How to Translate Easily | Marine Sediment Permeability Explained

The first distinction: permeability is not a universal flow speed

Marine sediment permeability describes how easily fluid can pass through connected pore space under specified conditions. To translate a marine sediment permeability report accurately, distinguish intrinsic permeability, often represented by κ with units of square metres, from hydraulic conductivity, often K with units of metres per second. The terms are related but they are not the same quantity. The intrinsic property describes the porous framework in Darcy-type flow, while hydraulic conductivity also depends on the fluid’s density and dynamic viscosity. Confusing the two can produce numerical errors of several orders of magnitude and can make comparisons between laboratories meaningless.

A second distinction is between flow rate, specific discharge and actual average movement through pores. A pump delivering a measured volume per time gives a volumetric rate, usually Q in cubic metres per second. Dividing Q by the specimen’s full cross-sectional area gives a Darcy flux or specific discharge in metres per second. That value is not generally the same as average velocity through connected pore space, because water occupies only part of the cross-section and flow paths are tortuous. A report must state which of these variables a figure contains. A neat number without its denominator or fluid conditions is incomplete evidence.

Marine sediment is also variable across small distances and orientations. Laminated mud, sand-rich seams, burrows, fractured clay and cemented layers may have very different flow characteristics. Testing a centimetre-scale core plug under imposed confining stress does not automatically determine the field-scale permeability of an entire coastal basin. The aim of this guide is to show how the measurements work and how to read them without inventing hidden certainty. All worked numeric cases are hypothetical teaching problems, not observations from an offshore site.

From pore geometry to Darcy’s law

Sediment grains form a framework with voids and connected passages that carry pore fluid. Two samples can have similar overall porosity but different permeability if their pore-throat sizes, connectivity or tortuosity differ. Clay-rich material can retain considerable water while transmitting it slowly, whereas interconnected coarse pores can permit more flow at the same driving gradient. Microfractures may contribute disproportionately to laboratory flow and may not survive or persist under field stress. This is why porosity alone cannot determine hydraulic conductivity. A good interpretation considers the pore network and stress-dependent fabric.

Darcy’s law describes the approximate proportionality between specific discharge and hydraulic gradient for appropriate saturated, laminar flow conditions. In one dimension, q = −K dh/dl, with q in metres per second and h the hydraulic head. The minus sign records flow down the head gradient. Hydraulic gradient itself is dimensionless because it is a head difference divided by a length. The equation is not a promise that all fluid motion is linear at arbitrary velocities or that every fractured, reactive or multiphase specimen follows the same relation. Its assumptions should be checked where the inference matters.

For a uniform specimen of length L, area A, a maintained head difference Δh and a collected flow volume V over time t, a simple constant-head reduction is K = V L/(A Δh t). The dimensions verify the result: cubic metres times metres divided by square metres times metres times seconds gives metres per second. A valid use also assumes that steady conditions were reached and that flow bypassing the sample, leakage and changes in head are properly controlled. The mathematics is short; the quality assessment of the test takes more care.

Worked calculation: a constant-head example

Consider an invented saturated specimen 0.020 m long with cross-sectional area 0.0020 m². Under a maintained head difference of 0.25 m, it transmits 0.72 mL of water in 86,400 seconds, one day. Convert 0.72 mL to 7.2 × 10^-7 m³. In the simple equation, K = (7.2 × 10^-7 × 0.020)/(0.0020 × 0.25 × 86,400), which is approximately 3.33 × 10^-10 m/s. That is a hypothetical result for teaching. The calculation does not tell us whether the low measured flow was truly steady, whether the specimen leaked or whether the head was accurately maintained.

A student might mistakenly treat 0.72 mL as 0.72 cubic metres, making K a million times too large. Another might use 24 rather than 86,400 seconds, confusing a day with twenty-four seconds. Dimensional checks expose both mistakes when the conversions are written beside the equation. A well-presented laboratory report gives the measured volumes and durations, not only the final hydraulic conductivity. Readers can then check the arithmetic and recognize the magnitude of the flow involved. At very small flow rates, leakage and fluid-system compliance can become particularly important relative to the signal.

Now suppose the laboratory reports a second result at a higher confining effective stress. The conductivity drops. That change could be a genuine stress-dependent narrowing of pore throats; it might also reflect experimental transients, altered saturation or apparatus changes. Rather than treating the two figures as fixed material constants, the reader should note the pressure conditions and whether equilibrium was attained at each step. In compacting marine mud, reporting conductivity without effective stress is often less informative than reporting the full relationship.

Intrinsic permeability and hydraulic conductivity

Intrinsic permeability κ has units m², and for a suitable single fluid under Darcy conditions it can be converted to hydraulic conductivity using K = κ ρg/μ, where ρ is fluid density, g gravitational acceleration and μ dynamic viscosity. A result measured with one fluid can therefore have a different K after fluid properties change even if the pore framework remains identical. It is incorrect to compare a value in m² directly with one in m/s and conclude which sediment is more permeable. The term “permeability” in the source should be expanded to the exact variable when ambiguity exists.

Take an illustrative κ = 1 × 10^-17 m², water density 1000 kg/m³, g = 9.81 m/s² and dynamic viscosity 0.001 Pa s. Then K ≈ 1 × 10^-17 × 1000 × 9.81/0.001 = 9.81 × 10^-11 m/s. The conversion is straightforward but depends on the fluid properties. A report using seawater or a laboratory brine at a different temperature needs the appropriate density and viscosity. The numeric value is not a universal conversion factor from square metres to metres per second.

Suppose one paper reports intrinsic permeability of 5 × 10^-18 m² and another reports conductivity of 5 × 10^-18 m/s. These are not equivalent numbers merely because the mantissas and exponents match. Before ranking samples, convert under stated fluid properties and effective stress conditions. If a comparison study cannot identify the test temperature, fluid composition or pressure state, the uncertainty should be made visible rather than hidden under a rounded mean. A precise conversion formula cannot repair missing experiment metadata.

The flow-pump method and why time series matter

In a constant-flow or flow-pump test, the apparatus supplies or withdraws fluid at a controlled rate while monitoring the resulting head or pressure difference across the specimen. This approach can be especially useful in low-conductivity fine sediment where collecting tiny effluent volumes directly over long periods is difficult. The imposed flow is known; the pressure response carries information about hydraulic resistance. The initial response can be transient because fluid and specimen storage, compliance and compressibility need time to equilibrate. Reporting an early gradient as the steady gradient may bias the conductivity estimate.

USGS research on low-gradient tests emphasizes the importance of the transient period and the advantages of controlled-flow measurements for fine material. A student should therefore inspect the pressure-versus-time trace, the duration of each flow stage and evidence of stabilization. If the pressure is still rising when the test stops, the simple steady-state reduction may not be justified. Some modelling approaches use the transient itself to estimate additional storage parameters, but that is a different and more assumption-dependent analysis. A good explanation distinguishes these two methods of extracting information from the same trace.

The direction of imposed flow also matters. A controlled reversal can help detect systematic offsets, apparatus asymmetry or different compression and rebound responses. It does not guarantee that a fractured or anisotropic specimen will behave identically in every condition. Pressure transducer zero, backpressure, gas bubbles and tubing compliance should be checked. If a paper presents several conductivity estimates at different imposed flows, ask whether Darcy proportionality held over the tested range. A linear-looking result can still be misleading if all points were taken during transients.

Orientation, lamination and anisotropy

Marine sediments often contain bedding-parallel fine layers, coarse streaks, cracks or biogenic structures. Horizontal and vertical hydraulic conductivities can differ because flow encounters different connected pathways along and across those layers. Some IODP investigations explicitly test horizontal and vertical directions on whole-round samples. The ratio K_h/K_v can summarize anisotropy when both values are determined under comparable conditions. However, a ratio from different specimens or pressures should not be presented as a definitive material property without noting the mismatch. The source must clarify orientation relative to bedding and to the core axis.

A vertical core sample can preserve an along-core flow direction, but a heavily tilted or deformed bed may not align with its original stratigraphic vertical. Translating “along core” as “perpendicular to bedding” can be wrong. Likewise, flow across a split core surface is not necessarily equivalent to field-horizontal flow unless the recovered orientation is known. The reader needs a geometry statement, not merely an arrow in an image. That distinction matters when hydraulic conductivity is used in a model of upward escape or along-layer migration.

Consider a hypothetical sample with K_h = 4 × 10^-10 m/s and K_v = 1 × 10^-10 m/s, both under comparable fluid and confining conditions. The anisotropy ratio is four. The statement “horizontal conductivity is four times vertical conductivity under the tested conditions” follows. It does not show that horizontal pore water moves exactly four times as fast in the field, because the actual head gradients and effective porosity in the two directions may differ. Velocity requires both the material property and the driving field.

Stress, sample disturbance and laboratory representativeness

Confining stress can compress pores and change the connectivity of fluid pathways. Recovering a core can release stress and open microcracks, potentially changing permeability before the specimen reaches the laboratory. Restoring an effective stress during testing may close some defects but cannot always recreate the original fabric. A specimen trimmed from a cracked core might flow much more readily than the surrounding intact mud. Conversely, pressing a sample into a holder may smear a boundary and reduce measured flow. The sampling and test history are part of the evidence.

A reported result at 0.1 MPa confining pressure is not automatically comparable with one measured at 1 MPa. Differences can reflect stress-dependent pore geometry rather than fundamental differences in composition. A useful table includes effective confining stress, flow direction, saturation fluid, temperature and sample quality alongside permeability. When a report plots conductivity against effective stress, the trend itself may be the important finding. Compressing all conditions into one “average permeability” can erase what a geotechnical or hydrogeological reader needs most.

A small sample can also miss rare but highly conductive sand layers or fractures, while a larger field test may integrate them. The direction of scale bias is not always predictable, because disturbance can make a laboratory specimen either more or less conductive. When applying a core measurement to a regional model, describe the representativeness assumptions and any supporting observations. The defensible claim is that a specimen had a measured response under stated conditions. A field-scale prediction requires upscaling, geological mapping and uncertainty analysis.

Falling-head tests and the changing driving gradient

A falling-head permeameter follows a declining water level in a standpipe while fluid passes through a saturated sample. The head difference is not constant, so a constant-head formula cannot be applied by substituting the initial head for the entire test. Under the standard ideal assumptions, K = (aL/(At)) ln(h1/h2), where a is standpipe area, A sample area, L sample length, t elapsed time and h1 and h2 the initial and final positive head differences. The logarithm is natural. Carefully reported dimensions and a documented head history are necessary for meaningful reduction.

Consider an invented example: a = 0.0001 m², A = 0.005 m², L = 0.05 m, t = 600 seconds, and head drops from 0.40 m to 0.20 m. The factor aL/(At) is 5 × 10^-6 divided by 3, or approximately 1.667 × 10^-6 m/s. Multiplying by ln(2) ≈ 0.693 yields K approximately 1.16 × 10^-6 m/s. This describes a more conductive illustrative sample than the low-flow marine mud example earlier. The two test numbers must not be combined as if measured under identical conditions or on a single real sediment specimen.

A common error is to replace ln(2) with log10(2), about 0.301, without adjusting the formula. That would reduce the calculated result by more than half. Another error is to reverse h1 and h2, creating a negative logarithm while using an unsigned conductivity formula. A declining head should have h1 greater than h2 in this setup. As with all laboratory methods, a mathematically consistent result may still be invalid if the fluid bypassed the specimen, if the sample contained trapped air or if the standpipe leaked. Arithmetic checking is only the first quality gate.

Flow rate, specific discharge and pore-water speed

A reported pump rate in millilitres per hour is a volume delivered per time, not a velocity. To obtain specific discharge, convert the rate into cubic metres per second and divide by full specimen area. If a hypothetical pump delivers 0.036 mL per hour through a specimen of area 0.002 m², its volume rate is 3.6 × 10^-8 m³ per hour, or 1 × 10^-11 m³/s. The corresponding Darcy flux is 5 × 10^-9 m/s. That value describes volume flux per full cross-section, not a particle-tracking result from individual connected pores.

In a simplified saturated uniform model, an average linear pore-water velocity may be estimated by dividing Darcy flux by effective porosity. If q = 5 × 10^-9 m/s and effective porosity is 0.25, the idealized mean advective speed is 2 × 10^-8 m/s. It would be wrong to use total porosity automatically as effective transport porosity, especially in fine sediments where some pore water participates differently in advection. The actual pathways are heterogeneous and tortuous. Such a calculation is useful as a teaching contrast, not a measured tracer travel time.

Diffusion can transport solutes even when bulk advection is weak. A low conductivity value does not demonstrate that nutrients or contaminants cannot move through pore water, because molecular diffusion and reactions can continue. Nor does a measured hydraulic conductivity directly specify a contaminant concentration. Interpreting marine pore-water chemistry requires transport gradients, diffusion coefficients, reaction rates, adsorption and sediment-water exchange. A clear translation says what flow measurement constrains and avoids turning it into a complete chemical fate forecast.

Hydraulic gradient, pressure difference and head

Hydraulic head combines pressure and elevation contributions under an appropriate reference and fluid-density assumption. A pressure difference measured across a core is not automatically a head difference of the same numerical size. For a constant-density fluid, a pressure difference Δp can be converted into equivalent head difference using Δh = Δp/(ρg), with consistent units. If a report changes fluid density between tests, the conversion must follow. Using kilopascals as though they were metres of head is a direct dimensional error. It can lead to completely incorrect conductivity values despite flawless algebra afterward.

For a hypothetical water density of 1025 kg/m³, a pressure difference of 1000 pascals corresponds to roughly 1000/(1025 × 9.81) ≈ 0.0995 m of water head. The pressure gradient across a 0.05 m specimen corresponds to hydraulic gradient near 1.99, if elevation effects are handled in the specified geometry. Both the pressure and head calculations should state their datum and assumptions. In a pressurized marine system, one must distinguish applied backpressure, differential pressure and effective confining stress; they perform different functions during the experiment.

Confusing absolute pressure with the pressure drop through a specimen is another common mistake. A high uniform backpressure can help maintain saturation but does not necessarily imply a high through-sample hydraulic gradient. The driving difference is what enters Darcy’s law, while confining stress influences the pore framework. A report may contain several pressures, each with a different role. An explanatory caption should label them explicitly rather than compress all of them into the phrase “test pressure.” That one phrase can hide an entire wrong physical model.

Temperature, salinity and fluid viscosity

Hydraulic conductivity is sensitive to viscosity. Water generally becomes less viscous as temperature rises within common laboratory ranges, so the same porous framework can transmit a different volume under the same gradient. Salinity can also influence fluid properties, while reactive clay minerals may respond to chemistry in ways that change the pore framework itself. The comparison must therefore distinguish a pure fluid-property correction from a possible alteration of the material. A temperature conversion formula should not be treated as proof that the specimen’s microstructure stayed constant.

An accurate methods section records the test fluid, temperature, density and viscosity or the convention used for normalization. If one laboratory reports conductivity at a given laboratory temperature and another normalizes to a reference temperature, either convert under compatible assumptions or explain that the values are not directly matched. A reader should be especially cautious when comparing freshwater and saline pore-water experiments on clay-rich specimens. A difference in measured flow may reflect fluid viscosity, material-fluid interactions or both. Reporting only a final number hides those possibilities.

Intrinsic permeability is sometimes used for comparisons precisely because it removes the fluid viscosity and density terms from the single-fluid Darcy conversion. But the phrase “intrinsic” does not promise complete independence from the history of how the fluid affected the sample. Mineral swelling, precipitation, dissolution or microbiological processes can change pore geometry during a test. The intrinsic parameter describes the framework in its current condition. To compare material structure credibly, ensure the condition itself was not altered by the experimental treatment.

Leakage, saturation and time-dependent transients

A low-conductivity mud may transmit so little fluid that a small leak through seals or tubing becomes large compared with the true sample flow. The apparatus should be tested for background leakage and its pressure response recorded. If the method includes a blank or dummy specimen, the meaning of that control should be explained. Simply subtracting an average leak from every reading is not always adequate because leakage may depend on pressure and time. A report that lacks such checks can display a smooth pressure trace yet still give biased conductivity.

Trapped gas bubbles are another source of trouble. Gas compressibility can create delayed pressure changes that resemble sample storage effects or prevent an apparently stable reading. De-aired fluids, appropriate backpressure and monitoring of saturation can improve the test, but the exact protocol depends on the material and instrument. Samples recovered from depth may expand or exsolve gas as pressure changes. Treating a transient pressure change as steady Darcy flow can therefore corrupt estimates even if the pump’s volumetric setting was accurately calibrated.

A constant-flow experiment may need a substantial stabilization interval before steady head difference emerges. In very low-permeability sediment, the delay can be long compared with convenient laboratory observation windows. USGS methodological studies describe how the transient response can be analyzed with more elaborate models when steady state is not yet reached, but such interpretation carries extra assumptions about storage and material behaviour. A quick guide should not swap a transient model result into a steady-state formula without naming the method. The two outputs may both be useful but have different evidentiary bases.

A profile through pressure-dependent material

Suppose a hypothetical specimen has K = 6 × 10^-10 m/s at a low effective confining stress, 3 × 10^-10 m/s at an intermediate stress and 1 × 10^-10 m/s at a higher stress. The decreasing trend can be described as stress-associated conductivity reduction under the tested conditions. It would not be valid to announce a universal exponential law or extrapolate the curve to all burial depths without a justified model. The result may depend on whether each pressure stage reached equilibrium and whether the specimen underwent irreversible compression.

Now suppose the pressure sequence is reversed and conductivity fails to return to its original value after unloading. That hysteresis could reflect irreversible fabric change, incomplete equilibrium, microcracking or another mechanism. The source should record loading order and repeat conditions. Averaging the loading and unloading curves into one profile could erase evidence of path dependence. Some geotechnical material properties depend on history as well as current stress, so the sequence of experimental operations belongs in the data record.

A separate sample from a nearby depth may produce a different response because of grain size, clay mineralogy, biogenic structure, cementation or cracks. That difference need not invalidate either test. It may reveal small-scale heterogeneity. A high-quality study uses supporting lithologic descriptions and adequate replication to separate a genuine stratigraphic pattern from laboratory scatter. If data are sparse, the publication should say so. Readers should not be handed a smooth field model as though it were directly observed at every depth.

Transfer problem: mismatched permeability units

A student reads one result κ = 1 × 10^-17 m² and a second result K = 9 × 10^-11 m/s, then reports the first as vastly less permeable because its exponent is smaller. The comparison is invalid until the quantities are converted. For a teaching fluid with density 1000 kg/m³ and viscosity 0.001 Pa s, κ = 10^-17 m² corresponds to K ≈ 9.81 × 10^-11 m/s, close to the second value. The apparent gulf was created by comparing different dimensions. Even after converting, confirm that both tests used comparable stresses and specimen orientations.

Now change the viscosity to 0.002 Pa s while holding κ and fluid density constant in the ideal conversion. Hydraulic conductivity would halve to approximately 4.905 × 10^-11 m/s. That arithmetic explains why a fluid-dependent parameter can shift without any change in intrinsic permeability. It does not guarantee that a real reactive marine clay would remain structurally unchanged under a different fluid chemistry. The report should separate the mathematical fluid-property effect from potential swelling, dissolution or other alterations of the sample.

If the source does not identify the fluid temperature or viscosity, it may be possible to compare orders of magnitude with a clearly stated assumption, but not to claim precise equivalence. A better article acknowledges the missing metadata instead of picking an unlabelled conversion constant. The lesson also applies to different unit systems: centimetres per second and metres per second differ by a factor of one hundred, while a permeability expressed in millidarcies requires a different conversion entirely. A unit label can matter more than the number of decimal places.

Transfer problem: the wrong pressure gradient

A flow-pump test maintains a uniform backpressure of 200 kPa and records a differential pressure of 2 kPa across its specimen. A draft article uses 200 kPa to compute the through-sample gradient. That confuses absolute or background pressure with the driving difference. The relevant term for Darcy flow is the differential head or pressure gradient under the test geometry. The higher backpressure may contribute to maintaining saturation, while effective confining stress influences the pore structure. Each pressure has a distinct role, and a good methods explanation explicitly names the role before presenting the calculation.

For a simplified water density 1000 kg/m³, the differential pressure 2 kPa equals 2000 Pa and corresponds to about 0.204 metres of head. If sample length is 0.050 m, the hydraulic gradient magnitude is about 4.08 when elevation differences are otherwise accounted for. Using 200 kPa would make the gradient one hundred times larger and could understate conductivity by a factor of one hundred in the simplified reduction. This example shows why an engineering report should distinguish pore pressure, confining pressure, backpressure and differential pressure even when all appear in the same units.

A further problem gives a pressure gradient still increasing ten minutes after flow starts. It asks for steady-state conductivity using the last reading. Without evidence of stabilization, the last reading is only the last transient reading. The appropriate repair is to continue the test if the protocol permits or apply a justified transient model rather than label the end value steady. The trend itself is relevant evidence of fluid and specimen storage. Reporting a provisional estimate with a clear caveat is more honest than inventing a steady state that never occurred.

Transfer problem: porosity is not enough

Two invented specimens both have measured porosity 50%, but specimen A has connected coarse pores and specimen B has extremely fine, tortuous pore throats. A student assigns identical conductivity because the pore fractions match. That is not justified. Darcy flow resistance depends strongly on pore geometry and connectivity, not just total void volume. The proper conclusion is that porosity alone is insufficient to determine K or κ. Supporting grain-size, fabric, mercury-intrusion, imaging or direct flow data may help, each with its own limitations and potential sample disturbance.

Another specimen is measured perpendicular to bedding while a neighbouring plug is measured parallel to bedding. A higher value in the latter could reflect anisotropy, but if the plugs also differ in stress or lithology, the observation does not isolate orientation. A careful design tests directions under matched conditions or explicitly reports the confounding differences. The translation should preserve “along core,” “across core,” “parallel to bedding” and “perpendicular to bedding” without substituting one for another. These spatial labels name different reference frames and may control the interpretation.

Imagine a profile with one thin sandy seam connecting two otherwise low-conductivity mud intervals. A small core plug missing that seam may report very low K, while field flow preferentially follows the seam. The laboratory result remains valid for the tested mud but may not represent the larger flow system. Conversely, a laboratory plug fractured during recovery may have artificially high conductivity. Both examples show why upscaling needs geology and sample-quality evidence, rather than assuming the core result is the field result with extra significant figures.

The reproducible reading and reporting workflow

Start with the original sample ID, recovered depth and a photograph or description of its condition. Record whether flow was imposed along the core, across it or relative to bedding. Note the sample’s dimensions and effective confining stress. Identify the fluid, temperature, saturation procedure and relevant viscosity. Then identify what the instrument directly recorded: collected volume, pump rate, pressure difference, time or fluid head. Only after that should a reader follow the equation used to derive conductivity or intrinsic permeability. This sequence prevents mixing measured and inferred quantities.

Next examine quality controls: stabilization, leakage, calibration, specimen disturbance, plausible saturation and whether an imposed-flow versus gradient relationship behaved consistently with the chosen Darcy interpretation. If the experiment repeated pressure stages or reversed flow, preserve the sequence. When a result was rejected, state why rather than substituting zero. When a measurement was below detection or outside range, retain the inequality or limitation. A later researcher needs those flags to decide whether the number can be used in a model, and a nonspecialist reader deserves the same honesty.

Finally check the last step from material property to real-world inference. A conductivity measured on a small marine mud specimen cannot alone determine groundwater contamination, methane escape, submarine landslide risk or construction settlement. Those outcomes involve field gradients, layer connectivity, reaction, stress and time. A strong article presents relevant calculations and the conditions under which they can transfer, while making clear where site-specific hydrogeological or geotechnical expertise is required. This approach gives readers a useful model of reasoning rather than an unjustified verdict.

Frequently asked questions

Is intrinsic permeability expressed in metres per second? No; it is ordinarily expressed in square metres. Is hydraulic conductivity a velocity? It shares the dimensions of velocity but describes flux per unit hydraulic gradient, not a measured particle trajectory. Can a sample have high porosity and low conductivity? Yes, fine and poorly connected pore throats can restrict flow. Does a low-conductivity mud prevent solute diffusion? No. Is a constant flow-pump setting proof of steady-state pressure? No. The pressure response may remain transient long after the flow rate is fixed.

Do horizontal and vertical conductivities have to match? No; lamination and fabric can create anisotropy. Can changing confining pressure change conductivity? Yes. Why does water temperature matter? It affects viscosity, among other things. Does a precise laboratory number automatically represent a field layer? No, particularly where fractures, seams and heterogeneous fabric control large-scale flow. Can an out-of-range reading be reported as zero? No. What is the fastest audit of any number? Write its measured quantity, unit, specimen geometry, pressure conditions and method on one line.

The practical principle is to preserve the whole evidence chain: specimen, fluid, imposed conditions, observed flow or pressure, reduction equation, derived quantity and field interpretation. Each stage offers a different kind of uncertainty. A clear guide does not need to reproduce every laboratory manual, but it should give enough information to check the arithmetic, understand the physical distinction between κ and K, and avoid turning a laboratory flow measurement into a claim about an entire marine system without independent support.