diff --git a/ebos/eclnewtonmethod.hh b/ebos/eclnewtonmethod.hh
index c45a3dfa8..62d9547e2 100644
--- a/ebos/eclnewtonmethod.hh
+++ b/ebos/eclnewtonmethod.hh
@@ -173,6 +173,16 @@ public:
         for (unsigned eqIdx = 0; eqIdx < numEq; ++eqIdx)
             errorSum_ = std::max(std::abs(componentSumError[eqIdx]), errorSum_);
 
+        // update the sum tolerance: larger reservoirs can tolerate a higher amount of
+        // mass lost per time step than smaller ones! since this is not linear, we use
+        // the cube root of the overall pore volume, i.e., the value specified by the
+        // NewtonSumTolerance parameter is the "incorrect" mass per timestep for an
+        // reservoir that exhibits 1 m^3 of pore volume. A reservoir with a total pore
+        // volume of 10^3 m^3 will tolerate 10 times as much.
+        sumTolerance_ =
+            EWOMS_GET_PARAM(TypeTag, Scalar, NewtonSumTolerance)
+            * std::cbrt(sumPv);
+
         // make sure that the error never grows beyond the maximum
         // allowed one
         if (this->error_ > newtonMaxError)
diff --git a/ebos/eclproblem.hh b/ebos/eclproblem.hh
index c9b8a33d4..ffd2c5876 100644
--- a/ebos/eclproblem.hh
+++ b/ebos/eclproblem.hh
@@ -236,10 +236,13 @@ SET_SCALAR_PROP(EclBaseProblem, EndTime, 1e100);
 // not millions of trillions of years, that is...)
 SET_SCALAR_PROP(EclBaseProblem, InitialTimeStepSize, 1e100);
 
-// increase the default raw tolerance for the newton solver because this is what everone
-// else seems to be doing...
+// set the tolerated amount of "incorrect" mass to ~1e-6 kg of oil per time step for a
+// reservoir that exhibits a pore volume of 1 m^3. larger reservoirs will tolerate larger
+// residuals.
+SET_SCALAR_PROP(EclBaseProblem, NewtonSumTolerance, 1e-6);
+
+// the default for the volumetric error for oil per second is 10^-2 kg/(m^3 * s).
 SET_SCALAR_PROP(EclBaseProblem, NewtonRawTolerance, 1e-2);
-SET_SCALAR_PROP(EclBaseProblem, NewtonSumTolerance, 1e-3);
 
 // set the maximum number of Newton iterations to 14 because the likelyhood that a time
 // step succeeds at more than 14 Newton iteration is rather small