Trace thermal-hydraulic regime for linear segment of district heating network

Trace values of thermal-hydraulic regime (temperature, pressure, flow_rate, and other) along the adjacent linear segments of pipeline using user-provided values of specific heat loss power.

Usage

traceline(
  temperature = 130,
  pressure = mpa_kgf(6),
  flow_rate = 250,
  g = 0,
  d = 700,
  len = c(600, 530, 300, 350),
  loss = c(348, 347.1389, 346.3483, 345.861),
  roughness = 0.006,
  inlet = 0,
  outlet = 0,
  elev_tol = 0.1,
  method = "romeo",
  forward = TRUE,
  absg = TRUE
)

Arguments

temperature

Traced thermal hydraulic regime. Sensor-measured temperature of heat carrier (water) inside the pipe sensor-measured at the inlet (forward tracing) or at the outlet (backward tracing) of path, [°C]. Type: assert_number.

pressure

Traced thermal hydraulic regime. Sensor-measured absolute pressure of heat carrier (water) sensor-measured at the inlet (forward tracing) or at the outlet (backward tracing) of path, [MPa]. Type: assert_number.

flow_rate

Traced thermal hydraulic regime. Amount of heat carrier (water) sensor-measured at the inlet (forward tracing) or at the outlet (backward tracing) of path, [ton/hour]. Type: assert_number.

g

amount of heat carrier discharge to network for each pipe segment in the tracing path enumerated along the direction of flow. If flag absg is TRUE then they treat argument g as absolute value in [ton/hour], otherwise they do as percentage of flow_rate in the pipe segment. Type: assert_double.

d

internal diameters of subsequent pipes in tracing path that are enumerated along the direction of flow, [mm]. Type: assert_double.

len

length of subsequent pipes in tracing path that are enumerated along the direction of flow, [m]. Type: assert_double.

loss

user-provided value of specific heat loss power for each pipe in tracing path enumerated along the direction of flow, [kcal/m/h]. Values of the argument can be obtained experimentally, or taken from regulatory documents. Type: assert_double.

roughness

roughness of internal wall for each pipe in tracing path enumerated along the direction of flow, [m]. Type: assert_double.

inlet

elevation of pipe inlet for each pipe in tracing path enumerated along the direction of flow, [m]. Type: assert_double.

outlet

elevation of pipe outlet for each pipe in tracing path enumerated along the direction of flow, [m]. Type: assert_double.

elev_tol

maximum allowed discrepancy between adjacent outlet and inlet elevations of two subsequent pipes in the traced path, [m]. Type: assert_number.

method

method of determining Darcy friction factor

romeo
vatankhan
buzelli

Type: assert_choice. For more details see dropp.

forward

tracing direction flag: is it a forward direction of tracing? If FALSE the backward tracing is performed. Type: assert_flag.

absg

Whether argument g (amount of heat carrier discharge to network) is an absolute value in [ton/hour] (TRUE) or is it a percentage of flow rate in the pipe segment (FALSE)? Type: assert_flag.

Value

list containing results (detailed log) of tracing for each pipe in tracing path enumerated along the direction of flow:

temperature: Traced thermal hydraulic regime. Traced temperature of heat carrier (water), [°C]. Type: assert_double.
pressure: Traced thermal hydraulic regime. Traced pressure of heat carrier (water) for each pipe in tracing path enumerated along the direction of flow, [MPa]. Type: assert_double.
flow_rate: Traced thermal hydraulic regime. Traced flow rate of heat carrier (water) for each pipe in tracing path enumerated along the direction of flow, [ton/hour]. Type: assert_double.
loss: User-provided specific heat loss power for each pipe in tracing path enumerated along the direction of flow, [kcal/m/h], - copy of input. Type: assert_double.
flux: Heat flux for each pipe in tracing path enumerated along the direction of flow, [W/m^2]. Type: assert_double.
Q: Heat loss for each pipe in tracing path enumerated along the direction of flow per day, [kcal]. Type: assert_double.

Type: assert_list.

Details

They consider only simple tracing paths which do not contain rings and any kind of parallelization. At the same time bidirectional (forward and backward) tracing is possible in accordance with sensor position. They also may consider discharges to network at the inlet of each pipeline segment as an approximation of actual forks of flows. Relevant illustration of adopted assumptions for 4-segment tracing path is depicted on the next figure.

They make additional check for consistency of inlet and outlet values for subsequent pipe segments. Discrepancy of appropriate elevations cannot be more than elev_tol.

Since inner diameter of the pipe is used as input, the the thickness of the pipe wall additionally considered in heat flux calculations. Pipe wall thickness is derived from pipe diameter using GOST 30732 specifications.

Examples

 library(pipenostics)

# Consider 4-segment tracing path.
# First, let sensor readings for forward tracing:
t_fw <- 130  # [°C]
p_fw <- mpa_kgf(6)*all.equal(.588399, mpa_kgf(6))  # [MPa]
g_fw <- 250  # [ton/hour]

# Let discharges to network for each pipeline segment are somehow determined as
discharges <- seq(0, 30, 10)  # [ton/hour]

# Experimentally obtained values of specific heat loss power are
actual_loss <- c(348.0000, 347.1389, 346.3483, 345.8610)

# Then the calculated regime (red squares) for forward tracing is
regime_fw <- traceline(t_fw, p_fw, g_fw, discharges, loss = actual_loss, forward = TRUE)
print(regime_fw)
#> $temperature
#> [1] 129.1799 128.4269 127.9628 127.3367
#> 
#> $pressure
#> [1] 0.5878607 0.5874226 0.5872143 0.5870330
#> 
#> $flow_rate
#> [1] 250 240 220 190
#> 
#> $loss
#> [1] 348.0000 347.1389 346.3483 345.8610
#> 
#> $flux
#> [1] 181.9600 181.5097 181.0963 180.8415
#> 
#> $Q
#> [1] 5011200 4415607 2493708 2905232
#> 

# $temperature
# [1] 129.1799 128.4269 127.9628 127.3367
#
# $pressure
# [1] 0.5878607 0.5874226 0.5872143 0.5870330
#
# $flow_rate
# [1] 250 240 220 190
#
# $loss
# [1] 348.0000 347.1389 346.3483 345.8610
#
# $flux
# [1] 181.9600 181.5097 181.0963 180.8415
#
# $Q
# [1] 5011200 4415607 2493707 2905232


# Next consider values of traced regime as sensor readings for backward tracing:
t_bw <- 127.3367  # [°C]
p_bw <- .5870330  # [MPa]
g_bw <- 190  # [ton/hour]

# Then the calculated regime (red squares) for backward tracing is
regime_bw <- traceline(t_bw, p_bw, g_bw, discharges, loss = actual_loss, forward = FALSE)
print(regime_bw)
#> $temperature
#> [1] 130.0009 129.1805 128.4272 127.9630
#> 
#> $pressure
#> [1] 0.5883998 0.5878611 0.5874228 0.5872144
#> 
#> $flow_rate
#> [1] 250 250 240 220
#> 
#> $loss
#> [1] 348.0000 347.1389 346.3483 345.8610
#> 
#> $flux
#> [1] 181.9600 181.5097 181.0963 180.8415
#> 
#> $Q
#> [1] 5011200 4415607 2493708 2905232
#> 

# $temperature
# [1] 130.000893685 129.180497939 128.427226907 127.963046346
#
# $pressure
# [1] 0.588399833660 0.587861095778 0.587422779315 0.587214377798
#
# $flow_rate
# [1] 250 250 240 220
#
# $loss
# [1] 348.0000 347.1389 346.3483 345.8610
#
# $flux
# [1] 181.959958158 181.509711836 181.096328092 180.841531863
#
# $Q
# [1] 5011200.000 4415606.808 2493707.760 2905232.400

# Let compare sensor readings with backward tracing results:
tracing <- with(regime_bw, {
  lambda <- function(val, constraint)
    c(val, constraint, constraint - val,
      abs(constraint - val)*100/constraint)
  first <- 1
  structure(
    rbind(
      lambda(temperature[first], t_fw),
      lambda(pressure[first],    p_fw),
      lambda(flow_rate[first], g_fw)
    ),
    dimnames = list(
      c("temperature", "pressure", "flow_rate"),
      c("sensor.value", "traced.value", "abs.discr", "rel.discr")
    )
  )
})
print(tracing)
#>             sensor.value traced.value     abs.discr    rel.discr
#> temperature  130.0008937   130.000000 -8.936853e-04 0.0006874502
#> pressure       0.5883998     0.588399 -8.261601e-07 0.0001404081
#> flow_rate    250.0000000   250.000000  0.000000e+00 0.0000000000

# sensor.value   traced.value          abs.discr         rel.discr
# temperature 130.00089368526 130.0000000000 -8.93685255676e-04 0.000687450196674
# pressure      0.58839983366   0.5883990075 -8.26160099998e-07 0.000140408139624
# flow_rate   250.00000000000 250.0000000000  0.00000000000e+00 0.000000000000000