diff --git a/lumen/lumen_index.md b/lumen/lumen_index.md
index aaf2dad0cac43391fe47ae9d71bcb140421ea47b..bdd0d80c4b081940216a5612cdeb5b5ac4ebb5ac 100644
--- a/lumen/lumen_index.md
+++ b/lumen/lumen_index.md
@@ -60,9 +60,9 @@ In total 10 test runs in the simulation domain for different fault scenarios are
 
 * Failure of the pump bearings: This fault results in an incresead torque $\tau_{\text{p}}$ absorbed by the pump of a factor $f$\
   $\tau_{\text{p}} = f \tau_{\text{p}}$, $f > 1.0$
-* Blockage of the turbine inlet nozzle: This fault results in a decreased are of the inlet inlet turbine nozzles $A_{\text{t}}$ by a factor $f$\
+* Blockage of the turbine inlet nozzle: This fault results in a decreased area of the inlet inlet turbine nozzles $A_{\text{t}}$ by a factor $f$\
   $A_{\text{t}} = f A_{\text{t}}$, $f < 1.0$
-* Pump leakage: This fault results in a leakage mass flow downstream of the pump. It is modeled with an additional valve which can be opened and thus inject a partial mass flow into the environment. The opening area of the valve $A_{\text{valve}}$ is a linear function of the throat are $A_{\text{0}}$ and the position of the valve $x_{\text{valve}}$\
+* Pump leakage: This fault results in a leakage mass flow downstream of the pump. It is modeled with an additional valve which can be opened and thus inject a partial mass flow into the environment. The opening area of the valve $A_{\text{valve}}$ is a linear function of the throat area $A_{\text{0}}$ and the position of the valve $x_{\text{valve}}$\
    $A_{\text{valve}} = x_{\text{valve}} A_{\text{0}}$, $x_{\text{valve}} > 0.0$
 * Stuck valve: This fault results in an additive offset $f$ in the command signal of a control valve $u_{\text{valve}}$\
    $u_{\text{valve}} = f u_{\text{valve}}$, $f = [-1.0, 1.0]$