Many different types of nuclear reactors can be envisaged. How many exactly ?
The enormous difficulty of choosing a proper path for reactor development is easily seen by estimating the number of conceivable reactor types. With 3 fissionable fuels (U235, Pu239, U233), 2 fertile materials (Th232 and U238), 3 neutron energy ranges (slow=thermal medium=epithermal or fast), at least 6 coolant types (light water, heavy water, CO2, molten sodium, helium, molten lead, air), 6 moderators (light water, heavy water, graphite, beryllium, beryllium oxide, or none), 2 general categories of geometrical arrangement of the fuel (heterogeneous and homogeneous), and at least two different fundamental designs (one main pressure vessel with fuel rods, or numerous pressure tubes) and four ways to integrate the heat exchanger (inside or outside the pressure vessel, direct cycle for gas-cooling or with intermediate heat exchanger for liquid coolants), not to speak about the various options available for heat extraction, choice of turbines, thermodynamic cycles and secundary circuits... there are thousands of possible combinations! (3 x 2 x 3 x 6 x 6 x 2 x 2 x 4 = 10 368).
Of course not all of these reactor types are sensible; for example a fast sodium reactor could not be cooled with water which would slow down the neutrons and also for safety reasons because the presence of sodium is not compatible with water inside the same reactor. Similarly, direct cycle reactor (without secundary circuit) can be envisaged only with a gas, i.e. CO2 or helium (and not liquids such as water, molten sodium or molten lead) as a coolant... Even so, there are probably at least hundreds of combinations of reactor types which are not obviously unfeasible.
A group of international experts from the most advanced nuclear countries (France, US, Japan, Switzerland, India, China...) forming the GENERATION IV nuclear forum, has retained six concepts of innovating nuclear reactors that seem to be most promising, to be tested by 2030, among these thousands of different combinations.
Source : EFN / inspired by a passage from : "Nuclear Power Reactors", Edited by James K. Pickard (1957), as part of "The Geneva Series on The Peaceful Uses of Atomic Energy" (page 25).