Pore-pressure gradient

Subsurface Fluid Pressure (Pore Pressure Gradient). The total overburden pressure is derived from the weight of the materials and fluids that lie above any particular depth level in the earth. Of interest to the petroleum industry are the sedimentary rocks derived from deposits in water, particularly, in seawater. Such sedimentary rocks contain rock particle grains and saline water within the pore spaces. Total theoretical maximum overburden pressure, P (Ib/ft-), is... 

Because the geologic column of sedimentary rock is usually filled with saline water, the pore pressure and pore pressure gradient can be obtained for nearly the entire column. Figure 2-57 shows a typical pore pressure gradient versus depth plot for a Gulf Coast region well. 

In Figure 2-57 the pore pressure gradient has been given as a function of depth for a typical Gulf Coast well. Determine the approximate fracture pressure gradient for a depth of 10,000 ft. From Figure 2-57, the pore pressure gradient at 10,000 ft is... 

In general. Equation 2-174 can be used to approximate fracture pressure gradients. To obtain an adequate approximation for fracture pressure gradients, the pore pressure gradient must be determined from well log data. ALso, the overburden stress gradient and Poisson s ratio versus depth must be known for the region. 

Gqb overburden gradient in psi/ft Gp = pore pressure gradient in psi/ft K = coefficient related to Poisson ratio... 

Hottman and Johnson developed an empirical correlation to relate the ratio of resisitivities to the pore pressure gradient. In 1972, Eaton developed an empirical relationship that he modified in 1975 to the following [122] ... 

It is suggested to evaluate the burst load based on the internal pressure expected, reduced by the external pressure of the drilling fluid outside the string. Internal pressure is based on the expected bottomhole pressure of the next string with the hole being evacuated from drilling fluid up to a minimum of 50%. In exploratory wells, a reasonable assumption of expected formation pore pressure gradient is required. 

The borehole is assumed to be infinitely long and inclined with respect to the in-situ three-dimensional state of stress. The axis of the borehole is assumed to be perpendicular to the plane of isotropy of the transversely isotropic formation. Details of the problem geometry, boundary conditions and solutions for the stresses, pore pressure and temperature are available in [7], The solution is applied to assess the thermo-chemical effects on stresses and pore pressures. Both the formation pore fluid and the wellbore fluid are assumed to comprise of two chemical species, i.e., a solute fraction and solvent fraction. The formation material properties are those of a Gulf of Mexico shale [7] given as E = 1853.0 MPa u = 0.22 B = 0.92 k = 10-4 md /r = 10-9 MPa.s Ch = 8.64 x 10-5 m2/day % = 0.9 = 0.14 cn = 0.13824 m2/day asm = 6.0 x 10-6 1°C otsf = 3.0 x 10-4 /°C. A simplified example is considered wherein the in-situ stress gradients are assumed to be trivial and pore pressure gradients of the formation fluid and wellbore fluid are assumed to be = 9.8 kPa/m. The difference between the formation temperature and the wellbore fluid temperature is assumed to be 50°C. The solute concentration in the pore fluid is assumed to be more than that in the wellbore fluid such that mw — mf> = —1-8 x 10-2. 

Pore pressure gradients are very difficult to estimate with the same accuracy in shales outside the reservoir zones, where RFT or DST measurements are impossible. We have, however, estimated pressure gradients in three wells on the border between the Melke and Gam Formations, based on the drilling data in Fig. 5. We have attempted to calculate the flow of water from the overpressured Upper Jurassic and Lower Cretaceous shales, into the underlying Middle Jurassic sandstones. The main uncertainty in... 

Analysis of the RFT-data combined with detailed sequence stratigraphic studies were performed to obtain representative pore-pressure gradients from top to base of the individual permeable sands. Fig. 7 shows the interpreted pressure gradients for the Juras-sic-Triassic sequences within hydraulic compartment I based on RFT data from wells 10-1 and 10-2. Figs. 8 and 10 illustrate the same for hydraulic compartment II (based on wells 7-1, 7-2 and 7-4) and hydraulic compartment III (based on wells 7-3 and 7-5) respectively. 

In Fig. 13 the aquifer pore-pressure gradients for the He and Tilje reservoir units have been extrapolated to their respective apexes within each hydraulic compartment. A common pore-pressure versus depth gradient can be drawn through the apex pressures of hydraulic compartments II and III, and is referred to as the maximum reservoir pore-pressure trend-line. The Tilje Formation apex pressure of hydraulic compartment I plots slightly below the said gradient. 

The effects of temperature can be prevalent for some formation rocks and in-situ conditions. Temperature-induced changes in pore pressure and rock matrix stress (thermo-poro-elasticity model) can be modelled using Equations 10 to 12. In addition, to take into account the chemical potential effects, gradient of rock water potential instead of pore pressure gradient is used in Equation 11. 

Electrokinetic phenomena arise from movement of ions in the electric double layer under a pore pressure gradient. In the case of a steady-state fluid circulation and for a saturated porous media, a linear relation exists between the electrical potential difference AV and the pressure difference AP. This ratio is called the electrokinetic coupling coefficient [11-12] ... 

Hudson (1981) also considers in his model individual fractures isolated with respect to fluid flow. This again is given for high frequencies (ultrasonic). At low frequencies, there is time for wave-induced pore pressure gradients resulting in a fluid flow. For this case, Mavko et al. (1998) recommend that it is better to find the effective moduli for dry cavities and then saturate them with the Brown and Korringa (1975) low-frequency relations". Assad... 

Within the interconnected pores, there is fluid pressure equilibrium and no pore pressure gradient as a result of passing waves. Thus, the low frequency allows an equilibration of the pore pressure within the pore space. Therefore, Gassmann s equation works best for seismic frequencies (<100 Hz) and high permeability (Mavko et ah, 1998). 

For a single fluid flowing through a section of reservoir rock, Darcy showed that the superficial velocity of the fluid (u) is proportional to the pressure drop applied (the hydrodynamic pressure gradient), and inversely proportional to the viscosity of the fluid. The constant of proportionality is called the absolute permeability which is a rock property, and is dependent upon the pore size distribution. The superficial velocity is the average flowrate... 

The foregoing minimum pressure gradient assumes also that the sedimentary column pores are completely filled with saline water and that there is communication from pore to pore within the rock column from surface to depth. 

The fluid pressure in the rock at the bottom of a well is commonly defined as pore pressure (also called formation pressure, or reservoir pressure). Depending on the maturity of the sedimentary basin, the pore pressure will reflect geologic column overburden that may include a portion of the rock particle weight (i.e., immature basins), or a simple hydrostatic column of fluid (i.e., mature basins). The pore pressure and therefore its gradient can be obtained from well log data as wells are drilled. These pore pressure data are fundamental for the solution of engineering problems in drilling, well completions, production, and reservoir engineering. 

Subsurface Rock Fracture Pressure (Fracture Pressure Gradient). The subsurface rock fracture pressure can be approximated by utilizing the known pore pressure at the same depth. The relationship between rock fracture pressure p (psi) and pore pressure p (psi) is [34]... 

Compute the pore pressure at 15,000 ft using Eaton s equation, a normal gradient of 0.453 psi/ft, and an overburden gradient of 1 psi/ft assuming the well vertical. 

Burst Assumed external pressure gradient of saltwater = 0.465 psi/ft and formation pore (gas) pressure gradient = 0.65 psi/ft. Gas weight is neglected. Safety factor = 1.1. 

Upward flow of pore water and dissolved material caused by pressure gradients. 

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