Reservoir height's effect on production in horizontal well

[TBone]

In a vertical well, the production rate is proportional to the height h. This is understandable, as one can imagine two reservoirs on top of each other if the h is doubled. However, according to popular equations (Joshi's and so on) this is also true for a horizontal well. This does not make sense to me.. Any ideas?

[vinomarky]

It does make sense if you think about the analogy of partial penetration - ie you have a 50 ft net pay reservoir with vertical well, which you only perforate 10ft of.... For sure you will have some rate reduction compared to perforating the entire zone, but it will not be one fifth of the production rate... and intuitively you'd expect the reduction to be affected in large part by the vertical perm over the unperforated section (ie how easily can the fluids migrate up to the pressure sink)

Similarly, horizontal wells benefit from more height

While the Joshi equation (1988) does have height terms in the denominator as well (which mean it will not predict rates increasingly directly in proportion with height), the more complex analytical horizontal well equations seem to take this effect into account better. Using the set of equations outlined in SPE 97190 by H.Y. Chen & N. Assad, and taking as example for the following geometry predict the following outcome;
Skin = 0
rw = 0.3ft
Visc = 0.8 cP
B = 1.08
Kx = Ky = 150mD
Kz = 1mD
Length = 500ft
Vertical Penetration = 10ft
Azimuthal Bearing = 0 degrees
Centered in reservoir 3000ft x 3000ft arealy
1,500 psi drawdown

Thickness (ft) Rate (bpd)
10 7,212
25 11,651
50 13,630
100 13,939

If you increase the vertical perm to 15mD, you get;
Thickness (ft) Rate (bpd)
10 8,659
25 18,646
50 29,119
100 38,631

Again, unsurprisingly you get (a) more rate with more net, (b) increased rate benefit per net ft addition with higher Kv/Kh and (c) Higher rates with higher Kv/Kh period

Takeaways are - while more net yields more rate, you need reasonable Kv/Kh to unlock the value

[Shakespear]

Do a little simulation like here.

[link Point to another website Only the registered members can access]

Vary reservoir parameters and see what happens. You will learn more this way than through words.

Take this one data set and modify using OFFICE to see what happens.

HORZWELL.DATA in ECL Data subdirectory.