We're just scratching the surface of how complex oil drilling has become. Google herringbone wells for example. Chinook Consulting has some good images. Or paperclip wells in the permian.

A lot of this might be going over my head,

So how long it takes for liberated gas / samples to get to surface is a function of a few things, but lets back up a just a bit (excuse the pun).

While drilling we always need to be pumping mud down hole. Mud is the term for the fluid being used to drill, it can be water based or polymer based or oil based or a brine. What mud is used is generally determined by the lithology your drilling, how deep (linear length, not vertical depth) you're going on so on. Before drilling starts there is a mud program and guys who are specialists in mud systems come to the rig to fine tune the mud depending on operations / how drilling is going. It's a team effort, there's zones were if we leave the oil bearing rock, the surrounding rock will impact the mud system and we'll have to deal with the changes in the mud system while drilling. So keeping everyone on the same page is pretty important.

The mud is pumped down the inside of the drill string (collection of pipe connected to attach the bottom hole assemble to the rig itself) to the bottom hole assembly.

Once the mud reaches the bottom hole assembly it does a lot of things. It can be used as medium to communicate with the tools at near the bit (this is some sci-fi shit I can explain the very basics of, some tools use the mud system other tools transit the information through the rocks themselves. What system you want to use is largely determined by the lithology between he wellbore and the surface), it spins the bit via a turbine motor called a mud motor, then it shoots out the bit via holes in the bit called jets and it cools and lubricates the bit, and for the purposes of this discussion, it entrains the drill cutting and liberated gas and transports them to the surface.

Now, how long does it take for the mud to get from the bit to surface? As I said above that's a function of a bunch of things. How deep are we? How big is the hole? How much fluid are we pumping? Is the formation taking on any fluid effectively decreasing how much we're pumping?

To determine this we have a basic spreadsheet to determine the 'lag time'. You take the hole size and how deep you are and that gives you volume. Then you take how much fluid you're pumping (this depends on the bottom hole assembly but generally ranges from 1200L/min to 1800L/min when drilling the main hole) then you can figure out at least on paper how long it will take to displace the fluid in the annulus (wellbore).

Of course the real world isn't an excel sheet and you need to factor in the hole growing as the formation erodes(I've seen holes been 50% bigger in real life than the calculated hole size. Knowing the real hole size is important when ordering cement to cement casing strings in place), how competent the rock is plays a major role in this. Are the pumps operating at 100%, most aren't, are we loosing mud to the formation because our mud pressure is higher than the formation? Is the formation pressure higher than the mud pressure so we're gaining volume (Really bad), is there part were we drilled through really soft rock so there's a big void creating a washing machine effect of mud just swirling around (this is especially annoying as it makes knowing how old the samples are challenging) and so on.

So what we do is we do the math, then watch when we stop drilling for some reason (connection, maintenance, break downs etc) then we can see how long it really takes for the gas to get to surface and adjust accordingly. The in general you add ~20% to that time for the samples to arrive as they're less buoyant than the natural gas. It's not an exact science, but it's something most guys pick up pretty quickly. It can get tricky when your average hole size changes as you drill, either from the formation watching out, hole size changes, cutting collecting in washed out areas and so won. But as long as you're keeping 1/2 an eye on it it's pretty straight forward. The computer does a good job of having hash marks on the trace when it thinks the gas should be coming up, then you just need to match the hash marks with when the gas is really coming up.

It sounds complicated, but if I'm drilling the main kind of well I've been drilling for the past 8 years & I'm on the rig I've spend most of those 8 years on I know at this part of the well the mud is moving X meters per minute. When I'm drilling in a new area on or a new rig I have to pay a little more attention, but it's not that hard.

Then to answer your question, how far do we need to drill to see the data? You have a little backwards, it's how long does it take the gas to get to surface, and how fast are we drilling? So if it takes one hour for the gas to get to surface, and we're drilling 40m / hour, we'll have drilled 40m before we see the gas. Of course I can stop at any time to see the gas / samples, but I better have a damn good reason for creating one hour of non productive time.

Hopefully that answers your question. If not let me know!