In the mid-1940s, Karl Terzaghi and Peck (1948) described the clay consolidation theory of supersaturated water, which was affirmed in soil mechanics.
Hubbert and Rubey( 1959) first proposed to apply this consolidation theory to the compaction of fine-grained clastic deposits. In their classic papers, it is clearly pointed out that the accumulated earth pressure S or б is supported by the effective intergranular stress (stress at the indirect contact point between particles) δ or б' of clay granular aggregate and the pore fluid pressure PP, accordingly:
Simulation and tracing of deep water formation and evolution and oil and gas migration and accumulation in the basin
The units of the accumulated earth pressure S are pounds per foot and kilograms per square centimeter, so it will be equal to:
Simulation and tracing of deep water formation and evolution and oil and gas migration and accumulation in the basin
Where: γ b refers to the total specific gravity of overlying sediments saturated with water, in pounds per cubic foot;
Z- depth (note: Z is D in the original text), feet.
Since the effective intergranular stress δ increases with the decrease of porosity φ, δ is a function of φ or residual water content m, that is:
Simulation and tracing of deep water formation and evolution and oil and gas migration and accumulation in the basin
Simulation and tracing of deep water formation and evolution and oil and gas migration and accumulation in the basin
Hubbert and Rubey believe that the accumulated soil load is shared by the sediment matrix in nature and the fluid in pores, so the vertical stress at any point consists of two components: intergranular stress and pore fluid stress. Effective stress is the difference between total accumulated earth pressure and pore pressure (Pc=Pt-Pp). If the vertical permeability of sediment allows pore fluid to escape, then the pressure distribution of pore fluid is the same as the hydrostatic pressure distribution of a continuous column of groundwater extending to the groundwater surface. The weight produced by mineral particles contained in a vertical water column is equal to the weight of mineral particles minus the weight (buoyancy) of water displaced by particles. Since the load supported by mineral particles is equal to the weight of all overlying water and particles minus the weight of water displaced by particles, the compaction force is equal to:
Simulation and tracing of deep water formation and evolution and oil and gas migration and accumulation in the basin
Where: Fe—— is the effective intergranular pressure on the horizontal plane;
Ft-total accumulated soil load;
FP- buoyancy.
Total accumulated earth pressure (Ft) is equal to:
Simulation and tracing of deep water formation and evolution and oil and gas migration and accumulation in the basin
Where: F0-the external force exerted on the studied sediment;
Ws (sediment weight) = γ s (1-φ) VB;
Wf (weight of sediment pore fluid) =γwφVb (Note: γS- solid density, g/cm3; φ-porosity,%; γ W-pore fluid density, g/cm3; VB-volume of sediment, cm3).
Because the buoyancy Fp is equal to the weight of the fluid displaced by the particle, then: FP = γ wvb (1-φ);
Sediment volume Vb=A×Z (note: a-total cross-sectional area of sediment; Z- depth) and pore pressure Pp=γwZ.
Then FP = PPA (1-φ)
Since surface porosity is the ratio of pore area to total area along surface A, the surface porosity and volume porosity on any plane are the same, that is, pore pressure is occupied by water and clay, and acts on any surface through porous solids, regardless of surface porosity.
Assuming that all pores are filled with water, at depth z, the total accumulated earth pressure Pt (lb/ft2) caused by overlying water and solids can be written as:
Simulation and tracing of deep water formation and evolution and oil and gas migration and accumulation in the basin
Since the effective pressure Pc (intergranular stress) is equal to the difference between the total accumulated earth pressure Pt and the pore pressure Pp, that is, Pc = Pt-PP, and the pore pressure at the depth z is equal to γfZ, the solution of the effective pressure Pc can be written as:
Simulation and tracing of deep water formation and evolution and oil and gas migration and accumulation in the basin
According to Hubbert and Rubey's mathematical analysis, the calculation method of effective pressure of sediment compaction can be calculated by calculating four parameters of sediment burial depth (z), density (γs), porosity (φ) and water density (γ w), which provides a theory and method for constructing basin compaction model and simulating the alternating seepage field of circulating squeezed water in sediment, and has important application value.