A process flow diagram (PFD) was constructed to represent the complete coffee preparation process, beginning with green coffee beans and cold water as inputs and ending with brewed coffee, spent grounds, and chaff as outputs. The PFD identifies roasting, grinding, and brewing as the primary unit operations and tracks the flow of mass through each step.
Volume of green, unroasted beans
Volume of roasted beans
Photographs of the coffee beans before and after roasting show a clear visual expansion of the beans accompanied by a color change characteristic of a light roast. Quantitatively, the volume increased from 90 mL (green beans) to 145 mL (roasted beans), corresponding to a percent volume increase of approximately 61%. This expansion is consistent with internal gas formation within the bean during roasting.
# -------------------------------# Input measured data# -------------------------------# Mass of dry coffee grounds (g)grounds_g <-c(29.8, 20.0, 10.2)# Mass of carafe with brewed coffee (g)carafe_with_coffee_g <-c(431.2, 456.3, 464.9)# Mass of empty carafe (g)empty_carafe_g <-193.0# -------------------------------# Calculate mass of brewed coffee# -------------------------------brewed_coffee_g <- carafe_with_coffee_g - empty_carafe_g# -------------------------------# Create data frame# -------------------------------brew_data <-data.frame(grounds_g = grounds_g,brewed_coffee_g = brewed_coffee_g)# -------------------------------# Linear regression# -------------------------------fit <-lm(brewed_coffee_g ~ grounds_g, data = brew_data)slope <-coef(fit)[2]absorption_ratio <--slope# -------------------------------# Plot with line of best fit# -------------------------------plot( brew_data$grounds_g, brew_data$brewed_coffee_g,xlab ="Mass of Dry Coffee Grounds (g)",ylab ="Mass of Brewed Coffee (g)",main ="Brewed Coffee Mass vs. Coffee Grounds",pch =16)abline(fit)
# -------------------------------# Output slope and absorption ratio# -------------------------------cat("Slope of best-fit line (g brewed coffee / g grounds):", slope, "\n")
Slope of best-fit line (g brewed coffee / g grounds): -1.719388
cat("Absorption ratio (−slope):", absorption_ratio, "\n")
Absorption ratio (−slope): 1.719388
The absorption ratio determined from the linear regression of brewed coffee mass versus dry coffee grounds was found to be 1.72 g water absorbed per g dry coffee. This value indicates that a substantial fraction of the input water is retained by the spent grounds rather than recovered as drinkable coffee.
Using this absorption ratio, a brew starting with 600 g of cold water and 50 g of coffee grounds would be expected to lose approximately 86 g of water to absorption by the grounds. The predicted mass of drinkable coffee produced is therefore 514 g. This calculation assumes that water losses other than absorption are negligible.
Comparison of the total water input to the measured mass of brewed coffee suggests that water loss to steam during brewing was minimal. Within experimental uncertainty, evaporation did not contribute significantly to mass loss.
During roasting, the mass of the coffee beans decreased from 60 g to 51.2 g, corresponding to a mass loss of approximately 9 g. Of this loss, 0.3 g was collected as chaff, representing about 3.3% of the total mass lost during roasting. The remaining mass loss is attributed primarily to the release of carbon dioxide, water vapor, and volatile organic compounds generated by thermal decomposition and Maillard reactions within the beans.
These results would not be expected to be identical for darker roasts. Darker roasting conditions generally lead to greater mass loss due to increased devolatilization and more extensive structural breakdown. As a result, darker roasts would likely exhibit higher mass loss during roasting and potentially different absorption behavior during brewing.
