This equation is derived from the Ergun equation for fixed bed pressure drop with two terms. Assuming that the bed friction pressure drop equals the pressure head of the bed at minimum fluidization, you will obtain an equation like what you wrote above, incorporating the definitions of the Reynolds number and Archimedes number.

This equation has two parameters, k1 and k2 (or C1 and C2). Thus, in theory, it only needs two data points to solve for their values. In practice, you need a large number of test data (each set of data should include at least the following: particle density, particle size distribution and Sauter mean diameter, static bed height and fluidized bed height, measured Umf, density and viscosity of the fluidizing agent, calculated Re and Ar).

Then you tabulate all your test data in an Excel spreadsheet, with Re (for example in Column K) and Ar (Col L) being the two self-variables, followed by two columns for measured and calculated Umf (Cols. M and N), respectively. Set up another column (Col. O) with a formula "= (N_i - M_i)^2, i.e. the error squared.

Then, assign any three unoccupied cells in your spreadsheet name them, and assign initial values for k1 and k2.

Sum err^2  (Cell A1)            k1 (B1)               k2 (C1)

=SUM of Col O (Cell A2)      10 (B2)              1 (C2)

Find Data\Solver on your spreadsheet, and define your optimization problem as one to minimize the objective function ($A$2) by varying parameters k1 and k2 ($B$2-$C$2). On the Solver interface, set the precision to 1E-6 and convergence to 1E-12. Set maximum number of iterations to 100 and maximum time to 120 s. Then click the Solve button. Accept the new values of k1 and k2 if they make sense.

You will figure it out. Good luck.

See slides 33-35 of the linked presentation for the theoretical background of this equation:

http://www2.msm.ctw.utwente.nl/sluding/TEACHING/ParticleTechnology/vanOmmen_Fluidization.pdf