| kAPIz |
As in equation (2) |
Silica |
API [4], DNV [5] |
|
{{\boldsymbol{k}}_{\boldsymbol{W}}}{\boldsymbol{z = z}}\,{{\boldsymbol{k}}_{{\bf{API}}}}{\left({{{{\boldsymbol{D}}_{\boldsymbol{p}}^{{\bf{ref}}}} \over {{{\boldsymbol{D}}_{\boldsymbol{p}}}}}} \right)^{{{{\boldsymbol{4(1 - a)}}} \over {{\boldsymbol{4 + a}}}}}}
|
a=0.6 for a medium dense sanda=0.5 for a dense sandDpref=1.0 m |
Silica |
Wiemann et al. [12] |
|
{{\boldsymbol{k}}_{{\boldsymbol{S1}}}}\,{\boldsymbol{z = a}}{\left({{{\boldsymbol{Z}} \over {{{\boldsymbol{Z}}_{{\bf{ref}}}}}}} \right)^{\boldsymbol{b}}}{\left({{{{{\boldsymbol{D}}_{\boldsymbol{p}}}} \over {{\boldsymbol{D}}_{\boldsymbol{p}}^{{\bf{ref}}}}}} \right)^{\boldsymbol{c}}}\,{\phi ^{\boldsymbol{d}}}
|
a=50,000, zref=1 m, Dpref=1.0 mb=0.6, c=0.5, d=3.6, ϕ in radians |
Silica |
Sorensen et al. [13] |
|
{{\boldsymbol{k}}_{\boldsymbol{K}}}\,{\boldsymbol{z =}}{{\boldsymbol{k}}_{{\bf{API}}}}{{\boldsymbol{z}}_{{\bf{ref}}}}{\left({{{\boldsymbol{Z}} \over {{{\boldsymbol{Z}}_{{\bf{ref}}}}}}} \right)^{\boldsymbol{m}}}{\left({{{{{\boldsymbol{D}}_{\boldsymbol{p}}}} \over {{\boldsymbol{D}}_{\boldsymbol{p}}^{{\bf{ref}}}}}} \right)^{{\boldsymbol{0}}{\boldsymbol{.5}}}}
|
m=0.6, zref=2.5 m, Dpref=0.61 m |
Silica |
Kallehave et al. [14] |
|
{{\boldsymbol{k}}_{{\boldsymbol{S2}}}}\,{\boldsymbol{z = a}}{\left({{{\boldsymbol{Z}} \over {{{\boldsymbol{Z}}_{{\bf{ref}}}}}}} \right)^{\boldsymbol{b}}}{\left({{{{{\boldsymbol{D}}_{\boldsymbol{p}}}} \over {{\boldsymbol{D}}_{\boldsymbol{p}}^{{\bf{ref}}}}}} \right)^{\boldsymbol{c}}}\,{\left({{{{{\boldsymbol{E}}_{\boldsymbol{s}}}} \over {{\boldsymbol{E}}_{\boldsymbol{s}}^{{\bf{ref}}}}}} \right)^{\boldsymbol{d}}}
|
a=1 MPa, zref=1 m, Dpref=1 mEsref=1 MPa, b=0.3, c=0.5, d=0.8 |
Silica |
Sorensen [15] |
, and | Feb 10, 2022
