 Here is the Python code based on your instructions. Please note that this code assumes that the `porepy` library is installed and the `soultz_grid` module is available.

```python
import os
import sys
import numpy as np
from scipy.sparse import linalg
import porepy as pp
from porepy.solvers import DualVEMMixDim
from porepy.grids.soultz_grid import SoultzGrid
from porepy.grids.test_grids import test_grids

# Append the directory containing the soultz_grid module to the system path
sys.path.append(os.path.dirname(os.path.abspath(__file__)))

def add_data_darcy(gb, tol, permeability, source, aperture, boundary_conditions):
    # Add Darcy's law parameters to the grid bucket
    gb.add_darcy_law(permeability, source, aperture, boundary_conditions)

def add_data_advection(gb, tol, source, porosity, discharge, boundary_conditions):
    # Add advection parameters to the grid bucket
    gb.add_advection(source, porosity, discharge, boundary_conditions)

# Set up parameters for creating a grid
grid_params = test_grids.square_grid_params(20, 20, 0.1)
grid = SoultzGrid(**grid_params)

# Compute grid geometry, coarsen if necessary, and assign node ordering
grid.compute_geometry()
grid.coarsen_if_necessary(tol=tol)
grid.assign_node_ordering()

# Create a Darcy problem and solve it
darcy_problem = pp.DarcyAndTransport(grid, tol=tol)
darcy_problem.set_parameters(permeability=1.0, source=1.0, aperture=1.0, boundary_conditions={'left': 0.0, 'right': 0.0, 'top': 0.0, 'bottom': 0.0})

A, b = darcy_problem.solve(solver=DualVEMMixDim)
gb.add_data_from_solution(A, b)

# Compute total flow rate
total_flow_rate = np.sum(gb.discharge)

# Set up parameters for a transport problem
transport_params = pp.test_transport_params(grid, tol=tol)

# Define solvers for advection and mass matrix
advection_solver = pp.solvers.Advection(grid, tol=tol)
mass_matrix_solver = pp.solvers.MassMatrix(grid, tol=tol)

# Add transport problem parameters to the grid bucket
gb.add_transport_parameters(source=1.0, porosity=1.0, discharge=1.0, boundary_conditions={'left': 0.0, 'right': 0.0, 'top': 0.0, 'bottom': 0.0})

# Compute matrices and right-hand side vectors
M, f = mass_matrix_solver(gb)
A_adv, b_adv = advection_solver(gb)

# Perform LU factorization
L, U = linalg.lu(M)

# Initialize solution vector
x = np.zeros(M.shape[0])

# Perform a time-stepping loop to update the solution and export it at certain time steps
for t in np.linspace(0, 1, 10):
    # Perform a time step
    k = (t**2) / 2
    x_new = linalg.solve(L, linalg.solve(U, -k * f - k * A_adv @ x))

    # Update the solution
    x = x_new

    # Export the solution at certain time steps
    if t == 0 or t == 0.5 or t == 1.0:
        grid.to_vtk(f'solution_{t}.vtk')

# Export the solution in PVD format
grid.to_pvd('solution.pvd')

# Save the production data to a text file
with open('production.txt', 'w') as f:
    f.write(str(total_flow_rate))
```

This code creates a 2D square grid, solves a Darcy problem, and performs a simple transport problem. It exports the solutions in VTK and PVD formats and saves the total flow rate to a text file. You may need to adjust the parameters and boundary conditions according to your specific needs.