the percent of post-vehicle-application batteries that are remanufactured. Design/methodology/approach: Equations in the mathematical model represent the capacity needed for remanufacturing, repurposing, and recycling as well as new battery production as dependent variables. Independent variables are exogenous quantities as such as the demand for electrified vehicles of all types, physical properties of batteries such as their


Introduction
Post-vehicle-application lithium-ion batteries can no longer hold a sufficient charge to meet regulatory standards for use in the power-train of moving vehicles such as hybrid electric cars and buses.A lithium-ion battery is a collection of lithium-ion cells that work together through electrical wiring and a control board.
Foster, Isely, Standridge and Hasan (2014) as well as Standridge and Corneal (2014) discuss three possible ways of further using such batteries as well as providing an extensive literature review: • Remanufacturing for intended reuse in vehicles.Replacement of damaged cells within the battery shows promises as an effective remanufacturing strategy.
• Repurposing by reengineering a battery for a non-vehicle, stationary storage application.This usually means reconfiguring the cells comprising the battery and developing a different control system as well as repairing any damage as in remanufacturing.
• Recycling that is disassembling each cell in the battery and safely extracting the precious metals, chemicals and other bi-products, which are sold on the commodities market or re-introduced into a battery manufacturing process.Recycling is limited to cells that are no longer suitable for remanufacturing or repurposing applications.
Eventually, each cell will need to be recycled.Furthermore, Foster et al. (2014) present a simple model which transforms existing forecasts of the number of electric vehicles and plug-in hybrid electric vehicles into the number of postvehicle-application batteries.In addition, these authors present cost-benefit analyzes showing that remanufacturing is more economical than repurposing as well as showing that recycling is not economical.This leads to the conclusion that remanufacturing, repurposing, and recycling must be integrated into a single process for handling post-vehicle-application batteries and that the cost of recycling must be borne by remanufacturing and repurposing applications.
The work of these authors is extended to a full mathematical model to help plan remanufacturing, repurposing, and recycling production capacity, as well as new battery production capacity, given any forecast of the number of electric vehicles and plug-in hybrid electric vehicles.The equations comprising the model are evaluated using simulation.Results estimate the needed capacity over time for various values of a single parameter: the percent of post-vehicle-application batteries that are remanufactured.Foster et al. (2014) as well as Standridge and Corneal (2014) present a comprehensive literature review concerning the processing of post-vehicle-application lithium-ion batteries.

Literature Review
Thus, the following discussion is limited to the literature used in developing the capacity planning mathematical model and specifically the development of the forecast of the vehicleapplication lithium-ion battery volume that is input to the model.Baum (2013) identifies multiple types of hybrid electric vehicles: micro hybrids, mild hybrids, full hybrids, plug-in electric vehicles, and electric vehicles.Micro hybrids offer only start/stop technology that turns the engine off when the car is stopped and restarts the engine when the gas pedal is again depressed.Full hybrids provide both gasoline and electrical systems to power a vehicle.Mild hybrids have technology between that in micro and full hybrids.
In addition, Baum provides a forecast of the number of vehicles in each category, except for micro-hybrids, produced in each year from 2013 through 2017 based on actual production data from 2009 through 2012.Furthermore, the Center for Automotive Research ( 2009) produced a forecasting model for the total number of electric vehicles of all types.Thus, the number of micro-hybrids can be computed by subtraction using both forecasts.
Hybrid vehicle batteries will have different energy capacities measured in watt-hours.Thus, the capacity planning model will use watt-hours as measure of capacity instead of the number of batteries.Pesaran (2011) gives a range for the energy of each type of electric vehicle which can used to convert number of vehicles into energy expressed in watt-hours.
Battery life impacts the number of post-vehicle-application lithium-ion batteries.Information provided by Smith, Earleywine, Wood and Pesaran (2011) is used to estimate the distribution of battery life for use in the capacity planning model.The distribution is generated by computing battery life for various combinations of daily driving distances and charge/discharge history.Results are given in the form of a histogram.
In general forecasting has to do with using a mathematical model to extrapolate historical data forward in time to make predictions regarding future values of the same quantities.In this case, producing a capacity forecast requires extending in time, combining, and rectifying data from the multiple sources identified above for input to the mathematical model.Caution is in order in drawing conclusions from a forecast based on such data.Primarily there is little experience with customer demand for all types of electrified vehicles as well as the life span, post-vehicle-application potential, and energy range of vehicle-application lithium ion batteries.
Thus, there is a great deal of uncertainty associated with the values of the model input data which implies that there is a great deal of uncertainty associated with the capacity values produced by simulating the model.Thus, conclusions have to do with the relationships between the quantities estimated by the simulation instead of the magnitude of these quantities.Experience has shown that such relationships are less impacted by uncertainty in model input data than are magnitudes of estimated quantities.

Methods
The mathematical model is described as well as the computations that produced the forecast of the vehicle-application lithium-ion batteries in watt-hours that is input to the model.

The Capacity Planning Model
The capacity planning model transfers a forecast of the demand for electric hybrid vehicles of all types into an estimate of the production capacity needed for remanufacturing, repurposing, and recycling post-vehicle-application lithium-ion batteries as well as that needed for new batteries.The single model parameter is the percent of such batteries that are remanufactured.The percent of batteries that are recycled is viewed as a physical constraint on the life of the batteries.The batteries that are not remanufactured and still can hold a charge are available for repurposing.
The variables used in the model are defined in Table 1.
At each point in time, the demand for hybrid electric vehicles results in the demand for batteries which may be either new batteries or remanufactured batteries.New batteries are manufactured to make up the difference between the demand and the number of remanufactured post-vehicle-application batteries as shown in Equation 1. (1) The three primary equations in the model determine the number of post-vehicle-application batteries that are remanufactured, repurposed, and recycled at a point in time.Note that the index i represents the year a vehicle, remanufacturing, or repurposing application began.The index j has to do with battery life in years which equals i -(t-MaxLife) + 1.The summation is over the values of i only.

Demandt
The demand for hybrid electric vehicle batteries at time t in watt-hours

Newt
The production of new batteries at time t in watt-hours

Remanufacturedt
Remanufactured post-vehicle-application batteries at time t in watt-hours

Repurposedt
Repurposed post-vehicle-application batteries at time t in watt-hours

Recycledt
Recycled post-vehicle-application batteries at time t in watt-hours

MaxLife
The maximum number of years of vehicle application life of a new battery

LifeDist(j)
The percent of new batteries that have a vehicle application life of exactly j years; The percent of remanufactured batteries that have a vehicle application of exactly j years; j = 1, … , MaxLife LifeDistRepurposed(j) The percent of repurposed batteries that have a vehicle application of exactly j years; The percent of new batteries at the end of vehicle application life of exactly j years that are remanufactured at time t; j = 1, … , MaxLife RepurposedNewPercentt(j) The percent of new batteries at the end of vehicle application life of exactly j years that are repurposed at time t; j = 1, … , MaxLife

RecycledNewPercentt(j)
The percent of new batteries at the end of vehicle application life of exactly j years that are recycled at time t; j = 1, … , MaxLife

RemanPrevPercentt(j)
The percent of batteries originally remanufactured after j years of vehicle application again at the end of vehicle application life that are again remanufactured at time t

RepurposedPrevPercentt(j)
The percent of batteries originally repurposed after j years of vehicle application at the end of repurposing application life that are again repurposed at time t

Repur2Recycledt(j)
The percent of batteries originally repurposed after j years of vehicle application at the end of repurposing application life that are recycled at time t

Reman2Recycledt(j)
The percent of batteries originally remanufactured after j years of vehicle application at the end of vehicle application life that are recycled at time t (2) The following should be noted regarding Equations 2-4.
• Substituting Equation 1 into Equation 2 results in an equation expressing remanufactured batteries at time t as a function of remanufactured batteries in prior years as well as the demand in prior years but not as a function of new battery production.
• Substituting Equation 1 into Equation 3 results in an equation expressing repurposed batteries at time t as a function of remanufactured and repurposed batteries in prior years as well as the demand in prior years but not as a function of new battery production.
• Substituting Equation 1 into Equation 4 results in an equation expressing recycled batteries at time t as a function of remanufactured and repurposed batteries in prior years as well as the demand in prior years but not as a function of new battery production.
• Thus, new battery production capacity is an output of the model, not an input to the model, as are remanufacturing, repurposing, and recycling capacity.
Equation 5 shows the relationship between the percent of batteries that are remanufactured, repurposed, and recycled.
(5) Equation 5states that all post-vehicle-application batteries are either remanufactured, repurposed, or recycled.The percent recycled quantifies a physical property: some cells in a post-vehicle-application or repurposed application battery can no longer hold a charge and must be recycled.The percent remanufactured is the model parameter.By Equation 5, the percent repurposed can be computed.

Assumptions and Model Constants
As the electrification of vehicles is relatively new, there is little experience with post-vehicle-application lithium-ion battery remanufacturing and repurposing particularly regarding the maximum life of batteries in these applications (Foster et al., 2014;Standridge & Corneal, 2014).The following model assumptions were based on this information.
• The maximum life of a battery (MaxLife) was set to 15 years about midway between the 95 th percentile and the maximum life estimations.
• A battery will have life for remanufacturing and repurposing applications as the maximum life is greater than the designed vehicle application life.
• End-of-repurposing-life batteries must all be recycled.A stationary storage repurposing application has fewer charge-discharge cycles than a vehicle application.Thus, lithium-ion batteries are premised to last in such applications until unable to hold a charge (RepurposedPrevPercentt(j) = 0 and Repur2Recycledt(j) = 100% for all t and j).
In addition, this implies that an end-of-repurposing application battery cannot be remanufactured for use in a vehicle.
• End-of-remanufacturing-life batteries may be remanufactured a second time or recycled.Our experience with remanufactured batteries is that they display the same performance and thus the same life characteristics as new batteries.Furthermore, the designed vehicle application life is about one half to two thirds of the maximum life.
Thus, a constraint that a battery can be remanufactured at most two times before re cycling is r easo nable and conse rvat ive (Rem anPre vPer cent t(j) =0 and Reman2Recycledt(j)=100% for all t and j if the battery was previously remanufactured).This assumption also implies that no remanufactured battery will be repurposed post-vehicle-application.The result of this constraint is that new battery production will increase in value in the model.Equation 6shows an end-of-remanufacturing-life battery must be either repurposed or recycled.
(6) Thus, it is sufficient to set the percent of end-of-remanufacturing-life batteries that are remanufactured again taking into a count the span of vehicle application life as new batteries and as remanufactured batteries, equivalent to the t and j indices.There is no recorded experience with such batteries.Therefore, it was assumed that the older the battery the less likely the battery could be used in a remanufacturing application, which seems reasonable.
Thus, the percent remanufactured was reduced by 5% for each year of battery life as shown in Equation 7. (7)

Battery Life Distribution
The battery life distribution in histogram form computed by Smith, Earleywine, Wood, and Pesaran (2011) was fit to a gamma distribution with parameters  = 39.072 and  = 0.267.
The percent points and mean reported by these authors are compared to the same quantities of the gamma distribution in Table 2.The mean and 5 th percent point are the same.The 95 th percent point of the gamma distribution is 0.2 greater (1.5%).The gamma distribution was used to model battery life.
There is little experience with the life of remanufactured and repurposed batteries.There is no information that indicates that remanufacturing or repurposing changes the life distribution of a battery.Thus, the life distribution following remanufacturing and repurposing is modeled as being the same, LifeDistReman(j) = LifeDistRepurposed(j) for all j.
This single life distribution is computed from the battery life distribution as a conditional distribution depending on the number of years of vehicle application, v, and the total application life of the battery (vehicle application + remanufacturing or repurposing application, u).This conditional distribution is shown in Equation 8, which is written in the form given in Devore (2015).
(8) As previously discussed, Baum (2013) provides a forecast the number of regular hybrid, mild hybrid, plug-in hybrid, and full electric vehicles through 2017 based on production data from 2009 through 2012.A model was created for each vehicle type by which the forecast could be extended through 2030, the end time of the remanufacturing, repurposing, and recycling capacity plan.This was done using simple regression based on the 8 data points, 2009-2017, provided by Baum.Linear growth is the simplest assumption as data and experience do not exist to support a more complex forecasting procedure.Results are shown in Table 3.

Vehicle Forecasts and Conversion to Energy
The forecasting model for the total number of electric vehicles of all types produced by the Center for Automotive Research ( 2009) is given in Equation 9: The number of micro-hybrids can be computed by subtraction from Equation 9of the equations in Table 3. (8) The number of electrified vehicles of each type is shown Table 4.Note that the number of micro-hybrid vehicles is declining slightly over time as the numbers of the each of the other vehicle types increases.
Table 5 shows the average power in the battery in each type of electrified vehicle as given by Pesaran (2011).
-832- Note that almost 95% of the power in batteries is forecast to be from fully electric and plug in electric vehicles.Also, any impact of any increase in uncertainty due to generating the number of micro hybrids by the subtraction of two other forecasts is greatly reduced in the simulation results as micro hybrids provide only 3.5% of the total energy capacity.Note that for 50% remanufactured and above, each increase of 5% in the percent remanufactured yields an increase of 2.2%-2.3% in the percent of demand met by remanufactured batteries up to about 25% for all available post-vehicle-application batteries remanufactured.
Table 8 shows the repurposing and recycling volume as a function of the percent remanufactured for 2030.Note that the recycled battery volume is nearly constant, varying slightly due to remanufacturing of post-vehicle-application batteries a second time.The repurposed battery volume decreases as the remanufactured battery volume increases as shown in Table 7.
Figure 1 shows the remanufactured battery capacity needed over time for 85% of post-vehicleapplication batteries remanufactured.Note that the need for recycling capacity becomes significant between 2022 and 2024.

Conclusions
The results in Tables 7 and 8 as well as Figure 1 support the following conclusions.A full commitment of all post-vehicle-application batteries to remanufacturing results in an approximate reduction of 25% in the demand for new batteries by 2030.Such a commitment is supported by Foster et al. (2014) whose analysis concluded that remanufacturing was more economical than repurposing.Such a commitment means that no post-vehicle-application batteries are available for repurposing applications such as stationary storage.
The capacity needed for repurposing decreases as the percent of post-vehicle-application batteries that are remanufactured increases.However, the sum of the repurposing and remanufacturing capacities is approximately constant on the order of 3.12M kWh.This is supports the idea of building capacity that is flexible between repurposing and remanufacturing tasks.Based on the discussion in Foster et al. (2014), such flexibility is reasonable to achieve as activities such as battery testing, disassembly, and controller development are common to both repurposing and remanufacturing.
The recycling capacity needed by 2030, regardless of the percent of post-vehicle-application batteries selected for remanufacturing, is about 2.69 kWh, approximately 85% of the combined repurposing-remanufacturing capacity.Recycling capacity is only 0.23% less for 85% of batteries remanufactured than no batteries remanufactured.This shows the small impact of remanufacturing a second time post-vehicle-application batteries that were previously remanufactured.For example in 2030 for the percent of batteries remanufactured equal to 85%, only 0.05% of the total number of remanufactured batteries were those remanufactured a second time.In addition, the need for recycling becomes significant for the first time between 2022 and 2024 growing steadily over time thereafter.
Smith et al. (2011) estimate the overall life distribution of lithium-ion batteries for vehicles as having a 95 th percentile of 13.2 years and a maximum of 16-17 years.The designed vehicle application life for a new lithium-ion battery for the Chevy Volt is 8 years(GM-Volt.com,2011).Marano, Onori, Guezennec, Rizzoni and Madella (2009) independently estimated the same life expectancy as 10 years.

Table 1 .
Capacity Planning Model Variables

Table 2 .
Comparison of Histogram with Gamma Distribution of Battery Life

Table 4 .
Count of Electrified Vehicles by Type (In Thousands)

Table 5 .
Journal of Industrial Engineering and Management -http://dx.doi.org/10.3926/jiem.1418AverageBatteryPowerMultiplying the forecast of the number of electrified vehicles shown in Table4by the average power in the battery of each type shown in Table5yields the forecast of the amount of battery power by vehicle type shown in Table6.

Table 6 .
Power in Batteries of Electrified Vehicles (in kWh)

Table 7 .
New and remanufactured batteries by percent remanufactured -

Table 8 .
New and remanufactured batteries by percent remanufactured -Simulation results for 2030