# Design rule purpose

The purpose of this design rule is to calculate all parameters related to pumping of water in a pressurised water pipeline. Based on pipe parameters, required flow, elevation changes and a variety of cost parameters, useful hydraulic and costing parameters can be calculated. Pumping is a major source of cost, especially due to long asset life cycles (usually minimum lifetime is around 50 years). Optioneer takes this into account and performs high-level pumping calculations which are used to generate options with the lowest whole-lifecycle cost (TOTEX).

# How to configure

This is a complex design rule that involves multiple steps and a large number of various parameters.

Step 1 - calculate the pipe loss parameters

There is a number of standard calculations this design rule is carrying out to find friction factors of the pipe based on its flow. The following steps are done:

1. Calculation of internal diameter based on outer diameter and standard dimensional ratio

2. Calculation of flow velocity based on internal area of the pipe and the required flow rate.

3. Calculation of the Reynolds number based on the velocity, pipe dimensions and water viscosity.

4. Calculation of the Swamee-Jain factor, a special case of Darcy’s equation, to calculate the friction factor of the pipe (formula for Swamee-Jain factor is provided below). Epsilon stands for pipe roughness, D stands for pipe internal diameter and Re is the Reynolds number.

Swamee-Jain factor:

Step 2 - calculate head loss along the pipe

Due to friction present during the flow, the pipe will exhibit an increasing head loss along its length. This head loss is the function of distance, pipe dimensions and the friction factor calculated in the previous step (Swamee-Jain factor). This factor is expressed ‘per unit length’.

Hydraulic slope factor:

Where ‘S' is the hydraulic slope factor, ‘f_D’ is the friction head loss, ‘g’ indicates the gravitational constant, ‘V’ is flow speed and 'D’ describes the diameter of the pipe.

Head loss at distance is then obtained by multiplying the hydraulic slope by the distance (chainage) of the pipe. The further away from the pump (starting point) the higher the total head loss is.

Step 3 - calculate the head loss due to potential energy change

Pumping the fluid ‘up’ requires power; the power required is proportional to the height difference. The height difference is measured from the starting point to the highest point in the pipeline (not to the end point).

Not allowing intermediate high-points, i.e. enforcing the end point as the highest point in the pipeline, can be enforced in this design rule by setting the parameter ‘allow high-points’ to False.

If the end point is the highest point on the pipeline, the required levels are found as depicted below. This will happen when the setting ‘allow intermediate high-points’ is set to False.

If the end point is not the highest point on the pipeline, the high-point of the pipeline is taken into account in calculation as in an example below. This is possible when the setting ‘allow intermediate high-points’ is set to True.

Step 4 - calculate the hydraulic profile

The total head supplied by the pumps is used to overcome the frictional losses in the pipe and supply enough head to make it over all high points along the route of the pipe with a minimum clearance (specified through the `min_static_head` variable).

The graph below depicts a plot of vertical profile along the chainage (x-axis). Pipeline elevation and hydraulic profile are plotted on the y-axis to demonstrate how minimum static head is enforced along the route.

To calculate the hydraulic profile, the losses are first calculated to create a hydraulic profile starting at 0 and falling into negative pressures over the length of the pipeline, static head is then added to adjust the hydraulic profile upwards until the hydraulic profile clears the terrain by a the amount specified in min_static_head.

The head calculated in this step can be passed directly to further calculations of pump power.

Step 5 - calculate required power

Power of the motor required to drive the pump is a function of flow rate, total head required, gravity constant and the efficiencies of the motor and the pump.

Operational power is used to calculate required OPEX in a year. Installed power is found by including the number of duty pumps (any duty pump is not necessarily used all the time if there is more than one and there is a significant diurnal flow variation) and applying the appropriate ‘capacity factor' (additional margin) on the operational power value (default set to 10%, configurable).

Step 6 - calculate initial CAPEX, systems' replacement cost and annual OPEX

Pump station CAPEX cost is disaggregated into two cost functions:

• Pump Station Civils costs - no replacement assumed within lifetime of the asset

• Pump Station MEICA costs - regular replacement within lifetime of the asset

Both of these functions follow a similar format and are configurable by the user within the following parameters:

• Civil Cost Curve [base £ and per kW £]

• MEICA Cost Curve [base £ and per kW £]

These functions are linear approximations of costs and require two input parameters, with linear function represented as:

The output of this calculation is the required CAPEX cost to be incurred before the asset goes operational, represented as a single value in £.

MEICA Pump Station Cost is further disaggregated into:

• Mechanical Pump Station Cost (percentage cost configurable by the user)

• EICA Pump Station Cost (remaining cost, after Mechanical Pump Station Cost is subtracted from MEICA Pump Station Cost).

Once the power required is found, the total energy expenditure for the year is calculated.

Step 7 - calculate lifetime costs of the pump station and operations

CAPEX and replacement

There are three main CAPEX parameters taken into account, as represented in the table below.

 Cost name Replacement cycle Pump Station Civils N/A Pump Station Mechanical User input: Mechanical Replacement Cycle [years]Default: 10 years Pump Station EICA User input: EICA Replacement Cycle [years]Default: 5 years

Cost of replacement of Mechanical and EICA components has to be discounted appropriately, using the same discount factor as later OPEX calculation.

Discounted OPEX

After annual OPEX is calculated, a cost of operations over the lifetime of the asset can be found, using a suitable discount rate (specified by the user).

The current formula is given below:

Where the starting year of the calculation is represented as year 0 and r represents the annual discount rate.

Example: asset goes live in year 2022 and is operational for 20 years, until 2042. The sum is calculated over year numbers between 1 and 20.

Cost structure - example

Assume replacement cycle of 4 years for Mechanical and 3 years for EICA.

It is assumed that first year OPEX is discounted, as if it is paid at the end of financial year. Year 1 CAPEX costs for Pump Station components are not discounted as it is assumed that the cost is incurred before operations begin.

 OPEX PS Mechanical PS EICA PS CIVIL Year 1 OPEX, discount 1 year Mech_CAPEX, no discount EICA_CAPEX, no discount Civ_CAPEX, no discount Year 2 OPEX, discount 2 years 0 0 0 Year 3 OPEX, discount 3 years 0 EICA_CAPEX, discount 3 years 0 Year 4 OPEX, discount 4 years Mech_CAPEX, discount 4 years 0 0 Year 5 OPEX, discount 5 years 0 0 0 Year 6 OPEX, discount 6 years 0 EICA_CAPEX, discount 6 years 0 … … … … … End of asset life Sum of all OPEX years Sum of all Mech_CAPEX years Sum of all EICA_CAPEX years Sum of all Civ_CAPEX yea

The total cost is found by summing up all of the through-life costs of different components. Users also get access to a table similar to the one presented above which gives breakdown by cost-type and year.

# Input / output summary

## Input parameters

This design rule doesn't require a dedicated dataset and draws terrain data from the 'elevation' dataset.

Pipe parameters:

 Name Default value Unit Pipe OD 0.355 meters Pipe ID 0.335 meters SDR 17 unit Pipe roughness 0.05 coefficient

Pumping parameters:

 Name Default value Unit Required flow rate 0.3 m3/s Minimum static head required 2 meters Cost of power 0.1 £/kWh (or other currency per kilowatt-hour) Discount rate 0.03 fraction3% = 0.03 Design life 50 years Pumping days per year 365 days Pumping hour per day 16 hours Motor efficiency 0.85 fraction85% = 0.85 Pump efficiency 0.90 fraction90% = 0.90 Number of duty pumps 1 unit Number of standby pumps 1 unit Pump capacity factor 1.1 number Mechanical Equipment replacement cycle 12 years Electrical, Instrumentation, Control, Automation (EICA) replacement cycle 5 years

## Output parameters

 Name Example value Unit Friction head 27.5 meters Static head 22 meters Total head 49.5 meters Required power 262.7 kW Installed power 450 kW OPEX 34,000 £ - currency OPEX discounted 2,200,000 £ - currency CAPEX for civil component of the pump station 550,000 £ - currency CAPEX for the EICA component of the pump station 420,000 £ - currency Hydraulic profile (head) plot Plot on Vertical Profile Chart Pressure profile plot Plot on Vertical Profile Chart