Skip to content

Update aem_benchmark.md #5

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
wants to merge 1 commit into
base: main
Choose a base branch
from
Open

Update aem_benchmark.md #5

Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
10 changes: 5 additions & 5 deletions docs/theory/aemmodel/aem_benchmark.md
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -1,7 +1,7 @@
# Analytical Element Method (AEM) model benchmark


The AEM implementation has been tested against doubletcalc1D, the analytical solution thiems
The AEM implementation has been tested against DoubletCalc1D, the analytical solution by Thiems
for a doublet with vertical wells in a homogeneous reservoir (Van Wees et al., 2012).

In addition, the AEM implementation has been benchmarked against analytical solutions of for deviated wells in homogeneous reservoirs by:
Expand All @@ -13,7 +13,7 @@ and against the NLOG spreadsheet based on Egberts and Fokker (2001) for horizont

## Thiem's solution for multiple wells in a homogeneous reservoir

The steady state pressure conditions at distance r from the well radius is given by Thiem’s solution for an infinite aquifer:
The steady-state pressure conditions at distance r from the well radius is given by Thiem’s solution for an infinite aquifer:

$p(r) = \frac{\mu q}{2 \pi k H} ( \ln\left(\frac{r}{r_w}\right) + S)$ (eq. 1)

Expand All @@ -39,11 +39,11 @@ This figure can be reproduced with the corresponding unittest in *test_benchmark

## Deviated wells in homogeneous reservoirs

In three dimensions we tested the a progressively inclined well, with deviations from vertical from 0 to 70 degrees.
In three dimensions we tested the a progressively inclined well, with deviations from 0 (vertical) to 70 degrees.
The center of the reservoir is at 2300 m depth, with a thickness of 100 m. the average distance between the perforated sections of the wells is maintained at 1300 m.
For a well with 0 degrees deviation, the results are compared with Thiem's solution and DoubletCalc1D for a doublet with vertical wells in a homogeneous reservoir according to eq. 2.
For increasing deviation from vertical, the AEM results are backbalculated to equivalent skin to a vertical which are required to obtain the same PI and II as the AEM results.
they are compared to the analytical solutions from Cinco et al. (1975), Rogers and Economides (1996), and Besson (1990).
They are compared to the analytical solutions from Cinco et al. (1975), Rogers and Economides (1996), and Besson (1990).


![Figure 2](../../images/skin_vs_deviation1.png)
Expand All @@ -64,7 +64,7 @@ This figure can be reproduced with the corresponding unittest in test_benchmark_

## horizontal wells in homogeneous reservoirs

For horizontal wells, relations are used that are based on the 3D-2D transition method that was developed by Egberts and Fokker (2001)., and available as spreadsheet tool at nlog.
For horizontal wells, relations are used that are based on the 3D-2D transition method that was developed by Egberts and Fokker (2001), and available as spreadsheet tool at nlog.
Possible permeability anisotropy is taken into account in this expression.We focus the comparison of the pressure on the injection well. The general input parameters our simulations are a viscosity of 0.817 mPa.s; an injection rate of 400 m3/hr;
a horizontal permeability of 100 md; a well radius of 0.1 m and an aquifer thickness of 100 m at a depth between 2300 and 2400 m.
In a first sensitivity exercise, we position two parallel horizontal wells at a distance of 1000 m. The length of the two wells is varied between 50 and 2000 m.
Expand Down