Optimal Well Positioning

Do you know your wellbore path, exactly? Each directional survey has some small uncertainty, and it all adds up to the “cone of uncertainty”. Do you know the shape of the geologic structure you’re drilling through, exactly? There’s additional uncertainty in the while-drilling well logs geologists use to gauge the well’s stratigraphic depth within the target zone. That translates into additional uncertainty about the geologic structure.

Conventional geosteering tools only draw pictures of one well path and one possible geologic structure. But geologists keep a richer model in their heads. If you used a tool having a rich, probabilistic model (like the one in your head, but tireless) that describes everything the LWD implies about the geology as you drilled through it, you could make well steering decisions that have lower risk and higher payoff. A sophisticated new generation of software now empowers you to evaluate steering choices objectively and quantitatively.

While you’re drilling the well, you occasionally adjust your well path, because the geology surprised you; the well has exited the productive zone, and you need to steer the well back into that zone. You know your well position, uncertainly, and you know the geologic structure, also uncertainly. Your job is to get the wellbore back into the target.

In the Permian basin, over the first six months of production, drillers have gotten about twelve barrels of production for every lateral foot [1]. At $60 per barrel, every foot your wellbore remains out of the productive zone costs you $720. And yet, there’s a cost to changing your well direction too sharply. Wells with too much tortuosity suffer production lost to low-point sumps, to completion problems, and to difficulty pushing casing. Let’s arbitrarily assign a penalty of $5 per remaining foot of lateral, for each degree of angle change (“dogleg severity”).

How aggressively should you steer back into the zone? That depends where you believe the wellbore is relative to the target zone. Factor Drive®, a real time computed geosteering tool, quantifies your knowledge about the well’s position relative to the structure as a probability distribution.

Gamma ray signatures from similar rocks can lead to uncertainty in your idea of the well's true depth.
Gamma ray signatures from similar rocks can lead to uncertainty in your idea of the well's true depth.

Say you’re drilling horizontally at 5,000 feet down a planned 10,000 ft lateral, and geosteering indicates you’ve drifted two feet above the zone. If you do nothing, the remainder of your well is a bust. If you steer down one degree, you’d miss 115 ft of production but would be in zone the rest of the 5,000 feet. You’d pay a $25,000 tortuosity penalty on the rest of the lateral. Your net payoff on the remaining lateral is $3,492,502. The best choice for this case is to steer down 1.8°, for the maximum payoff $3,509,178. Any steeper a change, and the tortuosity penalty outweighs the extra reward for more length in production.

If, instead of two feet above zone, you were twelve feet above, your best direction change would be 4.5°.

Usually, the picture is a little muddier. The type log for some areas can show a similar looking gamma ray for two beds, a few feet apart. If you’re drilling horizontally and reading a gamma ray value characteristic of those beds, you can’t tell from that alone whether you’re in the upper or the lower of the two. You can find yourself in this situation for many reasons. Maybe you crossed a fault without realizing it, leaving you in one or the other of the two beds.

Imagine a case where you think you’ve got a 60% chance of being in the lower bed, two feet above the zone, but a 40% chance of being in the upper bed, twelve feet above the zone. The bars of this chart show the probability your wellbore is in any one-foot interval above your target:

Probability distribution for feet above zone
Knowing a probability distribution for the well's distance from the productive zone is key to making quantitative steering decisions.

To steer back into the zone, we have to balance the payoff for getting back to the zone quickly, versus the penalty for turning too sharply. But this time, we have to account for our positional uncertainty – are we two feet or twelve feet above the zone, or a little in-between?

This next chart tells us the payoff probability, computed using all the example parameters above, for choosing to steer any particular angle. Despite the fact that we’re more likely two feet, rather than twelve feet, above the zone, we should steer aggressively (4.5°) to get back to the zone. There’s still a significant chance we’re twelve feet above the zone, and if that’s the case, the penalty for missing the hydrocarbons is so severe we have to steer sharply to avoid it.

Probability distribution over inclination for payoff
The math tells you that you get the highest payoff for the least risk by changing the inclination to 4.5°.

Setting the oil price to $30 instead of $60 makes it less urgent to get back to the zone. The optimal angle then would be 3°. Naturally, it would make sense to let oil price be a random variable too, so that we could make our steering decisions allowing for the normal volatility you expect in the oil price over six months.

Computed geosteering display from Factor Drive
Factor Drive continuously calculates probability distributions for the well's position relative to the geologic structure and identifies the single most probable structure°.

Factor Drive is the key piece that computes the probability that you’re two feet, or twelve feet, above the zone. The red and yellow “river of flame” in this screenshot tells you the rigorous probability for the depth of the geologic structure. (The light blue zone shows the single most likely structure). Factor Drive is a computed geosteering program that assists geologists, automating the drudgery of geosteering interpretation. It uses an innovative, computationally intensive technique that computes the probability of every possible geologic structure and summarizes it in a picture like this. While drilling, it continuously consumes new LWD and directional surveys and updates the computation so you can make the best real time decisions. And it keeps this picture up to date continuously. You probably want a demo.