grep 명령어 패턴에 변수를 넣을순 없나요?

#!/bin/bash
 user1='dwarp'
 user2='rush'
 
 HOME=/var/log/center
 cd $HOME
 
 if [ -f userinfo.txt ]; then
   sudo rm userinfo.txt
 fi
 
 for file in *
   do
     if [ 'log_' = ${file:0:4} ]; then
       grep -w 'LOG IN-2 : ['$0078dh']' $file >> userinfo.txt
       grep 'LOG IN-2 : dwarp' $file >> userinfo.txt
     fi
done