Gas log costs

OK...so my bro gave me a call last night and we discussed all the fun stuff that I've been doing while he was trying to convince me to go to Mexico with him.  Well...he did have one good point.  I have this vented natural gas log in my fireplace.  I haven't used it because I just see the vent (aka...the chimney) as a place for all my heat to be sucked up and out.  Also, it doesn't help that we never got our service started...which was because we only have natural gas to fuel the fireplace and the gas company charges us $10/month for service...so we pay $10/mo...used or unused.

OK...getting back on track...the gas log is rated for 90,000 BTU/hr or 26.4 kWh.  In electricity terms, that amount of heat would cost me about $2.24/hr.  For natural gas (we pay by the therm or 100,000 BTU), that equals 0.9 therm or roughly $1.18/hr.  However, we need to factor in that $10 somehow.  This is where the math gets tricky because  I don't have a handle on how often my auxiliary heat runs.  I'm going to make an assumption...looking at my TED graph for the last 24 hrs, I'd say the aux heat was on 25% of the time.  However, I only only going to count when I'm home since my gas log is manual. So, let's downgrade that to 10%.  That's 2.4 hrs.  When that occurs my aux heat boosts electricity use by 10 kWh.  So 10 kWh x 2.4 hrs x $0.085/kWh = $2.04/day x 30 days = $61.20/mo.

So, if I use my gas log instead, it's a little harder to control because its not on a thermostat.  But for comparison sake, I'm going to only add in an equivalent amount of heat.  That will cost me (10/26.4) x 2.4 = 0.91 hrs x $1.18/hr = $1.07/day x 30 days = $32.21 + $10 = $42.21/mo.  So I'd save $20/mo.

Now, there's a lot of assumptions here...first it assumes that all that 90k BTU/hr goes into the house.  Let's not forget that I have a chimney right above it.  So, let's assume we have 33% fugitive heat loss.   Is this number good?  I don't know.  Now that cost changes from $1.07/day to $1.60/day x 30 days = $48 + $10 = $58/mo.  So now it's nearly equal.  And that doesn't even factor in the fact that the gas log doesn't have a thermostat (BTW...it cost roughly $300 to purchase on for my set), so I'd have to sit diligently next to the thermostat to turn the heat off when its not needed.  Or I'd have to set a timer to make sure the gas log is not used more than 1.36 hrs/day (or 0.68 hrs in the AM and 0.68 hrs in the PM).  Oh...and I have to be diligent and close the chimney vent when I'm done using it.

Now I might try to remove some assumptions later by using TED to find 10 kWh jumps, but until then...this is how I see the math.  I'm going to try out using the gas log to see how it goes anyway.

Any thoughts?