Using Rock-Physics Trends

DUG Insight trends define depth-dependent relationships between key elastic properties of lithologies. Trends can be generated using DUG Rock, but can also be estimated using other software and spreadsheets.

The depth-dependent trends define the relationship between Depth and Vp, Vp to Vs, Vp to Rho and, for reservoir lithologies, Vp to porosity. The trend equation for each relationship is a linear function, except for Vp - Rho (non-reservoir) which is defined by a power law.

Each trend function also includes an error parameter to describe the uncertainty or scatter inherent to the lithology.

The linear trends are defined by the following formula:

  • f(x) = A*x + B

The power law trends are defined by the following formula:

  • f(x) = A*xB

where terms A and B are constant.

For example, the relationships for a reservoir lithology are:

  • Vp as a function of Depth:   Vp = A * TVDBML + B
  • Vs as a function of Vp:        Vs = A * Vp + B
  • Rho as a function of Vp:       Rho = A * Vp + B
  • Porosity as a function of Vp: Phi = A * Vp + B

For a non-reservoir, the relationships are the same, except for density:

  • Density = A*VpB

Adding trends to Insight

Trends can be imported into Insight using the Import menu from the Control Panel.

Trend files and format

A trend file contains structured text describing four main sections:

  • Units specification
  • Reference fluid specification
  • Lithology specification (repeated for each lithology)
    • Lithology specifications are slightly different for reservoir versus non-reservoir
    • Both specifications require information for trends: Vp, Vs, Rho
    • Non-reservoir lithologies also require information for trends: Phi and Grain
  • Fluid specification (repeated for each non-reference fluid)
    • Fluid parameters define values for Vp and Rho with standard deviation values.

Comments

Lines or sections of lines starting with the “#” character are comments and are not read or processed.

Units Specification

Every trend file must contain a section specifying the units. For example:

# Units specification
unit.velocity                         m/s
unit.porosity
unit.density                          g/cm³
unit.length                           m

Reference Fluid Specification

The “Reference Fluid” parameters describe the fluid in place for the reservoir trends.

Because different picks and log sections will have different in-situ fluids, Gassmann fluid substitution must be performed on inputs to trends to ensure they are consistent and are not affected by local hydrocarbon or fluid effects.

In Dug Rock, this is performed by enabling the “Gassmann” checkbox.

An example specification for the reference fluid:

# Gassmann Reference Fluid
reference.type                           fluid
reference.vp                          1517.0
reference.vp.error                       0
reference.rho                            1.000
reference.rho.error                      0

Reservoir Lithology Specification

An example specification for a reservoir lithology:

## Lithology: Sandstone
Sandstone.type                  	reservoir
Sandstone.vp.A                    	2672.936405
Sandstone.vp.B                       	0.283998
Sandstone.vp.C                       	0.000000
Sandstone.vp.error                 	166.185199
Sandstone.vs.A                     	129.231439
Sandstone.vs.B                       	0.547985
Sandstone.vs.C                       	0.000000
Sandstone.vs.error                  	45.370358
Sandstone.phi.A                         0.827061
Sandstone.phi.B                      	-0.000171
Sandstone.phi.C                         0.000000
Sandstone.phi.error                     0.019162
Sandstone.rho.A                         1.285350
Sandstone.rho.B                         0.000282
Sandstone.rho.C                         0.000000
Sandstone.rho.error                     0.031617
Sandstone.grain.vp                 	6050.000000
Sandstone.grain.vs                 	4120.000000
Sandstone.grain.rho                     2.650000

The single Vp-Depth trend is defined by these lines, where each line corresponds to one of the variables previously described:

Sandstone.vp.A                    	2672.936405
Sandstone.vp.B                       	0.283998
Sandstone.vp.C                       	0.000000
Sandstone.vp.error                 	166.185199

The grain properties define the rock matrix for the reservoir. Grain properties should be selected based on observational data and the expected reservoir lithology. A reference table of matrix densities is available in The Rock Physics Handbook [Mavko, G.]. These values can be used for a quartz reservoir:

Sandstone.grain.vp                 	6050.000000
Sandstone.grain.vs                 	4120.000000
Sandstone.grain.rho                   	2.650000

Three additional parameters can be specified for trends, but are not required. These values account for the covariance between the various pairs of errors (i.e. Vp-Vs, Vp-Rho and Vs-Rho).

Sandstone.vpvsrhoCorrelation._1_2        -0.113926
Sandstone.vpvsrhoCorrelation._1_3        0.157314
Sandstone.vpvsrhoCorrelation._2_3        -0.465274

Complete Example

# Units specification
unit.velocity                        	m/s
unit.porosity
unit.density                       	g/cm³
unit.length                             m
# Gassmann Reference Fluid
reference.type                           	fluid
reference.vp                            	1517.0
reference.vp.error                              0
reference.rho                            	1.000
reference.rho.error                             0
## LITHOLOGIES
## Lithology: Sandstone
Sandstone.type                  	reservoir
Sandstone.vp.A                    	2672.936405
Sandstone.vp.B                       	0.283998
Sandstone.vp.C                       	0.000000
Sandstone.vp.error                 	166.185199
Sandstone.vs.A                     	129.231439
Sandstone.vs.B                       	0.547985
Sandstone.vs.C                       	0.000000
Sandstone.vs.error                  	45.370358
Sandstone.phi.A                         0.827061
Sandstone.phi.B                      	-0.000171
Sandstone.phi.C                         0.000000
Sandstone.phi.error                     0.019162
Sandstone.rho.A                         1.285350
Sandstone.rho.B                         0.000282
Sandstone.rho.C                         0.000000
Sandstone.rho.error                     0.031617
Sandstone.grain.vp                 	6050.000000
Sandstone.grain.vs                 	4120.000000
Sandstone.grain.rho                     2.650000
## Lithology: Shale
Shale.type               	non-reservoir
Shale.vp.A                    	2705.388095
Shale.vp.B                      0.333620
Shale.vp.C                      0.000000
Shale.vp.error                 	131.380888
Shale.vs.A                     	444.462722
Shale.vs.B                      0.427230
Shale.vs.C                      0.000000
Shale.vs.error                  54.955190
Shale.rho.A                     1.576314
Shale.rho.B                     0.057629
Shale.rho.C                     0.000000
Shale.rho.error                 0.034788
## FLUIDS
## Fluid : Gas
gas.type fluid
gas.vp.error 	  32
gas.vp         	  621
gas.rho.error	  0.02
gas.rho      	  0.22
## Fluid : Brine
brine.type fluid
brine.vp.error 	  81
brine.vp       	  1572
brine.rho.error	  0.01
brine.rho      	  0.99