1 Correction to: Transport in Porous Media https://doi.org/10.1007/s11242-019-01367-y

The arguments in Eqs. (16) and (18) have typographical errors in the original publication of the article. The corrected equations are provided below.

$$ \begin{aligned} & {\mathscr{P}}(r_{d} |\{ p_{m} (t_{i} ),i = 1, \ldots ,N\} ) \\ & \quad \propto \exp \left[ { - \frac{1}{{2\sigma^{2} }}\sum\limits_{i = 1}^{N} {\{ p_{w} (t_{i} ;\bar{r}_{\text{d}} ) - p_{w} (t_{i} ;r_{d} )\}^{2} } } \right] \\ & \quad = \exp \left[ { - \frac{N}{{2\sigma^{2} }}\left\langle {\{ p_{w} (t_{i} ;\bar{r}_{d} ) - p_{w} (t_{i} ;r_{d} )\}^{2} } \right\rangle } \right] \\ & \quad \approx \exp \left[ { - \frac{1}{{2\sigma^{2} \Delta t}}\int_{0}^{T} {\{ p_{w} (t;\bar{r}_{d} ) - p_{w} (t;r_{d} )\}^{2} {\text{d}}t} } \right]. \\ \end{aligned} $$
(16)

and

$$ \begin{aligned} & {\mathscr{P}}(r_{d} |\{ p_{m} (t_{i} ),i = 1, \ldots ,N\} ) \\ & \quad \propto \exp \left[ { - \frac{{(r_{d} - \bar{r}_{d} )^{2} P^{2} }}{{2\sigma^{2} \bar{r}_{d}^{2} \Delta t}}\left( {T{\text{e}}^{{ - \frac{{2\bar{r}_{d}^{2} }}{\eta T}}} - \frac{{2\bar{r}_{d}^{2} }}{\eta }\varGamma \left( {0,\frac{{2\bar{r}_{d}^{2} }}{\eta T}} \right)} \right)} \right], \\ \end{aligned} $$
(18)

A factor two in the denominator of an argument in Eqs. (28), (30), and (32) is missing. These equations should read

$$ p_{p} (t) = p_{0} + \frac{q\mu }{{4kr_{p} }}{\mkern 1mu} {\text{erfc}}{\mkern 1mu} \left( {\frac{{r_{p} }}{{2\pi \sqrt {\eta t} }}} \right). $$
(28)
$$ p_{p} (t;z_{b} ) = p_{0} + P\left[ {{\text{erfc}}{\mkern 1mu} \left( {\frac{{r_{p} }}{{2\pi \sqrt {\eta t} }}} \right) + \frac{{r_{p} }}{{2\pi z_{b} }}{\mkern 1mu} {\text{erfc}}{\mkern 1mu} \left( {\frac{{z_{b} }}{{\sqrt {\eta t} }}} \right)} \right]. $$
(30)
$$ \begin{aligned} p_{p}^{(1)} (t;r_{p} ) & = p_{0} + P{\mkern 1mu} {\text{erfc}}{\mkern 1mu} \left( {\frac{{r_{p} }}{{2\pi \sqrt {\eta t} }}} \right) + \frac{{Pr_{p} }}{{2\pi \bar{z}_{b} }}{\mkern 1mu} {\text{erfc}}{\mkern 1mu} \left( {\frac{{\bar{z}_{b} }}{{\sqrt {\eta t} }}} \right) \\ & \quad - \frac{{Pr_{p} (z_{b} - \bar{z}_{b} )}}{{\pi \bar{z}_{b} }}\left[ {\frac{{{\text{e}}^{{ - \frac{{\bar{z}_{b}^{2} }}{\eta t}}} }}{{\sqrt {\pi \eta t} }} + \frac{{{\text{erfc}}{\mkern 1mu} \left( {\frac{{\bar{z}_{b} }}{{\sqrt {\eta t} }}} \right)}}{{2\bar{z}_{b} }}} \right]. \\ \end{aligned} $$
(32)