A way out from getting SystemOutOfMemoryException

we're using ZyWall to guard our servers from external intrusions. It generates daily log files with huge sizes, over a GB, sometimes 2 GBs. They ususally contain more than 10 millions of lines. Now my task is to write an application that will import these lines into Oracle database. I'm writing it in C#. What I'm currently doing is:

I read the logfiles line by line. I do not load the whole file at once:

using(StreamReader reader=new StreamReader("C:\ZyWall.log")) { while ((line=reader.ReadLine())!=null) ...... }
Every line read I split the line into parts according to the commas in it.

string[] lines = line.Split(new Char[] { ',' }, 10);
Then I iterate through the lines array, create a new Row for a predefined DataTable object and assign array values to the columns in the row. Then I add the row to the datatable.

After all the lines are read to the datatable I use OracleBulkCopy to write the data in it to a physical table in the database with the same structure. But the thing is I get SystemOutOfMemoryException as I add the lines to the Datatable object, that is the 3rd step. If I comment out the 3rd step then in the task manager I see that the application consumes the stable amount of memory which is something like 17000 K but if I uncomment that step the memory usage grows unless there's no enough memory to allocate. Is there still a way I can use BulkCopy to perform this or will I have to do it manually? I used BulkCopy becasue it's way faster than inserting lines one by one.

If I understand correctly, you are loading each line in a table that becomes so large as to reach the limits of the memory of your system.
If so, you should find this limit. (For example 1000000 lines). Stop reading the lines well before this point and write the rows loaded so far with OracleBulkCopy. Cleanup your memory and start again. So let me summarize everything with a pseudocode.

int lineLimit = GetConfiguration("lineLimit"); 
int lineNumber = 0;
DataTable logZyWall = CreateLogTable();

using(StreamReader reader=new StreamReader("C:\ZyWall.log")) 
{ 
    while ((line=reader.ReadLine())!=null)
    {
        DataRow row = ParseThisLine(line);
        logZyWall.Rows.Add(row);
        lineNumber++;
        if(lineNumber == lineLimit)
        {
            WriteWithOracleBulkCopy(logZyWall);
            logZyWall = CreateLogTable();
            lineNumber = 0;
        }
    }
    if(lineNumber != 0) WriteWithOracleBulkCopy(logZyWall);
}