diff --git a/opm/core/transport/reorder/TransportModelInterface.hpp b/opm/core/transport/reorder/TransportModelInterface.hpp
new file mode 100644
index 000000000..895ca6618
--- /dev/null
+++ b/opm/core/transport/reorder/TransportModelInterface.hpp
@@ -0,0 +1,35 @@
+/*
+  Copyright 2012 SINTEF ICT, Applied Mathematics.
+
+  This file is part of the Open Porous Media project (OPM).
+
+  OPM is free software: you can redistribute it and/or modify
+  it under the terms of the GNU General Public License as published by
+  the Free Software Foundation, either version 3 of the License, or
+  (at your option) any later version.
+
+  OPM is distributed in the hope that it will be useful,
+  but WITHOUT ANY WARRANTY; without even the implied warranty of
+  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+  GNU General Public License for more details.
+
+  You should have received a copy of the GNU General Public License
+  along with OPM.  If not, see <http://www.gnu.org/licenses/>.
+*/
+
+#ifndef OPM_TRANSPORTMODELINTERFACE_HEADER_INCLUDED
+#define OPM_TRANSPORTMODELINTERFACE_HEADER_INCLUDED
+
+namespace Opm
+{
+
+    class TransportModelInterface
+    {
+    public:
+	virtual ~TransportModelInterface() {}
+	virtual void solveSingleCell(int cell) = 0;
+    };
+
+} // namespace Opm
+
+#endif // OPM_TRANSPORTMODELINTERFACE_HEADER_INCLUDED
diff --git a/opm/core/transport/reorder/TransportModelTwophase.cpp b/opm/core/transport/reorder/TransportModelTwophase.cpp
new file mode 100644
index 000000000..f02a27582
--- /dev/null
+++ b/opm/core/transport/reorder/TransportModelTwophase.cpp
@@ -0,0 +1,152 @@
+/*
+  Copyright 2012 SINTEF ICT, Applied Mathematics.
+
+  This file is part of the Open Porous Media project (OPM).
+
+  OPM is free software: you can redistribute it and/or modify
+  it under the terms of the GNU General Public License as published by
+  the Free Software Foundation, either version 3 of the License, or
+  (at your option) any later version.
+
+  OPM is distributed in the hope that it will be useful,
+  but WITHOUT ANY WARRANTY; without even the implied warranty of
+  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+  GNU General Public License for more details.
+
+  You should have received a copy of the GNU General Public License
+  along with OPM.  If not, see <http://www.gnu.org/licenses/>.
+*/
+
+#include <opm/core/transport/reorder/TransportModelTwophase.hpp>
+#include <opm/core/fluid/IncompPropertiesInterface.hpp>
+#include <opm/core/grid.h>
+#include <opm/core/transport/reorder/nlsolvers.h>
+
+struct Opm::Parameters
+{
+    double s0;
+    double influx;  /* sum_j min(v_ij, 0)*f(s_j) */
+    double outflux; /* sum_j max(v_ij, 0)        */
+    double dtpv;    /* dt/pv(i)                  */
+    int cell;
+    const Opm::IncompPropertiesInterface* props;
+};
+
+static double residual(double s, void *data);
+static double fluxfun_props(double s, int cell, const Opm::IncompPropertiesInterface* props);
+
+namespace Opm
+{
+
+
+    TransportModelTwophase::TransportModelTwophase(const UnstructuredGrid* grid,
+						   const Opm::IncompPropertiesInterface* props,
+						   const double* darcyflux,
+						   const double* porevolume,
+						   const double* source,
+						   const double dt,
+						   double* saturation)
+	: grid_(grid),
+	  props_(props),
+	  darcyflux_(darcyflux),
+	  porevolume_(porevolume),
+	  source_(source),
+	  dt_(dt),
+	  saturation_(saturation),
+	  fractionalflow_(grid->number_of_cells, 0.0)
+    {
+    }
+
+
+    void TransportModelTwophase::solveSingleCell(int cell)
+    {
+	NonlinearSolverCtrl ctrl;
+	ctrl.maxiterations = 20;
+	ctrl.nltolerance   = 1e-9;
+	ctrl.method        = NonlinearSolverCtrl::REGULAFALSI;
+	ctrl.initialguess  = 0.5;
+	ctrl.min_bracket   = 0.0;
+	ctrl.max_bracket   = 1.0;
+
+	Parameters prm = getParameters(cell);
+	saturation_[cell] = find_zero(residual, &prm, &ctrl);
+	// double ff1 = fluxfun_props(d->saturation[cell], cell, d->props);
+	// double ff2 = fluxfun(d->saturation[cell], -999);
+	// printf("New = %f   old = %f\n", ff1, ff2);
+	fractionalflow_[cell] = fluxfun_props(saturation_[cell], cell, props_);
+    }
+
+
+    Opm::Parameters TransportModelTwophase::getParameters(int cell)
+    {
+	int i;
+	Opm::Parameters p;
+	double flux;
+	int f, other;
+
+	p.s0      = saturation_[cell];
+	p.influx  = source_[cell] >  0 ? -source_[cell] : 0.0;
+	p.outflux = source_[cell] <= 0 ? -source_[cell] : 0.0;
+	p.dtpv    = dt_/porevolume_[cell];
+	p.cell    = cell;
+	p.props   = props_;
+
+	for (i=grid_->cell_facepos[cell]; i<grid_->cell_facepos[cell+1]; ++i) {
+	    f = grid_->cell_faces[i];
+
+	    /* Compute cell flux*/
+	    if (cell == grid_->face_cells[2*f]) {
+		flux  = darcyflux_[f];
+		other = grid_->face_cells[2*f+1];
+	    }
+	    else {
+		flux  =-darcyflux_[f];
+		other = grid_->face_cells[2*f];
+	    }
+
+	    if (other != -1) {
+		if (flux < 0.0) {
+		    p.influx  += flux*fractionalflow_[other];
+		}
+		else {
+		    p.outflux += flux;
+		}
+	    }
+	}
+	return p;
+    }
+
+
+} // namespace Opm
+
+/* ====================== Internals =================================*/
+
+
+/* Residual function r(s) for a single-cell bvp */
+/*
+ *     r(s) = s - s0 + dt/pv*(influx - outflux*f(s) )
+ */
+/* influx is water influx, outflux is total outflux */
+static double
+residual(double s, void *data)
+{
+    Opm::Parameters *p = (Opm::Parameters*) data;
+    return s - p->s0 +  p->dtpv*(p->outflux*fluxfun_props(s, p->cell, p->props) + p->influx);
+}
+
+
+static double fluxfun_props(double s, int cell, const Opm::IncompPropertiesInterface* props)
+{
+    const double* visc = props->viscosity();
+    double sat[2] = { s, 1.0 - s };
+    double mob[2];
+    props->relperm(1, sat, &cell, mob, 0);
+    mob[0] /= visc[0];
+    mob[1] /= visc[1];
+    return mob[0]/(mob[0] + mob[1]);
+}
+
+
+/* Local Variables:    */
+/* c-basic-offset:4    */
+/* End:                */
diff --git a/opm/core/transport/reorder/TransportModelTwophase.hpp b/opm/core/transport/reorder/TransportModelTwophase.hpp
new file mode 100644
index 000000000..b2a2fb179
--- /dev/null
+++ b/opm/core/transport/reorder/TransportModelTwophase.hpp
@@ -0,0 +1,64 @@
+/*
+  Copyright 2012 SINTEF ICT, Applied Mathematics.
+
+  This file is part of the Open Porous Media project (OPM).
+
+  OPM is free software: you can redistribute it and/or modify
+  it under the terms of the GNU General Public License as published by
+  the Free Software Foundation, either version 3 of the License, or
+  (at your option) any later version.
+
+  OPM is distributed in the hope that it will be useful,
+  but WITHOUT ANY WARRANTY; without even the implied warranty of
+  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+  GNU General Public License for more details.
+
+  You should have received a copy of the GNU General Public License
+  along with OPM.  If not, see <http://www.gnu.org/licenses/>.
+*/
+
+#ifndef OPM_TRANSPORTMODELTWOPHASE_HEADER_INCLUDED
+#define OPM_TRANSPORTMODELTWOPHASE_HEADER_INCLUDED
+
+#include <opm/core/transport/reorder/TransportModelInterface.hpp>
+#include <vector>
+
+class UnstructuredGrid;
+
+
+namespace Opm
+{
+
+    class IncompPropertiesInterface;
+    class Parameters;
+
+
+    class TransportModelTwophase : public TransportModelInterface
+    {
+    public:
+	TransportModelTwophase(const UnstructuredGrid* grid,
+			       const Opm::IncompPropertiesInterface* props,
+			       const double* darcyflux,
+			       const double* porevolume,
+			       const double* source,
+			       const double dt,
+			       double* saturation);
+
+	virtual void solveSingleCell(int cell);
+
+    private:
+	const UnstructuredGrid* grid_;
+	const IncompPropertiesInterface* props_;
+	const double* darcyflux_;   /* one flux per face  in cdata::grid*/
+	const double* porevolume_;  /* one volume per cell */
+	const double* source_;      /* one source per cell */
+	double dt_;
+	double* saturation_;        /* one per cell */
+	std::vector<double> fractionalflow_;  /* one per cell */
+
+	Parameters getParameters(int cell);
+    };
+
+} // namespace Opm
+
+#endif // OPM_TRANSPORTMODELTWOPHASE_HEADER_INCLUDED