Request for power utility

Hello, I encountered some problems when checking the power of unit, may I ask you the following questions about power utility? Thanks for your help. Wish you a good day.

a)For @cost in Class PretreatmentReactorSystem, could I consult you why power is calculated at dry flow rate and what formula is used to get 83333 and 4578? Besides, why does the pretreatment reactor (which is just a tank with chemical reaction) have power consumption? Moreover, what is the use of dry flow rate in the results exported via sys.save_report? Shouldn't we focus on flow rate? In tutorial of Inheriting_from_Unit (https://biosteam.readthedocs.io/en/latest/tutorial/Inheriting_from_Unit.html), does the original size value in cost decorator refer to the flow into or out of the reactor?

b)In the example class ContinuousFermentation(bst.CSTR) from the tutorial on CSTR (https://biosteam.readthedocs.io/en/latest/API/units/cstr.html), according to the power calculation method in the CSTR source code self.add_power_utility(self.kW_per_m3*volume), the power obtained is 319*0.985*4= 1256.86 kW, which is different from 1340 kW in the result. May I ask you how is 1340 kW calculated? Since there is no pump in add_power_utility(self.kW_per_m3 * volume), so it doesn't seem to be the difference in pump power.

c)I modified kW_per_m3 in the following way, but the result seems to be still the power as kW_per_m3=0.985:
class ContinuousFermentation(bst.CSTR):
_N_ins = 1
_N_outs = 2
T_default = 32. + 273.15
P_default = 101325.
tau_default = 8.
kW_per_m3=0

d)When inheriting CSTR, the default kW_per_m3(0.985) in CSTR seems to be for liquid -- liquid reaction or extraction, if only stir for chemical reaction, could I consult you which power value should be used?

e)Do I need to add heat utility and power utility when create reactor by inheriting CSTR?

f)Could I consult you is it both OK to add the power consumption of unit in either of the following ways? Are there any differences or usage scenarios for them?
def _cost(self)：
self.add_power_utility
or
@cost('Dry flow rate', 'PretreatmentReactorSystem', units='kg/hr',S=83333, CE=522, cost=19812400 * 0.993, n=0.6, kW=4578, BM=1.5)
def _cost(self)
self._decorated_cost()

Start with the CSTR source and the ContinuousFermentation example linked in the issue, then inspect PretreatmentReactorSystem and the sys.save_report output. Reproduce the reported power values and the kW_per_m3 override, tracing the cost decorator and add_power_utility paths. Done means documenting the formulas, utility behavior, and the correct way to configure inherited reactors.

Written by the indexing model from the issue text.