Espresso Physics
By PetroRes Consulting
December, 2025
Your morning coffee
People indulging in their morning coffee may not know what it takes to make the best espresso shot. It falls upon skilled baristas to use precise techniques to extract the perfect flavor. These techniques surprisingly are grounded (no pun intended) on the same physics that petrophysicists and reservoir engineers use. These physics of fluid flow, pressure and temperature are instrumental in extracting the black stuff, whether it happens to be coffee or oil.
Espresso and the Darcy Connection
Darcy’s Law governs the movement of fluids through porous materials. This applies to coffee pucks too!
In this famous equation, Q is defined as flow rate, k permeability, A cross-sectional area, ΔP pressure differential, μ viscosity, and L flow length. Replace “core” with “coffee puck” and “reservoir fluid” with “hot water” — what follows is a functional espresso model not much different from a core permeameter setup. Petrophysicists and reservoir engineers with their knowledge of fluid dynamics can appreciate how variables like permeability, temperature, and pressure can drastically alter outcomes.
A well-pulled espresso shot serves as a practical demonstration of Darcy’s equation. For instance, a 25-second shot at a flow rate of 1.4 mL/s producing 35 mL total volume reflects an effective permeability around 5 milliDarcies (mD), comparable to fine-grained sandstone. Controlling the flow rate, temperature, pressure and permeability is essential in coffee brewing, significantly influencing the quality and taste of the coffee that is made.
The Crema: The delicate balance of pressure, flow, and contact time
Crema, the rich foam crowning an espresso shot, isn’t just about aesthetics; it’s a trademark of a well-crafted shot and represents the harmony of pressure, temperature, and fluid flow. Under the right temperature and pressure conditions, carbon dioxide and coffee oils emulsify to produce a foam known as crema. Crema carries aromatic compounds and completely changes the mouthfeel and taste of espresso.
Poor crema is often caused by incorrect pressure and extraction time. Many consumer espresso machines operate with a fixed-rate pump, so the barista cannot control Q. In this situation, more pressure does not improve extraction. It simply forces water through the puck too aggressively and reduces contact time.
Trying to fix this by grinding finer often makes the problem worse. When particle size decreases: the grounds hydrate and swell, permeability k decreases during extraction, and with a fixed and high Q, the system responds with an increase in ΔP (over-extraction). This behavior causes rapid extraction of acids at the start, followed by the release of bitter compounds. Crema breaks down, and the shot loses balance.
Pre-ground coffee used in a non-pressurized basket experiences the opposite issue. High k and low ΔP cause the water to pass through too quickly, resulting in minimal crema and weak flavor. Many pre-ground bricks of “espresso” actually fall somewhere in the grind range of fine to medium-fine so they are usable in Moka pots.
The goal here is not maximum pressure, but the right combination of Q, k and contact time to let the coffee oils emulsify and form a stable crema. The barista should aim for 25-30 seconds of extraction time at 6-9 bar and 90-95 °C to optimize dissolving CO₂ and oils.
Figure 1: Grind Size Impact on Permeability k, and Pressure (ΔP) under fixed Flow Rate (Q)
The Flavor: Balanced shots with crema also taste the best
During the extraction process the first 15 seconds produce acids, caffeine, sugars, and CO₂. If your extraction is only during this period, the coffee flavor is sour, bright and thin. The next 15 seconds generate balanced oils, more sugars and the remaining CO₂. If you’ve made it this far, you now have a thick, rich, reddish-brown crema and a sweet, balanced, and full-bodied espresso. Keep going another 15s+ and you’ll extract bitter tannins and astringents. The emulsification process now breaks down, and you wind up with poor crema and a bitter coffee. What is your recovery factor? In the case of good coffee, you may not want it to be too high!
Figure 2: Perfect Espresso with optimal extraction taste and appearance
Expensive commercial espresso machines with manual flow-control valves allow baristas to adjust the crucial parameter, Q to extract espresso at the right pressure over the correct amount of time. Tuning the temperature and permeability alone is just not enough to get the flavor, body, and balance in a good shot.
Side Bar: Espresso Machine thoughts…
We at PetroRes have been experimenting lately with different types of equipment to see what capabilities these machines have. This is what we learned:
- Semi-automatic electric machines in the $100-1000 price range, even the beloved Breville Bambino, etc. have fixed rate pumps and no way to control flow rate. They are all equivalent with minor differences in features, e.g., grinder availability, pre-infusion programming, temperature control, etc. Some have better equipment/components or boilers, but you won’t be controlling flow rate from the factory. Mostly these are designed to distract you with a flashy housing or fancy-looking setups with gauges and dials.
- There are ways that you CAN control flow rate with these machines, but it requires either installing a valve between the boiler and group head or trying to modify the pump circuit with a phase controller (chopper-or “dimmer switch”) to try and slow the pump rate down.
- Although they look nice on your bench and require less work and cleanup, they produce poor-quality coffee and are the worst value option. Ditch the semi-auto electric machine and save your money if you want good espresso.
- Lever-style machines such as a Flair Classic do the job properly. Some of the more expensive ones like the La Pavoni Europiccola has an integrated boiler and standard portafilter as well which is more convenient. In the case of the Flair Classic and lower-cost options, they require pre-heating and puck preparation that takes some time and is quite messy. The Flair Classic is also very sensitive to grind and has non-standard sized equipment (i.e., 40mm baskets and dispersion screens).
- Recommended here to pay the extra money and get a unit with a standard portafilter which makes preparation and cleanup so much easier, such as the La Pavoni or Flair 58.
- Hand-pump machines like the product offerings from Wacaco really blew us away. We have been using a Wacaco GR2 for over a year now and producing some of the best shots of espresso we’ve ever seen. The user can fully control the pump rate and the machine produces exceptional shots even with a range of acceptable grind sizes (from about Moka to just above an Espresso grind—i.e., you can use store bought pre-ground coffee) due to a small spring-loaded valve on the outlet port. If you grind too fine, it will lock the pump up and you’ll need to let the body cool before you can remove the head, empty it out and try again. Too coarse of coffee and you get poor quality shots.
- This is our favorite low-cost option. It is highly portable and comes with the same mess and prep/cleanup issues as the Flair Classic style presses.
Commercial grade machines with manual flow control valves are obviously the best. These have good equipment and components, but are prohibitively expensive for some, not portable, and quite large.
Due to the labor and mess with prep/cleanup and pre-heating, if you wanted the least expensive option for the best coffee, we would highly recommend one of the Wacaco hand-held products as they are cheaper and easier to use than a Flair Classic.
Our overall pick though for the serious espresso enthusiast would be a machine like the La Pavoni Europiccola where you have the integrated boiler and portafilter. Here your rig up and rig down is minimal, yet the most important feature of the machine (as it should be) is staring you right in the face—that manual lever to control flow rate. It also is not terribly more expensive than a Flair 58, which lacks the boiler. Henry Darcy would most certainly have one of these in his kitchen.
From coffee cups to petrophysical workflows
An espresso shot is not just coffee; it serves as a small-scale experiment in multi-phase flow. When hot water is forced through finely ground coffee under high pressure, three distinct phases interact under pressure within the coffee puck:
- Water: Acts as the injection fluid moving through the pore network.
- Coffee oils: Contain the organic compounds dissolved and carried by the water.
- Carbon dioxide: Released during brewing from gas trapped in roasted coffee.
These phases flow, mix, and separate dynamically, influenced by principles like relative permeability, capillary pressure, wettability, and surfactant effects. Issues with improper puck preparation can result in tortuosity, channeling and viscous fingering. The swelling of fine coffee particles during extraction parallels clay swelling in reservoirs. Uneven grinds can also produce a distribution of coffee particle sizes, and when the small ones migrate, they can parallel fines migration.
This makes espresso a very intuitive way to “see” the same physics that govern flow in subsurface reservoirs – simply scaled down and served in a cup.
The parallels do not stop here… Just like creating the best possible espresso requires in-depth knowledge of physical processes, skill and the right equipment, so does creating the best petrophysical interpretations.
If a barista uses the equivalent of a cheap store-bought espresso machine and pressurized portafilter baskets this is pretty analogous to a petrophysicist using store bought petrophysical software and workflows.
Properly preparing your log data with the right software and workflow is like setting up and tuning your equipment with a specific type of coffee and grinder to produce the perfect crema. These parameters change when you change reservoirs or coffee beans!
Using more advanced machine learning software (i.e. PetroRes ML) is like using a higher-end espresso machine that allows the user to have more control. Better data = better log interpretations! Just like that high-end espresso machine our software has all the controls to quantitatively evaluate and select the best training data, perform an in-depth assessment of model results (error), and visualize them (generate maps).
What does the crema on your logs look like?
