This document summarizes the design capacities of horizontal well systems. It reviews 6 cases for cylindrical horizontal wells derived in previous lectures, including a well below a recharge boundary, below an impermeable boundary, and below a leaky aquitard layer. It also derives the design capacities for 4 cases of rectangular horizontal galleries under constant head or recharge rate, with or without a filter bed. The document concludes by recommending the use of numerical models to extend the results to other well geometries, guided by the analytical results reviewed and derived within.

1. DESIGN CAPACITIES OF
HORIZONTAL WELL SYSTEMS
Leonardo Q. Liongson
Team Energy Professorial Chair
in Energy Engineering
Instituteof Civil Engineering
College of Engineering
University of the Philippines, Diliman
Quezon City, Philippines
6th Engineering Professorial Chair Colloquium
6 July 2009

2. Aim of the paper:
To review and derive the design capacities of horizontal wells
(infiltration gallery systems) under the ff. cases:
Part 1: Review for Cylindrical Horizontal Wells
(derived in previous Prof. Chair Lectures in 2007 and 2008):
Case 1. A horizontal well below a horizontal recharge boundary
in a semi-infinite aquifer (exact solution).
(Cases 2 and 3 are variations of Case 1 – not reviewed here).
Case 4. A horizontal well below a horizontal recharge boundary
and above a horizontal impermeable boundary in an infinite
strip of aquifer (exact solution).
Case 5. A horizontal well below a leaky aquitard layer
(silt or clay lenses ) under a horizontal recharge boundary in a
semi-infinite aquifer (approx. r<<b).
Case 6. A horizontal well lying below a finite silt or clay lens
represented by a doublet or a pair of counter-rotating vortices,
under a horizontal recharge boundary in a semi-infinite aquifer
(approx. r<<b).

3. Part 2: Derivation for Rectangular Horizontal Galleries :
Case 1. A rectangular gallery with a filter bed,
under constant head.
Case 2. A rectangular gallery without a filter bed,
under constant head.
Case 3. A rectangular gallery with a filter bed,
under constant recharge rate.
Case 4. A rectangular gallery without a filter bed,
under constant recharge rate.

4. Part 1: Review for Cylindrical Horizontal Wells
(derived in previous Prof. Chair Lectures in 2007) – Case 1

5. Part 1: Review for Cylindrical Horizontal Wells
(derived in previous Prof. Chair Lectures in 2007) – Case 4

6. Part 1: Review for Cylindrical Horizontal Wells
(derived in previous Prof. Chair Lectures in 2007) – Case 4

7. Part 1: Review for Cylindrical Horizontal Wells
(derived in previous Prof. Chair Lectures in 2007) – Case 5

8. Part 1: Review for Cylindrical Horizontal Wells
(derived in previous Prof. Chair Lectures in 2007) – Case 5

9. Part 1: Review for Cylindrical Horizontal Wells
(derived in previous Prof. Chair Lectures in 2008) – Case 6

10. Part 1: Review for Cylindrical Horizontal Wells
(derived in previous Prof. Chair Lectures in 2008) – Case 6

11. Part 1: Review for Cylindrical Horizontal Wells
(suggested in previous Prof. Chair Lectures in 2008) – Case 6

12. Part 2: Derivation for
Rectangular Horizontal Galleries -
Case 1

13. Part 2: Derivation for
Rectangular Horizontal Galleries –
Case 1 vs. Case 2

14. Part 2: Derivation
for Rectangular
Horizontal Galleries –
Case 2

15. Part 2: Derivation
for Rectangular
Horizontal Galleries –
Case 3

16. Part 2: Derivation
for Rectangular
Horizontal Galleries –
Case 4

17. Conclusion:
This paper has
• reviewed the design capacities of cylindrical horizontal wells
(with four (4) cases);
• derived the design capacities of rectangular infiltration gallery
systems (with four (4) cases) ;
• Explained the limitations in the asymptotic value of the design
capacity of rectangular gallery with filter bed, under constant
head, regardless of the length of the gallery.
General Recommendation:
Apply numerical seepage models to extend the results to other
2-D and 3-D layouts and geometries of horizontal wells, guided
by the analytical results reviewed and derived in this paper.

18. THANK YOU !