# Porosities, velocities, and densities of rocks

Series | Geophysical References Series |
---|---|

Title | Problems in Exploration Seismology and their Solutions |

Author | Lloyd P. Geldart and Robert E. Sheriff |

Chapter | 5 |

Pages | 141 - 180 |

DOI | http://dx.doi.org/10.1190/1.9781560801733 |

ISBN | ISBN 9781560801153 |

Store | SEG Online Store |

## Problem 5.3a

Assume that sandstone is composed only of grains of quartz, limestone only of grains of calcite, and shale of equal quantities of kaolinite and muscovite. For sandstone, limestone, and shale saturated with salt water , what porosities are implied by the densities shown in Figure 5.3a? (Mineral densities are: ; ; ; , all in g/cm.)

### Background

Gardner et al. (1974) plotted the log of velocity against the log of density for sedimentary rocks and obtained the empirical relation known as *Gardner’s rule*:

**(**)

Porosity | ||||||
---|---|---|---|---|---|---|

Rock | Density range | Density av. | Mineral density | Max | Av. | Min |

Ss | 2.00–2.60 g/cm | 2.35 g/cm | 2.68 g/cm | 41% | 20% | 5% |

Ls | 2.20–2.75 | 2.55 | 2.71 | 30 | 10 | 0 |

Sh | 1.90–2.70 | 2.40 | 2.72 | 48 | 19 | 0 |

being in g/cm and or 0.23 when is in m/s or ft/s, respectively. The rule is valid for the major sedimentary rock types, but not for evaporites or carbonaceous rocks (coal, lignite).

When a porous rock is saturated with a fluid, its density is given by the equation

**(**)

being the porosity, and the densities of the fluid and rock matrix, respectively.

### Solution

The density ranges in Table 5.3a were obtained from Figure 5.3a. The mineral densities are for , the values for shale being averages for kaolinite and muscovite.

We solve equation (5.3b) for , obtaining

**(**)

The histogram in Figure 5.3a does not encompass the complete range of samples and the range limits have been picked somewhat arbitrarily. Porosity in rocks ranges from about 50% to 0%. The upper limits of the density range sometimes exceed the mineral densities, hence heavier minerals must be present in the rocks; in these cases we assume that . We take as the fluid density.

## Problem 5.3b

What velocities would be expected for the density values in Table 5.3a according to Gardner’s rule? Plot these on Figure 5.3b.

### Solution

We solve equation (5.3a) for the velocity , obtaining

The velocities in Table 5.3b are plotted as triangles on Figure 5.3b.

Rock | |||
---|---|---|---|

Ss | 1.8 (41%) | 3.4 (20%) | 6.8 (0%) |

Ls | 2.6 (30%) | 4.6 (10%) | 6.8 (0%) |

Sh | 1.4 (48%) | 3.4 (19%) | 6.8 (0%) |

Note: The values in parentheses are the porosities. |

## Problem 5.3c

From Figure 5.3c, what densities would you expect at 7500 ft and how do these compare with Figures 5.3d and 5.3e from offshore Louisiana?

### Solution

Using and from Figure 5.3c, equation (5.3c) gives , which is in accord with Figure 5.3d. Using , equation (5.3c) gives , which is slightly lower than most values in Figure 5.3e.

## Continue reading

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---|---|

Relation between lithology and seismic velocities | Velocities in limestone and sandstone |

Previous chapter | Next chapter |

Geometry of seismic waves | Characteristics of seismic events |

## Also in this chapter

- Maximum porosity versus depth
- Relation between lithology and seismic velocities
- Porosities, velocities, and densities of rocks
- Velocities in limestone and sandstone
- Dependence of velocity-depth curves on geology
- Effect of burial history on velocity
- Determining lithology from well-velocity surveys
- Reflectivity versus water saturation
- Effect of overpressure
- Effects of weathered layer (LVL) and permafrost
- Horizontal component of head waves
- Stacking velocity versus rms and average velocities
- Quick-look velocity analysis and effects of errors
- Well-velocity survey
- Interval velocities
- Finding velocity
- Effect of timing errors on stacking velocity, depth, and dip
- Estimating lithology from stacking velocity
- Velocity versus depth from sonobuoy data
- Influence of direction on velocity analyses
- Effect of time picks, NMO stretch, and datum choice on stacking velocity