All calculations in this workflow use measured depth referenced to the Kelly bushing, reported as mKB. The well is treated as near vertical for the purpose of pore-pressure gradient calculation; therefore, mKB is used consistently as the working depth reference and converted to feet using 1 m = 3.28084 ft. Pore pressure, overburden pressure, hydrostatic pressure, and pressure gradients are therefore reported against the same mKB depth scale. This convention removes ambiguity caused by mixing measured depth, true vertical depth, and mKB descriptors.

Drilling-report inputs were averaged over 10 m mKB depth bins before D-exponent calculation. For each bin, rate of penetration, rotary speed, weight on bit, mud weight, and bit diameter were represented by the median of valid drilling records. Median averaging was selected to reduce the influence of short operational disturbances, connection effects, and isolated drilling dysfunction. Intervals affected by bit trips, major bit-size changes, motor runs, severe vibration, or obvious lithological discontinuity were not used for fitting the normal compaction trend.

The shale-screening rule used for corrected D-exponent interpretation was based on the gamma-ray-derived shale volume. The gamma-ray index was computed as IGR = (GR − GRclean)/(GRshale − GRclean), where GRclean and GRshale are the local clean-sand and shale endpoints selected in Interactive Petrophysics from the Hamra East-8 log response. Shale volume was then defined as Vsh = max (0, min (1, IGR)). Intervals with Vsh ≥ 0.35 were treated as shale-prone and eligible for corrected D-exponent trend interpretation. As a practical cross-check, intervals with gamma ray approximately ≥ 75 API were also considered shale-prone where local endpoint uncertainty existed. Clean sandstone intervals and mixed intervals with Vsh < 0.35 were excluded from normal compaction trend fitting and from pressure interpretation unless supported by lithological descriptions.

This screening was necessary because clean sandstone can drill faster than shale and may produce anomalously low D-exponent values unrelated to abnormal pore pressure. The screening criterion therefore restricts the pressure workflow to shale-dominated or argillaceous intervals where compaction-based pressure methods are more physically meaningful.

The drilling D-exponent was calculated from drilling parameters using Equation (1):

where D is drilling D-exponent, ROP is the rate of penetration in ft/h, N is the rotary speed in rev/min, WOB is the weight on bit in lb, and B is the bit diameter in in. The corrected D-exponent was then calculated using Equation (2):

where Dc is the corrected D-exponent, MWref is the reference normal mud weight, and MWa is the actual mud weight used in the drilled interval. The reference mud weight used in this workflow was 9.2 ppg, corresponding to the lowest initial mud-weight stage in the reported Hamra East-8 mud program. The actual mud weight varied from 9.2 to 10.8 ppg, as shown in Figure 2. Using a fixed 9.2 ppg reference made D-exponent values comparable across intervals drilled with different mud densities.

Figure 2.Reported mud-weight program used in the corrected D-exponent mud-weight correction. The shaded interval marks the 1600 - 1700 mKB watch zone.

Overburden pressure was derived from the bulk-density curve used in Interactive Petrophysics. The supplied workflow indicates that density was estimated from sonic input rather than taken entirely from a measured density log. Where measured density was unavailable or incomplete, the density curve was reconstructed from sonic velocity using a Gardner-type velocity-density transform:

where ρb is bulk density in g/cm³ and Vp is compressional velocity in ft/s. Sonic slowness was converted to velocity using Vp = 10^6/Δt, where Δt is sonic slowness in μs/ft. Gardner-type density-velocity transforms are commonly used when density logs are missing or incomplete; the standard coefficients 0.23 and 0.25 are widely reported for sedimentary rocks [9]. Because sonic-derived density is empirical, the resulting over-burden curve should be considered a screening-level estimate and should be recalibrated if measured densitylog or core-density data become available.

Overburden pressure was calculated by integrating density with depth. For discrete depth samples, the working expression was Equation (4):

where σov is overburden pressure in psi, ρb,i is interval bulk density in g/cm³, and Δzi is depth increment in ft. For manual single-point checking, the same relationship was applied using the cumulative density-derived overburden at the selected depth.

The normal compaction trend was fitted only through shale-screened intervals satisfying Vsh ≥ 0.35 and showing no obvious drilling dysfunction or sharp lithological break. The trend was constructed as a least-squares linear fit of corrected D-exponent against mKB depth through normally pressured shale-prone intervals above the interpreted watch zone. The Aradeiba Main Sand and other clean-sand intervals were excluded. The 1600 - 1700 mKB interval was not used to define the trend; it was retained as an independent interval for evaluation and verification.

Pore pressure was calculated with Eaton’s D-exponent form, Equation (5) [10]:

where PP is pore pressure in psi, σov is overburden pressure in psi, Pn is normal hydrostatic pore pressure in psi, Dco is observed corrected D-exponent at the depth of interest, and Dcn is the normal-trend corrected D-exponent at the same depth. Eaton exponent 1.2 was used. The exponent was adopted from the drilling-engineering practice documented in the original Hamra East-8 workflow and was locally checked through manual verification rather than recalibrated by direct formation-pressure measurements. Normal pressure was compared against freshwater and saline hydrostatic gradients of approximately 0.433 and 0.465 psi/ft, respectively. The principal parameter choices and screening rules are consolidated in Table 2.

Table 2.Reproducibility parameters.

The original four verification points at 900, 1000, 1200, and 1400 mKB showed an average absolute difference of 30.5 psi, RMSE of 36.2 psi, and mean absolute percentage difference of 2.0% an additional verification point was added at 1650 mKB within the 1600 - 1700 mKB watch zone. This point lies in the Aradeiba lower interval and directly checks the main interval where the pore-pressure curve showed a slight increase. The five verification calculations are reported in Table 3.

With the added 1650 mKB check, the five-point average absolute difference is 26.8 psi, RMSE is 32.8 psi, and mean absolute percentage difference is 1.7%. The 1650 mKB manual Eaton result is 2556 psi compared with an IP-read value of 2568 psi, giving an absolute difference of 12 psi and a pressure-gradient comparison. The software and manual pressure profiles are compared in Figure 3.

0.472 versus 0.474 psi/ft. This direct watch-zone check supports the interpretation that pressure is slightly above the saline hydrostatic reference but does not represent a strong abnormal-pressure condition.

Table 3.Manual verification of pore-pressure calculation, including added 1650 mKB watch-zone point.

Figure 3.Comparison between IP-derived pore pressure and manual Eaton-equation checks, including the 1650 mKB watch-zone verification point.

Figure 4.Pore-pressure gradients compared with freshwater and saline hydrostatic bounds. The added 1650 mKB point confirms only a modest watch-zone increase.

The calculated gradients at 900, 1000, 1200, and 1400 mKB remain between approximately 0.439 and 0.459 psi/ft for the manual calculations, which lie within or close to the normal freshwater-to-saline hydrostatic range. The added 1650 mKB point has a manual gradient of approximately 0.472 psi/ft and an IP gradient of approximately 0.474 psi/ft. This value is slightly above the 0.465 psi/ft saline hydrostatic reference, supporting the interpretation of a modest pressure increase in the 1600 - 1700 mKB interval. Figure 4 compares these results with the freshwater and saline hydrostatic reference gradients.

The result does not indicate a major abnormal-pressure zone because the gradient increase is small and the mud-weight program remains above the interpreted pore-pressure requirement. The interval should nevertheless be treated as an operational watch zone because it coincides with the deeper Aradeiba interval and precedes the Bentiu target section. Small pressure increases in this zone can reduce mud-weight safety margin and should be monitored with drilling parameters, gas readings, cuttings behavior, and any available pressure-while-drilling or formation-test data in future wells.