In blongworth/HybridGIS: Data, Functions, and Analysis for the NOSAMS Hybrid Gas Ion Source

Calculate concentration of CO2 in a vial/effluent when introducing helium as a displacement gas.

library(tidyverse)
library(HybridGIS)

I think this can be solved with ODE:

Change in volume of helium over time...

$$ C^\prime(t) = r - \frac{r}{V}C(t) $$

Add some math...

$$ C(t) = V(1-e^{-\frac{r}{V}t}) $$

The fraction of CO2 in the effluent should be:

$$ C(t) = e^{-\frac{r}{V}t} $$

Put this into functions. Main function moved to HGISFunctions.R and documented there.

Function definition:

concCO2

Helper function to calculate fraction/flow of helium:

concHe <- function(t, ...) {
  1 - concCO2(t)
}

Plotted as fraction of CO2 and helium

data.frame(x = 0:400) %>% 
  ggplot(aes(x)) +
  stat_function(fun=concCO2, aes(color = "CO2")) +
  stat_function(fun=concHe, aes(color = "Helium")) +
  scale_color_manual("Gas", values = c("green", "blue")) +
  labs(title = "Concentration of CO2 and Helium in vial over time",
       subtitle = "7mL vial, 100uL/min helium",
       x = "Time (min)",
       y = "Concentration (fractional)")

OK, what's the rate of flow of CO2 over time, in the effluent, and in a capillary taking Q/t ul/m?

If the vial is 7mL, flowing at 20ul/m and sampling 10ul/m with the open split, CO2 ul/m looks like:

data.frame(x = 0:400) %>% 
  ggplot(aes(x)) +
  stat_function(fun=function(x) concCO2(x, r = 20, flow = 10), aes(color = "CO2")) +
  stat_function(fun=function(x) 10 - concCO2(x, r = 20, flow = 10), aes(color = "Helium")) +
  scale_color_manual("Gas", values = c("green", "blue")) +
  labs(title = "Flow of CO2 to source over time",
       subtitle = "7mL vial, 20uL/min helium, 10uL/min to source",
       x = "Time (min)",
       y = "Flow (uL/min)")

Takes about 250 min to drop from 10 to 5 uL/min CO2.

High dillution

Model case of small amount of CO2 in He in vial. Requires higher capillary flow to source to maintain ~5uL/min CO2 to source in helium. This also requires higher displacement flow to maintain split ratio.

Flows are 200uL/min of displacement helium, and 100uL/min delivered to source. Aiming for 5uL/min CO2 to source.

Full plot starting at 100% CO2 in 7mL vial. Working on adding initial CO2 concentration in vial to concCO2(), but for now, use different start time to same effect.

data.frame(x = 0:400) %>% 
  ggplot(aes(x)) +
  stat_function(fun=function(x) concCO2(x, r = 200, flow = 100), aes(color = "CO2")) +
  stat_function(fun=function(x) 100 - concCO2(x, r = 200, flow = 100), aes(color = "Helium")) +
  scale_color_manual("Gas", values = c("green", "blue")) +
  labs(title = "Flow of CO2 to source over time",
       subtitle = "7mL vial, 0.2mL/min helium, 100uL/min to source",
       x = "Time (min)",
       y = "Flow (uL/min)")

Zooming in on flows around 5uL/min CO2 to source in 100uL/min He...

data.frame(x = 75:150) %>% 
  ggplot(aes(x)) +
  stat_function(fun=function(x) concCO2(x, r = 200, flow = 100), aes(color = "CO2")) +
  labs(title = "Flow of CO2 to source over time",
       subtitle = "7mL vial, 0.2mL/min helium, 100uL/min to source",
       x = "Time (min)",
       y = "Flow (uL/min)") +
  scale_color_manual("Gas", values = c("green", "blue")) +
  xlim(50, 450) +
  ylim(0, 10)

Takes about 50 min to drop from 10 to 5 uL/min CO2.

Dilution results in higher rate of change of CO2 entering source.

blongworth/HybridGIS documentation built on Dec. 19, 2021, 10:41 a.m.