Equations: Petroleum system and traps

dimensionless

Holds when: The elements are independent. If they depend on each other (for example, a reservoir and a seal from one depositional environment), we must not multiply them. We use conditional probabilities instead (the chance of one element given that another is present). Each $P_i$ is a subjective estimate. We calibrate it against drilling statistics in similar plays. Geological success is not the same as economic success: what is found may not be enough to pay for development.

dimensionless

Holds when: The common and local elements are split so that each element is counted once. $P_\text{loc}$ is a conditional probability: it is estimated on the assumption that the play works.

SI

Holds when: The channel is modelled as a cylinder. For a real rock, $r$ is the effective radius of the largest channels that form a connected path through the seal. The rock is water-wet ($\theta < 90^\circ$). In an oil-wet rock (one whose surface prefers oil) there is no capillary barrier for oil (Wettability and interfacial phenomena). Take $\sigma$ and $\theta$ at reservoir pressure and temperature.

SI

Holds when: The water in the layer is at rest (hydrostatics). When formation waters move, the contact tilts (Traps and timing). The column of hydrocarbons is continuous and connected to the water-bearing part of the layer. Densities are constant over the height of the accumulation.

SI

Holds when: The water is at rest. The seal is continuous, with no fractures or conducting faults. The height is measured from the contact. Measured from the free water level, the height held is larger by $p_{d,r}/[(\rho_w - \rho_h)\,g]$. The effective radius is the radius of the largest connected channels of the seal. Leakage follows the easiest path, not the average pore size. All properties are taken at reservoir conditions.

SI (or any consistent units of pressure)

Holds when: The channels are modelled as cylinders, and the geometry of the pores is the same for mercury and for reservoir fluids. The contact angle of mercury is measured through the mercury, so we take the modulus of the cosine. The sample is representative. Without the load of the surrounding rock, its channels may be wider than in the reservoir.

SI

Holds when: The pressures are taken at the depth of the top of the accumulation. $p_w$ is the water pressure continued along the gradient of the water-bearing part of the layer. The seal opens when the pressure in it exceeds the fracture pressure. We ignore its tensile strength (how well the rock resists being pulled apart). The estimate is rough: the fracture pressure of the seal is known with a considerable error.

as shown; $TOC/100$ is grams of organic carbon per gram of rock, so $100\,S_2/TOC$ is milligrams of HC per gram of carbon

Holds when: The sample is not contaminated by oil-based drilling fluid, migrated oil or weathering. To find the original kerogen type, you need an immature or only slightly mature sample, because HI falls as the rock matures.

dimensionless

Holds when: Some of the hydrocarbons that formed have already left the rock, so PI underestimates the share of kerogen that has converted. Migrated oil and drilling-fluid additives make $S_1$ and PI too high.

SI; temperature only in kelvin ($T = t + 273.15$)

Holds when: Treating the breakdown as a first-order reaction with one activation energy is a simplification: real kerogen is a mixture of structures with a range of activation energies. Laboratory pyrolysis at several heating rates gives $A$ and $E$, and we then apply them to geological time.

$R_o$ in %, $z$ in m; $\lg$ is the base-10 logarithm

Holds when: An empirical relation (based on data, not on theory) for a section with continuous burial and an unchanged geothermal regime (the same way temperature rises with depth). At erosion surfaces the profile jumps in a step. Where the heat flow has changed, the slope changes. The measurements have been screened, because caved cuttings (rock that fell into the hole from higher up), reworked vitrinite (vitrinite redeposited from older rocks) and underestimated values in hydrogen-rich rocks produce outliers (points far from the trend).

$A$ in m², $h$ in m, $\rho_r$ in t/m³ — their product gives the mass of rock in tonnes; $S_2^{\,0}$ in kg/t, so $M$ comes out in kilograms

Holds when: Thickness, TOC and kerogen type are averaged over the kitchen. In practice they are mapped. We estimate the transformation ratio from the fall in HI or from a heating model. The result is the mass generated, not the mass expelled, and certainly not the mass accumulated.

SI; $\ln$ is the natural logarithm

Holds when: A constant heating rate and a single activation energy. $\Delta T$ is small compared with $T$ (we ignore the change of the factor $T^2$).

any consistent system; slopes are conveniently expressed in metres per kilometre

Holds when: The water flow is steady (it does not change with time), and the oil in the trap does not move. We ignore capillary effects, and the densities are constant. For a gas–water contact, use the gas density $\rho_g$ instead of $\rho_o$.

thicknesses in any identical units, porosity as a fraction

Holds when: The grain volume is conserved: cement is neither added nor dissolved. The porosity is an average over the layer. We take it from the porosity–depth relation for the rock concerned.

dimensionless

Holds when: The elements are defined so that success happens when all of them have worked, and only then. Each uncertainty is counted in exactly one factor. The order of the elements does not matter, but we assess each following probability given that the elements before it have worked. For independent elements $P_{2|1} = P_2$ and so on, and the formula becomes the simple product $P_g = \prod_i P_i$.

dimensionless

Holds when: In the first formula the outcomes of the prospects are independent. In the second the prospects are linked only by the common play risk, and their local elements are independent. The probability of at least one discovery equals $1 - P_0$.

dimensionless; $V$ and $V_\text{min}$ in the same units

Holds when: The volume distribution is built given geological success and starts at the smallest volume that counts as success. $V_\text{min}$ depends on price, costs, taxes and infrastructure: for the same trap it differs between companies and between years. The chance of success and the volume distribution relate to the same accumulation under one definition of success.

volume units

Holds when: If the well fails, the volume is zero, so the mean over all outcomes is $P_g\bar V + (1 - P_g)\cdot 0$. We use the mean, not the P50, because the mean volumes of prospects add up, but the P50 values do not.

dimensionless (a number of wells)

Holds when: $\bar k$ holds whatever the dependence between the prospects. The formula for $\sigma_k$ is for independent prospects. A common play risk increases the scatter. The probabilities were recorded before drilling and were not corrected afterwards.

dimensionless

Holds when: The well was drilled on a prospect of the same segment, and the cause of the failure has not been established. The local elements of different prospects are independent. If the well data show that exactly a local element failed (for example, there is no closure), the common risk hardly changes. The formula does not suit that case.