The Archimedes porosity determination method measures: (1) the dry weight of a core sample, (2) the saturated weight of the core, and (3) the submerged weight of the saturated core. It uses these measurements along with the fluid density to calculate: (1) the pore volume, (2) the bulk volume, and (3) the percent porosity of the core sample. The porosity is calculated as the ratio of the pore volume to the bulk volume based on the measurements and fluid density.

1. Archimedes porosity determination
In the Archimedes porosity determination, one measures or is given the following quantities:
(1), (3), (5), and (7).
(1) is the weight of the air-dried core:
𝑊𝑑 = 𝑑𝑟𝑦 𝑔𝑟𝑎𝑖𝑛 𝑤𝑒𝑖𝑔ℎ𝑡 𝑁𝑒𝑢𝑡𝑜𝑛𝑠 (𝑁, 𝑘𝑔 ∙
𝑚
𝑠2
) (1)
𝑊𝑝𝑓 = 𝑝𝑜𝑟𝑒 𝑓𝑙𝑢𝑖𝑑 𝑤𝑒𝑖𝑔ℎ𝑡 (𝑁, 𝑘𝑔 ∙
𝑚
𝑠2
) (2)
𝑊𝑠𝑎𝑡 = 𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑒𝑑 𝑐𝑜𝑟𝑒 𝑤𝑒𝑖𝑔ℎ𝑡 (𝑁, 𝑘𝑔 ∙
𝑚
𝑠2
) (3)
𝑊𝑝𝑓 = 𝑊𝑠𝑎𝑡 − 𝑊𝑑 (𝑁, 𝑘𝑔 ∙
𝑚
𝑠2
) (4)
In (5), 𝑔 (
𝑚
𝑠2 ) is the local gravitational acceleration. 𝜌𝑓 (
𝑘𝑔
𝑚3 ) is the fluid density.
𝛾𝑓 = 𝑔𝜌𝑓 = 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑓𝑙𝑢𝑖𝑑 𝑤𝑒𝑖𝑔ℎ𝑡 (
𝑁
𝑚3
) (5)
𝑉𝑝 =
𝑊𝑝𝑓
𝛾𝑓
=
𝑊𝑠𝑎𝑡 − 𝑊𝑑
𝛾𝑓
= 𝑝𝑜𝑟𝑒 𝑣𝑜𝑙𝑢𝑚𝑒 ( 𝑚3) (6)
𝑊𝑠𝑢𝑏 = 𝑠𝑢𝑏𝑚𝑒𝑟𝑔𝑒𝑑 𝑐𝑜𝑟𝑒 𝑤𝑒𝑖𝑔ℎ𝑡 (𝑁, 𝑘𝑔 ∙
𝑚
𝑠2
) (7)
𝑉𝐵 = 𝑏𝑢𝑙𝑘 𝑣𝑜𝑙𝑢𝑚𝑒 ( 𝑚3) (8)

2. 𝐵 𝐹 = 𝑏𝑢𝑜𝑦𝑎𝑛𝑡 𝑓𝑜𝑟𝑐𝑒 (𝑁) (9)
Archimedes principle for submerged core:
𝐵 𝐹 = 𝛾𝑓 𝑉𝐵 (𝑁) (10)
Force balance on submerged core (Figure 1):
𝑊𝑠𝑢𝑏 = 𝑊𝑠𝑎𝑡 − 𝐵 𝐹 (𝑁, 𝑘𝑔 ∙
𝑚
𝑠2
) (11)
Figure 1: Force Balance on Submerged Core
Subbing (10) into (11):
𝑊𝑠𝑢𝑏 = 𝑊𝑠𝑎𝑡 − 𝛾𝑓 𝑉𝐵 (𝑁, 𝑘𝑔 ∙
𝑚
𝑠2
) (12)
𝐵 𝐹
𝑊𝑠𝑎𝑡

3. Rearranging:
𝑊𝑠𝑎𝑡 − 𝑊𝑠𝑢𝑏
𝛾𝑓
= 𝑉𝐵 (𝑚3
) (13)
(13) may be used as a check on volume measured by calipers or by fluid displacement.
Archimedes porosity is determined by:
𝜙 𝑎 = 𝑝𝑜𝑟𝑜𝑠𝑖𝑡𝑦 =
𝑉𝑝
𝑉𝐵
(14)
Subbing (6) and (13) into (14):
𝜙 𝑎 =
(
𝑊𝑠𝑎𝑡 − 𝑊𝑑
𝛾𝑓
)
(
𝑊𝑠𝑎𝑡 − 𝑊𝑠𝑢𝑏
𝛾𝑓
)
(14)
Simplifying:
𝜙 𝑎 =
𝑊𝑠𝑎𝑡 − 𝑊𝑑
𝑊𝑠𝑎𝑡 − 𝑊𝑠𝑢𝑏
(15)
You can use anything proportional to weight ( 𝑊, 𝑁𝑒𝑢𝑡𝑜𝑛𝑠) in (15), observing consistent units.
For example:
𝜙 𝑎 =
𝑀𝑠𝑎𝑡 − 𝑀𝑔
𝑀𝑠𝑎𝑡 − 𝑀𝑠𝑢𝑏
(16)
Here, 𝑀 indicates mass. 𝑀𝑠𝑢𝑏 indicates the apparent submerged mass.

4. Once 𝜙 is known, we may state:
𝑉𝑔 = 𝑔𝑟𝑎𝑖𝑛 𝑣𝑜𝑙𝑢𝑚𝑒 = (1 − 𝜙) 𝑉𝐵 (𝑚3
) (17)
Further:
𝛾𝑔 = 𝑔𝜌 𝑔 = 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑔𝑟𝑎𝑖𝑛 𝑤𝑒𝑖𝑔ℎ𝑡 (
𝑁
𝑚3
) (18)
Therefore:
𝑊𝑑 = 𝛾𝑔 𝑉𝑔 = 𝑔𝜌 𝑔 𝑉𝑔 (𝑁, 𝑘𝑔 ∙
𝑚
𝑠2
) (19)
Solving for grain density:
𝑊𝑑
𝑔𝑉𝑔
= 𝜌 𝑔 (
𝑘𝑔
𝑚3
) (20)