Attack drones carrying nukes and long-range fuel tanks
I also don't see any restrictions about "wishing for infinite wishes" i.e. creating more duplicate portals, so I'm going to go with Von Neumann probe attack drones, carrying nukes and a duplicator portal kit (just to speed things up). Although as it turns out, even if duplicating the portal isn't allowed, I don't think being limited to a single replicator will end up mattering that much.
You haven't provided any capacity limitations other than "about 5 per minute" and the requirement that any duplicates have been continuous operating exactly like the original (e.g. battery / food consumption), so the main restrictions for any solution are going to be either speed in replication/distribution, or sufficient firepower to maintain an advancing front at a slower pace. I'm going with some of both, and allowing for decentralized production.
I'm going to just stick with back-of-the-envelope estimates on the math, but this actually looks a lot easier than I anticipated.
Delivery System Design - Range and Coordination
Let's start with a standard Reaper drone, a existing, real-world, combat-proven design. We'll need to modify it slightly so the wings (and maybe the tail and landing gear) fold back to fit through the car-sized entryway, but otherwise this looks like a pretty good starting point:
- Max speed 300 mph (480 km/h)
- Max payload 3,800 lb (1700 kg)
- Flight time 23-42 hours (depending on loadout)
- Range 1150 mi (1850 km)
- Altitude 50k ft (15 km)
These drones will have plenty of speed to clear the production area, especially if you put the original portal in the back of a cargo plane already in the air and let them come blasting through at full speed and out the back of the plane, where they untuck their wings and disperse. This is only a boost to the 1st generation, but it gives you a needed jumpstart before anyone can respond and try to down your tide of doom. If in-flight deployment from a 'fixed' point in the bay of the plane turns out to be forbidden by the OP, it's not a deal-breaker though.
2nd modification is going to be the power/fuel supply - we need to get a clone of the original to the other side of the planet to achieve full annihilation. It either needs an in-flight recharging system, or enough power to go the full distance on it's own. Let's check our initial range for an example loadout with 2 external fuel tanks and 'only' 1000 pounds of munitions - 42 hours of operation. At 300 mph, that's a 12,600 mile max range; we'll talk about the operating limitations in a minute, but our drone can already fly that far out of the box.
Getting halfway around the globe requires a range of 1/2 the Earth's circumference - 24,900 / 2 = 12,450 miles. Ok, we're already there! But, we need some allowances for replication time, opposing winds, lost units from aerial defense, etc... But we don't have to actually spread our swarm all the way to the antipode of Ground Zero; we just need to cover the land masses, and honestly after getting a majority of those completely coated with nukes, the fallout and weather are going to take care of the rest in a few months.
Location, location, location
Let's start our doomsday plan off the coast of central Africa, say over São Tomé and Príncipe, because all super-villain plans to destroy the world should start on a volcanic island. We'll save the islands of the Pacific for straggler drones to clean up (or just let them perish from fallout/starvation after a few months). The farthest land radially from there, from eyeballing a globe, is only about 2/3 of the way around (either New Zealand, Japan, or Alaska), so 12,450 * 2/3 = 8,300 miles. Totally doable for the Mark 0 (and any derivates) on a single tank, so no refueling to deal with! Perfect, because carrying and transferring fuel for future generations was going to be a huge hassle.
Okay, so our drones can reach the far ends of every continent - how do we control them? The original range limit of 1150 miles is based on communicating with a single, central control location; but our drones are going to be autonomous. They just need to divide up the work. This isn't terribly complicated - the Mark 0 could have a set of pre-planned routes, and each copy would get assigned one while coming through the portal (with plenty of redundancy for some getting shot down). Or just let them play zone coverage and collaborate with the nearest drones about who's going left or right. They'd need a securely encrypted, on board, distributed communication network to coordinate with, but a wi-fi mesh isn't exactly new technology.
So, while other villains might introduce a super-plague, or accelerate global warming with a moon laser, our plan is good ol'-fashioned nukes. Rather than try to re-invent the wheel, Mark just needs to steal a single nuke and crack its command codes. And probably replace them with his own well-tested system, since every single copy will have the exact same vulnerabilities.
We could go for the biggest one we could find... The Tsar Bomba was ridiculously large at around 50 megatons, but is not a production weapon, so let's try the largest currently in the US arsenal, the B83 with a yield of 1.2 megatons. Yield is almost always compared to the Hiroshima yield (1bout 15 kilotons), so around 80 of those. Sadly, this firepower comes with a weight of 2400 lb (1100 kilos), which is double our weight budget after loading up on fuel tanks.
On the other other of the spectrum is the portable hand-held mini nuke, which weighed only 51 pounds - our drone could hold 20 of those! Sadly it only had a yield of 20 tons, or .02 kilotons, or 0.0002 megatons... ok, the technology has improved, so a similar size would yield a lot more these days, but that's still far too small for total world destruction on a schedule. Let's find some middle ground - I picked the recently-retired W87 warhead at random from a Wikipedia list. A design yield of 300 kilotons, upgrade-able to 475; only 1/3 to 1/4 of the B83's yield, but at a weight somewhere between 440-600 lbs (200-270 kg) we can carry 2 of them. There's probably some similar design with a comparable yield and lower weight, and we could strip off some safety shielding at the last minute to save weight, so we could potentially carry 3 or even 4 with a yield in that range.
Attack Plan basics - no re-replication
Ok, we've got autonomous nuke-carry drones streaming out of a portal - where do we send them?
Our lair on São Tomé and Príncipe has not just the advantage of being centrally located geographically, but is also about as far as possible from most of the nuclear countries. This maximizes how many drones will be in the air before the initial strikes and counter-defense. You'd obviously want a lot of firepower in play before starting, but let's assume you're going to going to start things off in the Middle East because of the history of nuclear tension in the area - might as well try to trigger some MAD attacks and get some help from the existing nuke arsenals around the world.
I'm not sure what air defense most of Africa has, but it's a fair bet that a constant stream of drones would be world news within a few hours. Obviously you'd plan ahead to map out ideal routes, but even with high altitude flight some airports are going to see you and demand to know what's going on over their airspace. No one's going to start shooting immediately, so let's pick Egypt as the first point of attack for our expanding fleet where interception begins.
The middle of Egypt is 2400 mi (3880 km) away, or 8 hours of flight time. If we've been pumping out 5 drones per minute the entire time, our fleet consists of (5 * 60 * 8) 2400 drones, either spread semi-evenly across all of Africa, or more likely weighted toward the north to deal with the impending resistance from nuclear countries. With 4 nukes each, that's 9600 nukes to start neutralizing defense threats with across the entire continent, plus an additional 2400 kamikaze kinetic drone attacks after bomb/missile deployment that can continue much farther afield to start softening up future targets.
Without even looking for maps of international defense installations (I'm sure my search patterns are already raising some flags), I'm going to assume that's enough to do some serious damage and erase response capability over a several hour radius. If our drones have some simple air-to-air measures as well, that's probably enough to put up a pretty impenetrable barrier; even without self-defense, they could just fly to intercept and scatter their payload on a short fuse for a pretty formidable blast wall.
So, just keep pumping drones farther and farther afield until we've coated the entire Earth to a sufficient degree. Starting with Africa (aside from a small clear zone around the base) - 20% of Earth's land area, ~12 million square miles, divided among our 9600 nukes, is 1 city-killer every 1250 square miles (or a square ~35 miles per side) in the first wave of attacks. Not exactly carpet-bombing, but given that human population is mostly gathered in cities we wouldn't actually spread the attack evenly across a grid. That's pretty thorough coverage for the first wave.
At that point, drones emerging from our base still have 34 hours of flight time, and can still reach the far edges of our target areas. We could let a dozen or so of the first wave head over the Antarctic or South America to deal with the stray islands in the Pacific before later drones could no longer reach.
Attack Plan 2 - infinite wishes
Now, we've done this all with a single portal - what about thinking with portals? The basic plan seems pretty formidable already, but what if we could expand production?
We don't know anything about the portal itself except that it needs to be fixed to something to start operating, and can't be moved again once it starts operation. I think the intent of that restriction was probably to prevent just moving it all over spraying materiel, so I think replicating the 2nd prototype seems reasonable. It's definitely the first thing any self-respecting mad scientist would try after inventing it. It also blows up expansion, if you'll forgive the term, incredibly fast and leads to overwhelming forces that tend to ruin a story if left unchecked, which is why Von Neumann probes are a) not written about that often, b) are a terrifying idea that are generally expected to result in the destruction of everything they touch if some lunatic ever actually builds one, and c) would have rate/generational limiters built in if there was really a reason to use them. But, we're here to destroy the world, so don't worry about any of that.
Let's make it a square metal frame that's relatively thin, so the assembled version can a) be carried and deployed on the back of the drone, b) contain its own unobtainium power supply, and c) be angled to fit diagonally through its clone's opening. Let's also assume it takes a negligible amount of time to set up and switch on, and starts working immediately. Adding a small delay (5-10 minutes) slows things down a bit, but doesn't really affect the math long term. So hey, to keep things simple let's make The Device air-droppable, so the drone can slow down, drop it low and slow over an open field, and then do a barrel roll and dive into it just after it comes to rest and powers on.
Obviously you need to spread your base of operations to a) provide redundancy when the counterattacks start, and b) improve your coverage and rate of production. This may be Earth's last day, but you still don't want it to take all day.
Let's skip the advanced calculus of exponential growth rates, acceleration/deceleration times, etc, and just look at replication as batches of drones, with a new wave every 30 minutes flight time. That gives you a production ring every 150 miles (240 km). Each portal running at 5 copies/minute will make 5 * 30 = 150 new copies every generation. Every single drone then continues to disappear into its newly-deployed portal every 30 minutes, until after a set number of generations we decide there's enough to carry out the actual attack and stop making new portals. Turns out, that's probably only 3 generations, after which we can quit worrying about enough drones and start worrying seriously about air traffic control.
- Gen 0, t+00:00 - 1 drone; 1 portal
- Gen 1, t+00:30 - 150 drones; 150 portals
- Gen 2, t+01:00 - 22,500 drones; 22,500 portals
- Gen 3, t+01:30 - 3,375,000 drones; 3,375,000 portals (end portal reproduction)
- Gen 4, t+02:00 - 506,250,000 drones (every 30 minutes)
So only 2 hours in, we're producing 500 million drones, with 4 huge nukes each, every 30 minutes, somewhere within an expanding cloud with a radius of only 600 miles. Or in other words, 2 billion nukes (1 for every 3.85 people on earth), loaded in long-range drones, every 30 minutes. In the 8 hours before first strike in our initial scenario, there will now be something like (500M + 6*2*500M) 6.5 billion drones (26 billion nukes) dimming the sun over the entirety of Africa and much of the south Atlantic.
Forget about targeting just the continents at this point. Earth's total surface area is only 196.9M square miles, so we're at 1 nuke for every 0.0076 square miles, or a square ~460 feet (140 m) per side. Better 20 Hiroshima explosions per city block, with uniform coverage worldwide.
...I'm not even sure you need an attack plan at this point, international nuclear defense capabilities just can't deal with those sorts of numbers. Just assign each drone a coordinate, and sit back to watch the show.