An Easily Used Mathematical Model of Porosity Change With Depth and Geologic Time in Deep Shale Compaction

Abstract

Shale compaction behavior is complex and differs from sandstone. The compaction trend shows marked changes in the physical properties with increasing depth. Therefore, the porosity-depth curve in the shallow section is not well established. Several authors published porosity-depth curves in which vary considerably, particularly in the shallow part of the compaction trend. Deep shale compaction curves show deviations in the trend of porosity decreasing with depth, especially at shallow depths where mechanical compaction is dominant and this suggests that mechanical compaction is not the only factor causing porosity change and that geological time is another important factor to be considered. In this study twenty-two sets of published data on deep shale compaction up to a depth of 5 km from various sedimentary basins around the world were synthesized and analyzed to depict the effect of geological age on deep shale compaction curves. A time-dependent solution of the compaction equation with porosity as the variable was revisited, based on which and in combination with multivariate curve-fitting of the collected compaction data, a new and easilyused mathematical model of porosity-depth-geological time was derived. Finally, research results substantiate that a burial depth (overburden pressure) cannot be considered only for studying mechanical compaction of shales, the geological age (an effect of time) is necessary to take into account.

Compaction Model for Shale in Differences of Geological Ages Using A 3D Empirical Relationship in Northeastern Thailand

“…The variation of the Thailand shale data due to the different geological ages was found in this study. Finally, the standard curve of shale compaction proposed by Puttiwongrak et al [9] was examined and confirmed by this research findings.…”

“…The classical Athy's model [7] on the empirical equation of exponential porosity reduction with depth has been widely used in a large number of studies for the shale compaction [8]. However, there are large variations in the porosity-depth curves of the mechanical compaction for shales [8][9][10], several factors may play an important role in porosity change with depth, e.g., temperature, geological age, clay diagenesis, overpressure, etc., resulting in the scatter plots of combined shale data [3,9,[11][12][13][14]. Nowadays, various porosity-depth trends for shales [8] have been proposed based on empirical localisms.…”

“…Early studies from Burst [16], who is a pioneer in studying the effect of the geological ages on shale compactions, concluded that the porosity of shales tends to reduce with increasing geological age. Furthermore, Puttiwongrak et al [9] emphasized the effect of geological ages by re-plotting porosity-time plots to quantify the porosity changing with time at the same depth. The relationship among porosity, burial depth, and geological age was first established.…”

“…Then the research findings propose the empirical relationship among porosity, depth, and geological age. The new shale compaction models in each geological age are established based on earlier work by Puttiwongrak et al [9] and the empirical analysis is carefully described.…”

Shale Compaction Kinetics

“…) = a + b*(depth)+c*depth^1.1 a=6.50e-01, b=-1.16e-03, c=4./0.55) = a + b*depth^(2.0) a=-5.70e-04, b=2.27e-08 ,porosity std=0.049) Makran2 well porosity data trend(Fowler 1985) Depth m /0.6) = a*depth + b*depth^2 a=-1.09e-03, b=1.41e-07, porosity std=0.048) SuluSea" well porosity data trend(Velde 1996) Depth m + b*depth^(1.05)+c*depth^(0.9 ) a=4.90e-01, b=8.03e-04, c=-3.show the experimental example porosity-depth relations which were discussed recently[10] [11]. Curve fit equations are shown at the top of each plot.…”