Hi Kim,
You will need 19 weeks with two draws per night to complete all but one of the draws. I have put a possible schedule below where the 18 teams are represented by the letters A to R:
(K R) (A M) (G Q) (C H)
(E P) (B O) (D N) (F I)
------------------------
(M N) (C F) (E R) (A L)
(B H) (I K) (J Q) (D G)
------------------------
(A I) (L O) (B E) (G R)
(D P) (F Q) (J N) (H K)
------------------------
(H I) (K P) (M Q) (G L)
(F J) (A O) (D R) (C N)
------------------------
(E G) (A R) (O P) (D Q)
(J L) (H M) (C I) (K N)
------------------------
(B F) (J K) (I M) (D O)
(L R) (A P) (H N) (E Q)
------------------------
(F R) (I N) (G P) (E M)
(B Q) (C J) (K L) (A H)
------------------------
(I P) (J M) (D F) (G O)
(E N) (L Q) (C K) (B R)
------------------------
(C P) (F G) (B L) (A N)
(E K) (I O) (D M) (J R)
------------------------
(N O) (H R) (F M) (I Q)
(G K) (E L) (A J) (B P)
------------------------
(D I) (G N) (A B) (J P)
(M R) (E H) (F L) (C O)
------------------------
(A Q) (C R) (N P) (D L)
(K O) (B M) (F H) (E I)
------------------------
(J O) (E F) (C L) (B I)
(D H) (N Q) (A G) (K M)
------------------------
(L N) (D E) (B K) (H J)
(G I) (O Q) (C M) (F P)
------------------------
(G M) (L P) (H O) (F K)
(A C) (B D) (I J) (Q R)
------------------------
(B J) (D K) (H Q) (A E)
(F O) (C G) (P R) (L M)
------------------------
(C Q) (B N) (O R) (E J)
(M P) (I L) (G H) (A F)
------------------------
(K Q) (H P) (I R) (B C)
(A D) (G J) (E O) (F N)
------------------------
(H L) (D J) (A K) (M O)
(B G) (N R) (C E) (P Q)
The missing draw is (C D) which could usefully by played on some other day during week 10 when these are the two teams with byes. There is some balance to the schedule, with teams 4 or 5 times on each sheet and 8 or 9 times in the early and late slots.
Ian