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GAC costing documentation into template dedicated file #1375

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initial migration of gac costing documentation into dedicated file
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83 changes: 71 additions & 12 deletions docs/technical_reference/costing/gac.rst
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Expand Up @@ -4,12 +4,40 @@ Granular Activated Carbon Costing Method
Costing Method Parameters
+++++++++++++++++++++++++

The following parameters are constructed for the unit on the FlowsheetCostingBlock (e.g., `m.fs.costing.gac`) when applying the `cost_gac` costing method in the ``watertap_costing_package``:
The following parameters are constructed for the unit on the FlowsheetCostingBlock (e.g., `m.fs.costing.gac_pressure` or `m.fs.costing.gac_gravity`) when applying the `cost_gac` costing
method in the ``watertap_costing_package``:

.. csv-table::
:header: "Description", "Symbol", "Parameter Name", "Default Value", "Units"

"description", ":math:`Symbol_{example}`", "parameter_name", "1", ":math:`\text{dimensionless}`"
"Number of contactors operating in parallel", ":math:`N_{op}`", "num_contactors_op", "1", ":math:`\text{dimensionless}`"
"Number of redundant contactors in parallel", ":math:`N_{red}`", "num_contactors_redundant", "1", ":math:`\text{dimensionless}`"
"Fraction of spent GAC adsorbent to be regenerated and reused", ":math:`f_{regen}`", "regen_frac", "0.70", ":math:`\text{dimensionless}`"
"Reference maximum value of GAC initial charge mass where economy of scale no longer discounts the unit price (U.S. EPA, 2021)", ":math:`M_{GAC}^{ref}`", "bed_mass_max_ref", "18143.7", ":math:`kg`"
"Contactor polynomial cost coefficients", ":math:`x`", "contactor_cost_coeff", "tabulated", ":math:`\text{dimensionless}`"
"Adsorbent exponential cost coefficients", ":math:`y`", "adsorbent_unit_cost_coeff", "tabulated", ":math:`\text{dimensionless}`"
"Other process costs power law coefficients", ":math:`z`", "other_cost_param", "tabulated", ":math:`\text{dimensionless}`"
"Unit cost to regenerate spent GAC adsorbent", ":math:`C_{unit,regen}`", "regen_unit_cost", "4.28352", ":math:`USD\_2020/kg`"
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"Unit cost to makeup spent GAC adsorbent with fresh adsorbent", ":math:`C_{unit,makeup}`", "makeup_unit_cost", "4.58223", ":math:`USD\_2020/kg`"
"Energy consumption polynomial coefficients", ":math:`alpha`", "energy_consumption_coeff", "tabulated", ":math:`\text{dimensionless}`"

Parameters which are tabulated have costing methods available for either steel pressure vessel contactors (default) or concrete gravity basin contactors. Given that the form of the costing
component equations are different (polynomial, exponential, and power law), the units associated with the parameters are embedded in the constraints and not directly applied to the variable.
Additionally, the index is generalized to its position ``([0:len(parameter_data)])`` in the list, although some parameters are coefficients while others are exponents (see equations below for details).
Variables with the (U.S. EPA, 2021) citation are directly taken from previously determined expressions. Other variables are regressed from higher detailed costing methods in (U.S. EPA, 2021).

.. csv-table::
:header: "Parameter Name", "Contactor Type", "Index 0", "Index 1", "Index 2", "Index 3"

"adsorbent_unit_cost_coeff (U.S. EPA, 2021)", "n/a", "4.58342", "-1.25311e-5", "", ""
"contactor_cost_coeff (U.S. EPA, 2021)", "pressure", "10010.9", "2204.95", "-15.9378", "0.110592"
"contactor_cost_coeff", "gravity", "75131.3", "735.550", "-1.01827", "0"
"other_cost_param", "pressure", "16660.7", "0.552207", "", ""
"other_cost_param", "gravity", "38846.9", "0.490571", "", ""
"energy_consumption_coeff_data", "pressure", "8.09926e-4", "8.70577e-4", "0", ""
"energy_consumption_coeff_data", "gravity", "0.123782", "0.132403", "-1.41512e-5", ""

\*Energy consumption is the sum of energy required to operate booster, backwash, and residual pumps.

Costing Method Variables
++++++++++++++++++++++++
Expand All @@ -19,35 +47,65 @@ The following variables are constructed on the unit block (e.g., m.fs.unit.costi
.. csv-table::
:header: "Description", "Symbol", "Variable Name", "Default Value", "Units"

"description", ":math:`Symbol_{example}`", "variable_name", "1", ":math:`\text{dimensionless}`"
"Total unit capital cost", ":math:`C_{cap}`", "capital_cost", "10,000", ":math:`USD\_2020`"
"Capital cost of contactor(s)", ":math:`C_{cap,bed}`", "contactor_cost", "10,000", ":math:`USD\_2020`"
"Mass of GAC initial charge used to determine the unit cost", ":math:`M_{GAC}^{min}`", "bed_mass_gac_ref", "4", ":math:`kg`"
"Unit cost of GAC adsorbent for initial charge", ":math:`C_{unit,carbon}`", "adsorbent_unit_cost", "2", ":math:`USD\_2020/kg`"
"Capital cost of GAC adsorbent", ":math:`C_{cap,carbon}`", "adsorbent_cost", "10,000", ":math:`USD\_2020`"
"Capital costs of other process supplements", ":math:`C_{cap,other}`", "other_process_cost", "10,000", ":math:`USD\_2020`"
"Approximate GAC system energy consumption*", ":math:`P`", "energy_consumption", "100", ":math:`kW`"
"Fixed operating costs", ":math:`C_{op}`", "fixed_operating_cost", "10,000", ":math:`USD\_2020/yr`"
"Operating costs to regenerate spent GAC adsorbent", ":math:`C_{op,regen}`", "gac_regen_cost", "10,000", ":math:`USD\_2020/yr`"
"Operating costs to makeup spent GAC adsorbent with fresh adsorbent", ":math:`C_{op,makeup}`", "gac_makeup_cost", "10,000", ":math:`USD\_2020/yr`"

Capital Cost Calculations
+++++++++++++++++++++++++

Describe capital costs..keep it concise where possible
Costing GAC contactors is defaulted to purchasing 1 operational and 1 redundant contactor for alternating operation with minimal downtown. For large systems, this may be a poor
assumption considering vessel sizing and achieving pseudo-steady state. The number of contactors input by the user should justify reasonable (commercially available) dimensions
of identical modular contactors in parallel. When costing several operational vessels, the area reported in the unit model should be interpreted as the sum of the areas across
all operating GAC contactors. The costing parameters may be selected from either steel pressure-fed vessels or concrete gravity-fed basins by the ``contactor_type`` argument.
Note this only affects costing calculations. Volume dimensions calculations within the model remain assuming a cylindrical bed. Capital costs are determined by the summation of
three costing terms. Each term is is calculated by a one parameter (different for each term) function considering economy of scale.

.. math::

C_{cap,tot} = C_{cap,example1}+C_{cap,example2}+C_{cap,other}
C_{cap,tot} = C_{cap,bed}+C_{cap,carbon}+C_{cap,other}

Contactor and GAC adsorbent capital costs are estimated using functions and parameters reported in US EPA, 2021. Contactors are assumed to be carbon steel pressure vessels with
plastic internals and are determined as a polynomial function of individual contactor volume. The unit cost per kilogram of GAC adsorbent needed is calculated using an exponential
function. A maximum reference mass is imposed in the costing method to define a best available price where above this required charge, the price would no longer be discounted.
Other process costs (vessels, pipes, instrumentation, and controls) included in the US EPA, 2021 model are aggregated into a separate term. The parameters for the power law function
with respect to the total system contactor volume were regressed using results from the US EPA, 2021 model.

.. math::

C_{cap,example1} = fill in equation for each component in total capex equation
& C_{cap,bed} = \left( N_{op}+N_{red} \right)\left( x_0+x_1\left( \frac{V}{N_{op}} \right)+x_2\left( \frac{V}{N_{op}} \right)^2+x_3\left( \frac{V}{N_{op}} \right)^3 \right) \\\\
& M_{GAC}^{min} = \text{min}\left(M_{GAC}^{model}, M_{GAC}^{ref}\right) \\\\
& C_{carbon} = y_0e^{y_1M_{GAC}^{min}} \\\\
& C_{cap,carbon} = C_{carbon}M_{GAC} \\\\
& C_{cap,other} = z_0\left( \left( N_{op}+N_{red} \right)\frac{V}{N_{op}} \right)^{z_1}


Note that given the the ability to alter the parameters in these correlations, GAC adsorbent unit costs (:math:`C_{carbon}`) may be fixed to a value (:math:`y_0`) by setting :math:`y_1=0`.


Operating Cost Calculations
+++++++++++++++++++++++++++

Describe operating/maintenance costs..keep it concise where possible
Operating costs are calculated as the cost to replace spent GAC adsorbent in the contactor beds. Energy is costed as a flow term by the WaterTAP costing method.

.. math::

C_{op,tot} = C_{op,example1}+C_{op,example2}+C_{op,other}
C_{op,tot} = C_{op,regen}+C_{op,makeup}

.. math::
Since the replacement adsorbent purchases are expected to be purchased in bulk at smaller quantities than the initial charge, the cost of fresh GAC adsorbent for makeup has an different
cost per unit mass, expected to be higher than the initial charge unit cost.

C_{op,example1} = fill in equation for each component in total opex equation
.. math::

& C_{op,regen} = f_{regen}C_{unit,regen}\dot{m}_{GAC}^{model} \\\\
& C_{op,makeup} = \left( 1-f_{regen} \right)C_{unit,makeup}\dot{m}_{GAC}^{model} \\\\
& P = \alpha_0+\alpha_1V+\alpha_2V^2

Code Documentation
------------------
Expand All @@ -56,4 +114,5 @@ Code Documentation

References
----------
Aim to include at least one reference in most cases, but delete this section if no references used for cost relationships/default values
United States Environmental Protection Agency. (2021). Work Breakdown Structure-Based Cost Model for Granular Activated
Carbon Drinking Water Treatment.
104 changes: 0 additions & 104 deletions docs/technical_reference/unit_models/gac.rst
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Expand Up @@ -232,107 +232,6 @@ if ``surface_diffusion_coefficient_type`` is set to ``calculated``:

"surface diffusion parameter (Crittenden, 1987)", ":math:`D_s=\left( S\!P\!D\!F\!R \right)\left( \frac{\epsilon_pC_0D_l}{\rho_aq_e\tau_p} \right)`"

Costing Method
---------------

Costing Method Variables
+++++++++++++++++++++++++

The following parameters are constructed when applying the GAC costing method in the ``watertap_costing_package``:

.. csv-table::
:header: "Description", "Symbol", "Variable Name", "Default Value", "Units"

"Number of GAC contactors in operation in parallel", ":math:`N_{op}`", "num_contactors_op", "1", ":math:`\text{dimensionless}`"
"Number of off-line redundant GAC contactors in parallel", ":math:`N_{red}`", "num_contactors_redundant", "1", ":math:`\text{dimensionless}`"
"Fraction of spent GAC adsorbent that can be regenerated for reuse", ":math:`f_{regen}`", "regen_frac", "0.70", ":math:`\text{dimensionless}`"
"Reference maximum value of GAC mass needed for initial charge where economy of scale no longer discounts the unit price (U.S. EPA, 2021)", ":math:`M_{GAC}^{ref}`", "bed_mass_gac_max_ref", "18143.7", ":math:`kg`"
"Contactor polynomial cost coefficients", ":math:`x`", "contactor_cost_coeff", "tabulated", ":math:`\text{dimensionless}`"
"Adsorbent exponential cost coefficients", ":math:`y`", "adsorbent_unit_cost_coeff", "tabulated", ":math:`\text{dimensionless}`"
"Other process costs power law coefficients", ":math:`z`", "other_cost_param", "tabulated", ":math:`\text{dimensionless}`"
"Unit cost to regenerate spent GAC adsorbent by an offsite regeneration facility", ":math:`C_{regen}`", "regen_unit_cost", "4.28352", ":math:`$/kg`"
"Unit cost to makeup spent GAC adsorbent with fresh adsorbent", ":math:`C_{makeup}`", "makeup_unit_cost", "4.58223", ":math:`$/kg`"
"Energy consumption polynomial coefficients", ":math:`alpha`", "energy_consumption_coeff", "tabulated", ":math:`\text{dimensionless}`"

Costing methods are available for steel pressure vessel contactors (default) and concrete gravity basin contactors. Given that the form of the costing component equations are different (polynomial, exponential, and power law), the units associated with the parameters are embedded in the constraints and not directly applied to the variable. Additionally, the index is generalized to its position ``([0:len(parameter_data)])`` in the list, although some parameters are coefficients while others are exponents (see equations below for details). Variables with the (U.S. EPA, 2021) citation are directly taken from previously determined expressions. Other variables are regressed from higher detailed costing methods in (U.S. EPA, 2021). The variations in costing parameters are tabulated below:

.. csv-table::
:header: "Variable Name", "Contactor Type", "Index 0", "Index 1", "Index 2", "Index 3"

"adsorbent_unit_cost_coeff (U.S. EPA, 2021)", "n/a", "4.58342", "-1.25311e-5", "", ""
"contactor_cost_coeff (U.S. EPA, 2021)", "pressure", "10010.9", "2204.95", "-15.9378", "0.110592"
"contactor_cost_coeff", "gravity", "75131.3", "735.550", "-1.01827", "0"
"other_cost_param", "pressure", "16660.7", "0.552207", "", ""
"other_cost_param", "gravity", "38846.9", "0.490571", "", ""
"energy_consumption_coeff_data", "pressure", "8.09926e-4", "8.70577e-4", "0", ""
"energy_consumption_coeff_data", "gravity", "0.123782", "0.132403", "-1.41512e-5", ""

Costing GAC contactors is defaulted to purchasing 1 operational and 1 redundant contactor for alternating operation. For large systems this may be a poor
assumption considering vessel sizing and achieving pseudo-steady state. The number of contactors input by the user should justify reasonable
(commercially available) dimensions of identical modular contactors in parallel. When costing several operational vessels, the area reported
in the unit model should be interpreted as the sum of the areas across all operating GAC contactors. The costing
parameters may be selected from either steel pressure-fed vessels or concrete gravity-fed basins by the
``contactor_type`` argument. Note this only affects costing calculations. Volume dimensions calculations
within the model remain assuming a cylindrical bed.

The following variables are constructed when applying the GAC costing method in the ``watertap_costing_package``:

.. csv-table::
:header: "Description", "Symbol", "Variable Name", "Units"

"Unit contactor(s) capital cost", ":math:`C_{cap,bed}`", "contactor_cost", ":math:`$`"
"GAC adsorbent cost per unit mass", ":math:`C_{carbon}`", "adsorbent_unit_cost", ":math:`$/kg`"
"Unit adsorbent capital cost", ":math:`C_{cap,carbon}`", "adsorbent_cost", ":math:`$`"
"Unit other process capital cost", ":math:`C_{cap,other}`", "other_process_cost", ":math:`$`"
"Cost to regenerate spent GAC adsorbent by an offsite regeneration facility", ":math:`C_{op,regen}`", "gac_regen_cost", ":math:`$/year`"
"Cost to makeup spent GAC adsorbent with fresh adsorbent", ":math:`C_{op,makeup}`", "gac_makeup_cost", ":math:`$/year`"
"Approximate GAC system energy consumption*", ":math:`P`", "energy_consumption", ":math:`kW`"

\*Energy consumption is the sum of energy required to operate booster, backwash, and residual pumps.

Capital Cost Calculations
+++++++++++++++++++++++++

Capital costs are determined by the summation of three costing terms. Each term is is calculated by a one parameter
(different for each term) function considering economy of scale.

.. math::

C_{cap,tot} = C_{cap,bed}+C_{cap,carbon}+C_{cap,other}

Contactor and GAC adsorbent capital costs are estimated using functions and parameters reported in US EPA, 2021. Contactors
are assumed to be carbon steel pressure vessels with plastic internals and are determined as a polynomial function of
individual contactor volume. The unit cost per kilogram of GAC adsorbent needed is calculated using an exponential
function. A maximum reference mass is imposed in the costing method to define a best available price where above
this required charge, the price would no longer be discounted. Other process costs (vessels, pipes, instrumentation,
and controls) included in the US EPA, 2021 model are aggregated into a separate term. The parameters for the power law
function with respect to the total system contactor volume were regressed using results from the US EPA, 2021 model.

.. math::

& C_{cap,bed} = \left( N_{op}+N_{red} \right)\left( x_0+x_1\left( \frac{V}{N_{op}} \right)+x_2\left( \frac{V}{N_{op}} \right)^2+x_3\left( \frac{V}{N_{op}} \right)^3 \right) \\\\
& C_{carbon} = y_0e^{y_1M_{GAC}^{ref}} \\\\
& C_{cap,carbon} = C_{carbon}M_{GAC} \\\\
& C_{cap,other} = z_0\left( \left( N_{op}+N_{red} \right)\frac{V}{N_{op}} \right)^{z_1}

Note that given the the ability to alter the parameters in these correlations, GAC adsorbent unit costs (:math:`C_{carbon}`)
may be fixed to a value (:math:`y_0`) by setting :math:`y_1=0`.

Operating Cost Calculations
+++++++++++++++++++++++++++

Operating costs are calculated as the cost to replace spent GAC adsorbent in the contactor beds. Energy is costed as a
flow term by the WaterTAP costing method. Since the replacement adsorbent purchases are expected to be purchased in bulk
at smaller quantities than the initial charge, the cost of fresh GAC adsorbent for makeup has an independent cost per
unit mass variable, expected to be higher than the initial charge unit cost.

.. math::

& C_{op,tot} = C_{op,regen}+C_{op,makeup} \\\\
& C_{op,regen} = f_{regen}C_{regen}\dot{m}_{GAC} \\\\
& C_{op,makeup} = \left( 1-f_{regen} \right)C_{makeup}\dot{m}_{GAC} \\\\
& P = \alpha_0+\alpha_1V+\alpha_2V^2

Code Documentation
-------------------

Expand All @@ -349,6 +248,3 @@ John Wiley & Sons.

Crittenden, J. C., Berrigan, J. K., Hand, D. W., & Lykins, B. (1987). Design of Rapid Fixed‐Bed Adsorption Tests for
Nonconstant Diffusivities. Journal of Environmental Engineering, 113(2), 243–259.

United States Environmental Protection Agency. (2021). Work Breakdown Structure-Based Cost Model for Granular Activated
Carbon Drinking Water Treatment. https://www.epa.gov/system/files/documents/2022-03/gac-documentation-.pdf_0.pdf