Massively trace backwards thermal-hydraulic regime for district heating network

Trace values of thermal-hydraulic regime (temperature, pressure, flow rate, and other) in the bunched pipeline against the flow direction using user-provided values of specific heat loss power.

Algorithm also suits for partially measurable district heating network with massive data lack conditions, when there are no temperature and pressure sensor readings on the majority of terminal nodes.

Usage

tracebw(
  sender = 6,
  acceptor = 7,
  temperature = 70,
  pressure = pipenostics::mpa_kgf(6),
  flow_rate = 20,
  d = 100,
  len = 72.446,
  loss = 78.4,
  roughness = 0.001,
  inlet = 0.5,
  outlet = 1,
  method = "romeo",
  opinion = "median",
  verbose = TRUE,
  csv = FALSE,
  file = "tracebw.csv"
)

Arguments

sender

identifier of the node which heat carrier flows out. Type: any type that can be painlessly coerced to character by as.character.

acceptor

identifier of the node which heat carrier flows in. According to topology of test bench considered this identifier should be unique for every row. Type: any type that can be painlessly coerced to character by as.character.

temperature

Sensor-measured temperature of heat carrier (water) sensor-measured on the terminal acceptor node, [°C]. Use NA_float_s for (terminal) nodes without temperature sensor. Type: assert_double.

pressure

Sensor-measured absolute pressure of heat carrier (water) inside the pipe (i.e. acceptor's incoming edge), [MPa]. Type: assert_double.

flow_rate

Sensor-measured amount of heat carrier (water) on terminal node that is transferred by pipe (i.e. acceptor's incoming edge) during a period, [ton/hour]. Type: assert_double. Use NA_float_s for nodes without flow rate sensor.

d

internal diameter of pipe (i.e.diameter of acceptor's incoming edge), [mm]. Type: assert_double.

len

pipe length (i.e. length of acceptor's incoming edge), [m]. Type: assert_double.

loss

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

roughness

roughness of internal wall of pipe (i.e. acceptor's incoming edge), [m]. Type: assert_double.

inlet

elevation of pipe inlet, [m]. Type: assert_double.

outlet

elevation of pipe outlet, [m]. Type: assert_double.

method

method of determining Darcy friction factor:

romeo
vatankhan
buzelli

Type: assert_choice. For more details see dropp.

opinion

method for aggregating values of regime parameters on each node for the next tracing step:

mean: values of parameter are averaged before the next tracing step
median: median of parameter values are used for the next tracing step

Type: assert_choice.

verbose

logical indicator: should they watch tracing process on console? Type: assert_flag.

csv

logical indicator: should they incrementally dump results to csv- file while tracing? Type: assert_flag.

file

name of csv-file which they dump results to. Type: assert_character of length 1 that can be used safely to create a file and write to it.

Value

data.frame containing results (detailed log) of tracing in

narrow format:

node: Tracing job. Identifier of the node which regime parameters is calculated for. Values in this vector are identical to those in argument acceptor. Type: assert_character.
tracing: Tracing job. Identifiers of nodes from which regime parameters are traced for the given node. Identifier sensor is used when values of regime parameters for the node are sensor readings. Type: assert_character.
backward: Tracing job. Identifier of tracing direction. It constantly equals to TRUE. Type: assert_logical.
aggregation: Tracing job. Identifier of aggregation method: span, median, mean, or identity. Type: assert_character.
loss: Traced thermal hydraulic regime. Normative specific heat loss power of adjacent pipe, [kcal/m/h]. Type: assert_double.
flux: Traced thermal hydraulic regime. Normative heat flux of adjacent pipe, [W/m^2]. Type: assert_double.
Q: Traced thermal hydraulic regime. Normative heat loss of adjacent pipe per day, [kcal]. Type: assert_character.
temperature: Traced thermal hydraulic regime. Traced temperature of heat carrier (water) that is associated with the node, [°C]. Type: assert_double.
pressure: Traced thermal hydraulic regime. Traced pressure of heat carrier (water) that is associated with the node, [MPa]. Type: assert_double.
flow_rate: Traced thermal hydraulic regime. Traced flow rate of heat carrier (water) that is associated with the node, [ton/hour]. Type: assert_double.
job: Tracing job. Value of tracing job counter. Type: assert_count.

Type: assert_data_frame.

Details

They consider the topology of district heating network represented by m325testbench:

The network may be partially sensor-equipped too:

In latter case no more than two nodes must be equipped with pressure and temperature sensors whereas for other nodes only flow rate sensors must be installed.

Tracing starts from sensor-equipped nodes and goes backwards, i.e against the flow direction.

Though some input arguments are natively vectorized their individual values all relate to common part of district heating network, i.e. associated with common object. It is due to isomorphism between vector representation and directed graph of this network. For more details of isomorphic topology description see m325testbench.

Before tracing starts for the next node, previously calculated values of thermal-hydraulic parameters are aggregated by either averaging or by median. The latter seems more robust for avoiding strong influence of possible outliers which may come from actual heating transfer anomalies, erroneous sensor readings or wrong pipeline specifications.

Aggregation for values of flow rate at the node is always sum.

Examples

library(pipenostics)

# It is possible to run without specification of argument values:
m325tracebw()
#> 
#> 2024-04-08 14:44:23.163179 m325tracebw | start backward tracing; segments 1;
#> 2024-04-08 14:44:23.163179 m325tracebw | start job; job 0;
#> 2024-04-08 14:44:23.163179 m325tracebw | now process; 1 node(s); [7]
#> 2024-04-08 14:44:23.163179 m325tracebw | seen tracing; [1/1] are TP-sensor-equipped;
#> 2024-04-08 14:44:23.163179 m325tracebw | tracing loss;;
#> 2024-04-08 14:44:23.163179 m325tracebw | OK! Specific heat loss power traced from 1 nodes;[7];
#> 2024-04-08 14:44:23.163179 m325tracebw | tracing heat flux;;
#> 2024-04-08 14:44:23.163179 m325tracebw | OK! Heat flux traced from 1 nodes;[7];
#> 2024-04-08 14:44:23.163179 m325tracebw | tracing heat loss per day;;
#> 2024-04-08 14:44:23.163179 m325tracebw | OK! Heat loss per day traced from 1 nodes;[7];
#> 2024-04-08 14:44:23.163179 m325tracebw | tracing temperature;;
#> 2024-04-08 14:44:23.163179 m325tracebw | OK! Temperature traced from 1 nodes;[7];
#> 2024-04-08 14:44:23.163179 m325tracebw | tracing pressure;;
#> 2024-04-08 14:44:23.163179 m325tracebw | OK! Pressure traced from 1 nodes;[7];
#> 2024-04-08 14:44:23.163179 m325tracebw | tracing flow_rate;;
#> 2024-04-08 14:44:23.163179 m325tracebw | finish job; job 0; processed node(s) 1
#> 2024-04-08 14:44:23.163179 m325tracebw | finish backward tracing;;
#>        node tracing backward aggregation loss     flux        Q temperature
#> 1         7  sensor     TRUE    identity 78.4 279.0696 136314.4          70
#> span      7  sensor     TRUE        span  0.0   0.0000      0.0           0
#> median    7  sensor     TRUE      median 78.4 279.0696 136314.4          70
#> mean      7  sensor     TRUE        mean 78.4 279.0696 136314.4          70
#>        pressure flow_rate job
#> 1      0.588399        20   0
#> span   0.000000        20   0
#> median 0.588399        20   0
#> mean   0.588399        20   0

# Consider isomorphic representation of District Heating Network graph:
DHN <- pipenostics::m325testbench

# * Adapt units:
DHN$d <- 1e3*DHN$d  # convert [m] to [mm]

# * Adapt node identifiers for ordering representation simplification:
DHN[["sender"]]   <- sprintf("N%02i", DHN[["sender"]])
DHN[["acceptor"]] <- sprintf("N%02i", DHN[["acceptor"]])

# * Provided actual values of specific heat loss power (say, field measurements) for each
#   pipe in DHN, [kcal/m/h]:
 actual_loss <- c(
               # acceptor:
      96.236,  #  1 
      96.288,  #  2
      70.584,  #  3
     116.045,  #  4
      70.734,  #  5
      96.211,  #  6
      78.400,  #  7
     116.016,  #  8
      28.115,  #  9
      24.918,  # 10
     116.679,  # 11
       0.000,  # 12, may be unmeasured!
     153.134,  # 13 
      96.733,  # 14 
      96.600,  # 15 
     116.667,  # 16
      24.960,  # 17
     115.923,  # 18
      28.166,  # 19
      96.123,  # 20
      77.824,  # 21
     115.946,  # 22
      70.690,  # 23
      96.184,  # 24
      96.236,  # 25
      70.540   # 26
 )

# * Remove inappropriate attributes of the graph:
DHN.1 <- DHN[, setdiff(colnames(DHN), c("year", "insulation", "laying", "beta", "exp5k"))]

# * Trace thermal-hydraulic regime for DHN:
tracebw_report <- do.call("tracebw", c(as.list(DHN.1), list(loss = actual_loss)))
#> 
#> 2024-04-08 14:44:23.186121 tracebw | start backward tracing; segments 26;
#> 2024-04-08 14:44:23.186121 tracebw | start job; job 0;
#> 2024-04-08 14:44:23.186121 tracebw | now process; 13 node(s); [N01,N02,N03,N07,N09,N10,N15,N17,N19,N21,N24,N25,N26]
#> 2024-04-08 14:44:23.186121 tracebw | seen tracing; [13/13] are TP-sensor-equipped;
#> 2024-04-08 14:44:23.186121 tracebw | tracing loss;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Specific heat loss power traced from 13 nodes;[N01,N02,N03,N07,N09,N10,N15,N17,N19,N21,N24,N25,N26];
#> 2024-04-08 14:44:23.186121 tracebw | tracing heat flux;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Heat flux traced from 13 nodes;[N01,N02,N03,N07,N09,N10,N15,N17,N19,N21,N24,N25,N26];
#> 2024-04-08 14:44:23.186121 tracebw | tracing heat loss per day;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Heat loss per day traced from 13 nodes;[N01,N02,N03,N07,N09,N10,N15,N17,N19,N21,N24,N25,N26];
#> 2024-04-08 14:44:23.186121 tracebw | tracing temperature;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Temperature traced from 13 nodes;[N01,N02,N03,N07,N09,N10,N15,N17,N19,N21,N24,N25,N26];
#> 2024-04-08 14:44:23.186121 tracebw | tracing pressure;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Pressure traced from 13 nodes;[N01,N02,N03,N07,N09,N10,N15,N17,N19,N21,N24,N25,N26];
#> 2024-04-08 14:44:23.186121 tracebw | tracing flow_rate;;
#> 2024-04-08 14:44:23.186121 tracebw | finish job; job 0; processed node(s) 13
#> 2024-04-08 14:44:23.186121 tracebw | start job; job 1;
#> 2024-04-08 14:44:23.186121 tracebw | now process; 5 node(s); [N04,N05,N14,N22,N23]
#> 2024-04-08 14:44:23.186121 tracebw | seen tracing; [5/5] are TP-sensor-equipped;
#> 2024-04-08 14:44:23.186121 tracebw | tracing loss;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Specific heat loss power traced from 5 nodes;[N04,N05,N14,N22,N23];
#> 2024-04-08 14:44:23.186121 tracebw | tracing heat flux;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Heat flux traced from 5 nodes;[N04,N05,N14,N22,N23];
#> 2024-04-08 14:44:23.186121 tracebw | tracing heat loss per day;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Heat loss per day traced from 5 nodes;[N04,N05,N14,N22,N23];
#> 2024-04-08 14:44:23.186121 tracebw | tracing temperature;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Temperature traced from 5 nodes;[N04,N05,N14,N22,N23];
#> 2024-04-08 14:44:23.186121 tracebw | tracing pressure;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Pressure traced from 5 nodes;[N04,N05,N14,N22,N23];
#> 2024-04-08 14:44:23.186121 tracebw | tracing flow_rate;;
#> 2024-04-08 14:44:23.186121 tracebw | finish job; job 1; processed node(s) 5
#> 2024-04-08 14:44:23.186121 tracebw | start job; job 2;
#> 2024-04-08 14:44:23.186121 tracebw | now process; 2 node(s); [N06,N20]
#> 2024-04-08 14:44:23.186121 tracebw | seen tracing; [2/2] are TP-sensor-equipped;
#> 2024-04-08 14:44:23.186121 tracebw | tracing loss;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Specific heat loss power traced from 2 nodes;[N06,N20];
#> 2024-04-08 14:44:23.186121 tracebw | tracing heat flux;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Heat flux traced from 2 nodes;[N06,N20];
#> 2024-04-08 14:44:23.186121 tracebw | tracing heat loss per day;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Heat loss per day traced from 2 nodes;[N06,N20];
#> 2024-04-08 14:44:23.186121 tracebw | tracing temperature;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Temperature traced from 2 nodes;[N06,N20];
#> 2024-04-08 14:44:23.186121 tracebw | tracing pressure;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Pressure traced from 2 nodes;[N06,N20];
#> 2024-04-08 14:44:23.186121 tracebw | tracing flow_rate;;
#> 2024-04-08 14:44:23.186121 tracebw | finish job; job 2; processed node(s) 2
#> 2024-04-08 14:44:23.186121 tracebw | start job; job 3;
#> 2024-04-08 14:44:23.186121 tracebw | now process; 2 node(s); [N08,N18]
#> 2024-04-08 14:44:23.186121 tracebw | seen tracing; [2/2] are TP-sensor-equipped;
#> 2024-04-08 14:44:23.186121 tracebw | tracing loss;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Specific heat loss power traced from 2 nodes;[N08,N18];
#> 2024-04-08 14:44:23.186121 tracebw | tracing heat flux;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Heat flux traced from 2 nodes;[N08,N18];
#> 2024-04-08 14:44:23.186121 tracebw | tracing heat loss per day;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Heat loss per day traced from 2 nodes;[N08,N18];
#> 2024-04-08 14:44:23.186121 tracebw | tracing temperature;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Temperature traced from 2 nodes;[N08,N18];
#> 2024-04-08 14:44:23.186121 tracebw | tracing pressure;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Pressure traced from 2 nodes;[N08,N18];
#> 2024-04-08 14:44:23.186121 tracebw | tracing flow_rate;;
#> 2024-04-08 14:44:23.186121 tracebw | finish job; job 3; processed node(s) 2
#> 2024-04-08 14:44:23.186121 tracebw | start job; job 4;
#> 2024-04-08 14:44:23.186121 tracebw | now process; 2 node(s); [N11,N16]
#> 2024-04-08 14:44:23.186121 tracebw | seen tracing; [2/2] are TP-sensor-equipped;
#> 2024-04-08 14:44:23.186121 tracebw | tracing loss;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Specific heat loss power traced from 2 nodes;[N11,N16];
#> 2024-04-08 14:44:23.186121 tracebw | tracing heat flux;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Heat flux traced from 2 nodes;[N11,N16];
#> 2024-04-08 14:44:23.186121 tracebw | tracing heat loss per day;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Heat loss per day traced from 2 nodes;[N11,N16];
#> 2024-04-08 14:44:23.186121 tracebw | tracing temperature;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Temperature traced from 2 nodes;[N11,N16];
#> 2024-04-08 14:44:23.186121 tracebw | tracing pressure;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Pressure traced from 2 nodes;[N11,N16];
#> 2024-04-08 14:44:23.186121 tracebw | tracing flow_rate;;
#> 2024-04-08 14:44:23.186121 tracebw | finish job; job 4; processed node(s) 2
#> 2024-04-08 14:44:23.186121 tracebw | start job; job 5;
#> 2024-04-08 14:44:23.186121 tracebw | now process; 1 node(s); [N13]
#> 2024-04-08 14:44:23.186121 tracebw | seen tracing; [1/1] are TP-sensor-equipped;
#> 2024-04-08 14:44:23.186121 tracebw | tracing loss;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Specific heat loss power traced from 1 nodes;[N13];
#> 2024-04-08 14:44:23.186121 tracebw | tracing heat flux;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Heat flux traced from 1 nodes;[N13];
#> 2024-04-08 14:44:23.186121 tracebw | tracing heat loss per day;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Heat loss per day traced from 1 nodes;[N13];
#> 2024-04-08 14:44:23.186121 tracebw | tracing temperature;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Temperature traced from 1 nodes;[N13];
#> 2024-04-08 14:44:23.186121 tracebw | tracing pressure;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Pressure traced from 1 nodes;[N13];
#> 2024-04-08 14:44:23.186121 tracebw | tracing flow_rate;;
#> 2024-04-08 14:44:23.186121 tracebw | finish job; job 5; processed node(s) 1
#> 2024-04-08 14:44:23.186121 tracebw | start job; job 6;
#> 2024-04-08 14:44:23.186121 tracebw | now process; 1 node(s); [N12]
#> 2024-04-08 14:44:23.186121 tracebw | seen tracing; [1/1] are TP-sensor-equipped;
#> 2024-04-08 14:44:23.186121 tracebw | tracing loss;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Specific heat loss power traced from 1 nodes;[N12];
#> 2024-04-08 14:44:23.186121 tracebw | tracing heat flux;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Heat flux traced from 1 nodes;[N12];
#> 2024-04-08 14:44:23.186121 tracebw | tracing heat loss per day;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Heat loss per day traced from 1 nodes;[N12];
#> 2024-04-08 14:44:23.186121 tracebw | tracing temperature;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Temperature traced from 1 nodes;[N12];
#> 2024-04-08 14:44:23.186121 tracebw | tracing pressure;;
#> 2024-04-08 14:44:23.186121 tracebw | OK! Pressure traced from 1 nodes;[N12];
#> 2024-04-08 14:44:23.186121 tracebw | tracing flow_rate;;
#> 2024-04-08 14:44:23.186121 tracebw | finish job; job 6; processed node(s) 1
#> 2024-04-08 14:44:23.186121 tracebw | finish backward tracing;;

# * If the actual values of specific heat loss power presented above are close 
#   to those in Minenergo-325, then the results of regime tracing match the 
#   normative procedure:
m325_report <- do.call("m325tracebw", DHN)
#> 
#> 2024-04-08 14:44:23.273599 m325tracebw | start backward tracing; segments 26;
#> 2024-04-08 14:44:23.273599 m325tracebw | start job; job 0;
#> 2024-04-08 14:44:23.273599 m325tracebw | now process; 13 node(s); [N01,N02,N03,N07,N09,N10,N15,N17,N19,N21,N24,N25,N26]
#> 2024-04-08 14:44:23.273599 m325tracebw | seen tracing; [13/13] are TP-sensor-equipped;
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing loss;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Specific heat loss power traced from 13 nodes;[N01,N02,N03,N07,N09,N10,N15,N17,N19,N21,N24,N25,N26];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing heat flux;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Heat flux traced from 13 nodes;[N01,N02,N03,N07,N09,N10,N15,N17,N19,N21,N24,N25,N26];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing heat loss per day;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Heat loss per day traced from 13 nodes;[N01,N02,N03,N07,N09,N10,N15,N17,N19,N21,N24,N25,N26];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing temperature;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Temperature traced from 13 nodes;[N01,N02,N03,N07,N09,N10,N15,N17,N19,N21,N24,N25,N26];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing pressure;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Pressure traced from 13 nodes;[N01,N02,N03,N07,N09,N10,N15,N17,N19,N21,N24,N25,N26];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing flow_rate;;
#> 2024-04-08 14:44:23.273599 m325tracebw | finish job; job 0; processed node(s) 13
#> 2024-04-08 14:44:23.273599 m325tracebw | start job; job 1;
#> 2024-04-08 14:44:23.273599 m325tracebw | now process; 5 node(s); [N04,N05,N14,N22,N23]
#> 2024-04-08 14:44:23.273599 m325tracebw | seen tracing; [5/5] are TP-sensor-equipped;
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing loss;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Specific heat loss power traced from 5 nodes;[N04,N05,N14,N22,N23];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing heat flux;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Heat flux traced from 5 nodes;[N04,N05,N14,N22,N23];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing heat loss per day;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Heat loss per day traced from 5 nodes;[N04,N05,N14,N22,N23];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing temperature;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Temperature traced from 5 nodes;[N04,N05,N14,N22,N23];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing pressure;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Pressure traced from 5 nodes;[N04,N05,N14,N22,N23];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing flow_rate;;
#> 2024-04-08 14:44:23.273599 m325tracebw | finish job; job 1; processed node(s) 5
#> 2024-04-08 14:44:23.273599 m325tracebw | start job; job 2;
#> 2024-04-08 14:44:23.273599 m325tracebw | now process; 2 node(s); [N06,N20]
#> 2024-04-08 14:44:23.273599 m325tracebw | seen tracing; [2/2] are TP-sensor-equipped;
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing loss;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Specific heat loss power traced from 2 nodes;[N06,N20];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing heat flux;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Heat flux traced from 2 nodes;[N06,N20];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing heat loss per day;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Heat loss per day traced from 2 nodes;[N06,N20];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing temperature;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Temperature traced from 2 nodes;[N06,N20];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing pressure;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Pressure traced from 2 nodes;[N06,N20];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing flow_rate;;
#> 2024-04-08 14:44:23.273599 m325tracebw | finish job; job 2; processed node(s) 2
#> 2024-04-08 14:44:23.273599 m325tracebw | start job; job 3;
#> 2024-04-08 14:44:23.273599 m325tracebw | now process; 2 node(s); [N08,N18]
#> 2024-04-08 14:44:23.273599 m325tracebw | seen tracing; [2/2] are TP-sensor-equipped;
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing loss;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Specific heat loss power traced from 2 nodes;[N08,N18];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing heat flux;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Heat flux traced from 2 nodes;[N08,N18];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing heat loss per day;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Heat loss per day traced from 2 nodes;[N08,N18];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing temperature;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Temperature traced from 2 nodes;[N08,N18];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing pressure;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Pressure traced from 2 nodes;[N08,N18];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing flow_rate;;
#> 2024-04-08 14:44:23.273599 m325tracebw | finish job; job 3; processed node(s) 2
#> 2024-04-08 14:44:23.273599 m325tracebw | start job; job 4;
#> 2024-04-08 14:44:23.273599 m325tracebw | now process; 2 node(s); [N11,N16]
#> 2024-04-08 14:44:23.273599 m325tracebw | seen tracing; [2/2] are TP-sensor-equipped;
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing loss;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Specific heat loss power traced from 2 nodes;[N11,N16];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing heat flux;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Heat flux traced from 2 nodes;[N11,N16];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing heat loss per day;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Heat loss per day traced from 2 nodes;[N11,N16];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing temperature;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Temperature traced from 2 nodes;[N11,N16];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing pressure;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Pressure traced from 2 nodes;[N11,N16];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing flow_rate;;
#> 2024-04-08 14:44:23.273599 m325tracebw | finish job; job 4; processed node(s) 2
#> 2024-04-08 14:44:23.273599 m325tracebw | start job; job 5;
#> 2024-04-08 14:44:23.273599 m325tracebw | now process; 1 node(s); [N13]
#> 2024-04-08 14:44:23.273599 m325tracebw | seen tracing; [1/1] are TP-sensor-equipped;
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing loss;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Specific heat loss power traced from 1 nodes;[N13];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing heat flux;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Heat flux traced from 1 nodes;[N13];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing heat loss per day;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Heat loss per day traced from 1 nodes;[N13];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing temperature;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Temperature traced from 1 nodes;[N13];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing pressure;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Pressure traced from 1 nodes;[N13];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing flow_rate;;
#> 2024-04-08 14:44:23.273599 m325tracebw | finish job; job 5; processed node(s) 1
#> 2024-04-08 14:44:23.273599 m325tracebw | start job; job 6;
#> 2024-04-08 14:44:23.273599 m325tracebw | now process; 1 node(s); [N12]
#> 2024-04-08 14:44:23.273599 m325tracebw | seen tracing; [1/1] are TP-sensor-equipped;
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing loss;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Specific heat loss power traced from 1 nodes;[N12];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing heat flux;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Heat flux traced from 1 nodes;[N12];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing heat loss per day;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Heat loss per day traced from 1 nodes;[N12];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing temperature;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Temperature traced from 1 nodes;[N12];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing pressure;;
#> 2024-04-08 14:44:23.273599 m325tracebw | OK! Pressure traced from 1 nodes;[N12];
#> 2024-04-08 14:44:23.273599 m325tracebw | tracing flow_rate;;
#> 2024-04-08 14:44:23.273599 m325tracebw | finish job; job 6; processed node(s) 1
#> 2024-04-08 14:44:23.273599 m325tracebw | finish backward tracing;;

stopifnot(
   all.equal(tracebw_report$temperature, m325_report$temperature, tolerance = 1e-4),
   all.equal(tracebw_report$pressure   , m325_report$pressure   , tolerance = 1e-4),
   all.equal(tracebw_report$flow_rate  , m325_report$flow_rate  , tolerance = 1e-4)
  )