Welge's Graphical Method: 2018 #9

Problem 9. The following statement most TRUE concerning modifying the saturation distribution with Welge’s graphical method is:

(A) For gas displacement, the tangent to the fractional flow curve is drawn from the irreducible water saturation.
(B) In actual fact, the saturation front tends to be smeared by gravity at the trailing edge and smeared by capillary action at the leading edge.
(C) For waterdrive reservoirs, a line from the irreducible-water saturation tangent to the fractional-flow curve is drawn; the saturation at the tangent is the flood trailing edge.
(D) For waterdrive reservoirs, a line drawn from the irreducible-water saturation tangent to the fractional-flow curve may be extended to an oil saturation of 1 to find the average water saturation at breakthrough.

This problem is a confusing word garbage dump; it looks like it's written by a lawyer. Be ready for this sort of thing.

So I don't read the details yet. Once I know the theme (Welge) I just run to the Guidebook TOC and scan for Welge. It's on 14 WFL 4. At 10 seconds, I've eliminated (A), since it says that for gas reservoirs you start the line at fw = 0. In the next 30 seconds, (C) and (D) are as easy to eliminate just by looking at the graph and sorting things out.

So by process of elimination I'm selecting (B). And if you understand this whole capillary action, leading edge, and saturation front business, you can see how it makes sense. Need more confirmation? I prefer it. There must be an SPE direct quote here somewhere...

The Handbook Series? I check the index, and I get 1106-1108. Sorting through this mess I find nothing helpful, but do finally find Welge mentioned on page 1108 without any clue for this problem. So I cut my losses and move on.

The Textbook Series? It's a waterflood question so I check TS3 index and find Welge on page 122. But again, this page merely refers me to another section, and neither section gets answers. Ouch.

But it's also a reservoir question. So I check TS8, which has an index entry for Welge with two reference pages (161-162). After several minutes of scanning, I find (B) is a direct quote from page 161! Bingo. As I mentioned last post: be warned that while SPE TS8 is not popular, it is the "official" SPE reservoir reference, and it's got some gems that few other texts have, like hydrodynamic traps and Welge. Of course, by now I'm 5+ minutes down (at least).

The Guidebook would have got you through this one in a minute or less. My general approach? Scan the Guidebook TOC (the cover) and review the relevant page. If I strike out here and have time later on I move to the HS index. Finally, I'm in the TS series, checking books I think relevant.

Honestly, you wouldn't even need to be a petroleum engineer, or even really understand much, to solve this one with the Guidebook. But many, many engineers get flustered by this sort of problem. Just reading the dang thing is a frustrating experience. 

Note: now we have the CBT and no extra resources allowed, one would have to just work through the solution as they best knew how. However, I doubt the CBT will have this level of difficulty for this reason. Only time will tell, but it doesn't hurt to study and understand difficult problems!

Fractional Flow Water: 2018 #8

An oil reservoir dipping at 20 degrees has a flow area of 1 MM square ft and a total fluid flow of 2,830 barrels per day. The oil has a permeability, relative permeability, viscosity, and specific gravity of 40 md, 0.4 md, 1.5 cp, 0.8, respectively. The water has a relative permeability of 0.02 md, with a water/oil viscosity ratio is 0.1. Assuming standard water density and specific gravity, and that the formation permeability averages 100 md, the fractional flow of water is closest to: (A) 0.2 (B) 0.3 (C) 0.4 (D) 0.5.

This problem is nearly the same as the Guidebook example on 14 WLF 2; only the flow area has doubled. The computation then changes to (1-0.4)/(1+2) = 0.6/3 = 0.2, or (A).

To better understand fractional flow in a dipping reservoir, see page 158 of TS8 (Towler). Slider has some good practice problems as well. These problems are not common, but being directly from SPE Textbook Series reservoir text, it's fair game.

Waterflood: 2016 #70

A 2000 acre, 15 ft thick, 15% porosity waterflood reservoir with a Sgi of 20% and a producer/injector distance of 330 ft is started on injection.

How much water volume (barrels) must be injected until interference within a single 5-spot pattern?
Wii = [3.14159/(2*5.615)](330^2)15(0.15)(.2) = 13,710 bbl (B)

How much total volume to pattern's fill-up?
Wif = (2/5.615)](330^2)15(0.15)(.2) = 17,455 bbl (B)

Waterflood Volume: 2005 #38 (similar)

Waterflood has a whole chapter (14 WFL) in the Guidebook. There are a lot of "special" equations.

Yet many (even most) "waterflood" questions are just simple reservoir volumetrics, so you never need to leave the 13 RES chapter. But know the basic volume equations well, such as N = 7,758 Vb phi (1-Swi)/Boi. Note also that 1 - Swi can include 1 - Swi - Sgr - Sor.

A standard problem uses initial water saturation. More complex problems include residual gas and residual oil. For an example:

Vb = 1,400 acre-ft
Porosity = 20%
Swi = 25%, Sgr = 10%, & Sor = 30%
Bo = 1.3 RB/STB, Bw = 1 RB/STB

These are all typical values. Then calculate the max oil that can be removed from the reservoir, by waterflood or otherwise:

[7,758(1,400)0.2(1 - 0.25 - 0.1 - 0.3)]/1.3 = 580 MSTB