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Mass conservation model in coffee brewing

New study on the mass conservation model in pour-over coffee brewing

Brew ratio does not capture the full process: The 2026 model simulates water flow paths in pour-over

A pour-over recipe is typically described by a few numbers: 20 g of coffee, 300 g of water, a 1:15 ratio, medium grind size, and a brew time of about three minutes. These details help others replicate the recipe, but they do not reveal what is happening within the coffee bed as water flows through.

How does water move through the voids between ground coffee particles? How much water is retained in the coffee bed? How are solubles released over time? Why do two brews with the same coffee and water amounts yield different flow times, TDS, and beverage masses?

A study published in npj Science of Food on 15/08/2026 addressed these questions using a mathematical model constrained by mass conservation.

Brewing recipes describe inputs, not the entire process dynamics

When recording a pour-over recipe, brewers typically note directly observable parameters:

These parameters define how a batch of coffee is brewed. However, they do not directly describe the amount of water present in the coffee bed at any given moment, the amount of solubles remaining in the grounds, or the amount extracted into the final beverage.

Three categories of variables must be distinguished:

Category Example Significance
Inputs Dose, water volume, grind size, pouring schedule Operating conditions of the recipe
Measured outputs Drawdown time, beverage mass, TDS Results can be weighed or measured after brewing
Internal state Water retained in the coffee bed, dissolved solids over time Dynamics are reconstructed by the model, not necessarily measured directly

How does the mass conservation model work?

During pour-over, water is poured onto the ground coffee layer. Part of it moves through the voids between particles, part is retained within the structure of the coffee bed, and part exits the brewer to become the beverage.

Alongside the water flow, soluble compounds are released from the coffee particles into the liquid phase. They may continue to move within the coffee bed before exiting with the extracted liquor.

Physically, this process can be described by the following balances:

The key point is that these quantities are not independent. Drawdown time, beverage mass, and TDS all reflect the same ongoing transport and extraction processes within the coffee bed.

Sơ đồ khái niệm mô hình chiết xuất pour-over Nước và cà phê xay đi vào lớp cà phê. Nước được giữ lại một phần, chất hòa tan được giải phóng và một phần chất lỏng đi xuống bình chứa. Mô hình tái dựng các trạng thái theo thời gian. Đầu vào Dose · Nước · Lịch rót Lớp cà phê Dòng nước · Hòa tan Đầu ra đo được Thời gian · Khối lượng · TDS Trạng thái được tái dựng Nước giữ lại · Chất hòa tan Diễn biến theo thời gian Sơ đồ khái niệm, không phải dữ liệu đo thực nghiệm.
The model links recipe parameters to measured outputs and reconstructs internal states of the coffee bed over time.

What was the prediction error achieved in the 2026 study?

Lee and Chang developed a reduced-order model based on conservation laws. First, the research team conducted controlled brewing trials with coarse, medium, and fine particle size distributions. Effective parameters were estimated from these brews and then held constant to predict two conditions not used in the estimation step: medium-coarse and medium-fine.

For these two test conditions, the reported mean absolute error was:

Predicted quantity Mean absolute error
Drawdown time 6.7 seconds
Beverage mass 0.58 g
TDS 0.020 percentage points

All six predicted output values for the two test conditions fell within one standard deviation of the corresponding experimental values. This is a notable result because the model can predict measured outputs from recipe parameters and previously determined effective quantities.

However, the scope of testing remains limited to the specific grind conditions and brewing systems investigated. This error margin cannot be regarded as a guarantee that the model will accurately predict outcomes for every dripper, filter paper type, water source, or coffee variety.

Why can a 1:15 ratio still yield different results?

The brew ratio only describes the correlation between the mass of coffee and the input water. It does not indicate the pouring rhythm into the coffee bed, the amount of water retained within the coffee bed, or the rate at which solubles are extracted.

Consider two recipes both using 20 g of coffee and 300 g of water. One recipe may divide the water into multiple pours with long intervals; the other may involve continuous pouring or fewer pours.

Although the total water volume is identical, the pouring schedule can alter when water contacts different zones within the coffee bed. Grind size and coffee bed structure also affect flow resistance, water retention, and the contact time between water and the material.

Therefore, the same brew ratio does not necessarily result in the same drawdown time, beverage yield, or TDS. This is why the brew ratio should be viewed as an important input parameter, but not a complete description of the extraction process.

TDS and extraction yield are not the same quantity.

TDS indicates the proportion of dissolved solids in the beverage. Extraction yield describes the amount of solubles obtained relative to the initial dry coffee mass.

In the common calculation:

Extraction yield (%) = Beverage mass × TDS / Dry coffee mass

In this formula, TDS must be used as a decimal fraction. For example, 1.30% is entered as 0.013.

Two brews may have similar TDS but different beverage yields, leading to different extraction yields. Conversely, two brews with similar extraction yields can produce different beverage concentrations if the water output differs.

This is why evaluating a recipe based solely on TDS or solely on brew time can overlook significant differences.

The model was applied to 53 publicly available pour-over recipes.

Following the controlled experiments, the research team applied the modeling framework to 53 publicly published pour-over coffee recipes.

In this section, it is essential to distinguish between observed data and model results. The total brew time reported in the recipes is the only observed output directly compared with the drawdown time calculated by the model. Quantities such as beverage composition and the amount of solubles within the coffee bed are presented as conditional computational results, not as independent experimental measurements for all 53 recipes.

The authors themselves explicitly state that the model has not directly validated internal states nor demonstrated general predictive capability across diverse brewing systems.

This does not diminish the value of the study. It correctly identifies the current role of the model: a physico-mathematical tool that links recipe data to measurable outputs while generating quantitative hypotheses about internal dynamics within the coffee bed.

Best practices for recording pour-over data to improve batch control.

Even without using a mathematical model, brewers can improve reproducibility by recording data in a more comprehensive structure.

When conducting experiments, keep most parameters constant and change only one variable per test sequence. If you simultaneously alter grind size, pour profile, temperature, and filter paper, it becomes difficult to determine which factor caused the difference.

The value of Lee and Chang’s research lies in shifting the brewing process from a static recipe to a time-evolving system. While a 1:15 ratio remains useful, understanding why a brew flows quickly or slowly, or tastes strong or weak, requires a deeper look at how water and dissolved solids move through the coffee bed.

Read more about extraction and brewing knowledge at SAVINA Coffee Knowledge.

References

  1. Lee, H. S. & Chang, B.-Y. (2026). Coffee brewing trajectories from recipe-level records: a conservation-constrained framework for filter coffee. npj Science of Food. Published 15 August 2026. https://doi.org/10.1038/s41538-026-01074-1
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