Export big amount of data from XLSX - OutOfMemoryException

The OpenXML SDK is the right tool for this job but you need to be careful to use the SAX (Simple API for XML) approach rather than the DOM approach. From the linked wikipedia article for SAX:

Where the DOM operates on the document as a whole, SAX parsers operate on each piece of the XML document sequentially

This vastly reduces the amount of memory consumed when handling large Excel files.

There's a good article on it here - http://polymathprogrammer.com/2012/08/06/how-to-properly-use-openxmlwriter-to-write-large-excel-files/

Adapted from that article, here's an example that outputs 115k rows with 30 columns:

public static void LargeExport(string filename)
{
    using (SpreadsheetDocument document = SpreadsheetDocument.Create(filename, SpreadsheetDocumentType.Workbook))
    {
        //this list of attributes will be used when writing a start element
        List<OpenXmlAttribute> attributes;
        OpenXmlWriter writer;

        document.AddWorkbookPart();
        WorksheetPart workSheetPart = document.WorkbookPart.AddNewPart<WorksheetPart>();

        writer = OpenXmlWriter.Create(workSheetPart);            
        writer.WriteStartElement(new Worksheet());
        writer.WriteStartElement(new SheetData());

        for (int rowNum = 1; rowNum <= 115000; ++rowNum)
        {
            //create a new list of attributes
            attributes = new List<OpenXmlAttribute>();
            // add the row index attribute to the list
            attributes.Add(new OpenXmlAttribute("r", null, rowNum.ToString()));

            //write the row start element with the row index attribute
            writer.WriteStartElement(new Row(), attributes);

            for (int columnNum = 1; columnNum <= 30; ++columnNum)
            {
                //reset the list of attributes
                attributes = new List<OpenXmlAttribute>();
                // add data type attribute - in this case inline string (you might want to look at the shared strings table)
                attributes.Add(new OpenXmlAttribute("t", null, "str"));
                //add the cell reference attribute
                attributes.Add(new OpenXmlAttribute("r", "", string.Format("{0}{1}", GetColumnName(columnNum), rowNum)));

                //write the cell start element with the type and reference attributes
                writer.WriteStartElement(new Cell(), attributes);
                //write the cell value
                writer.WriteElement(new CellValue(string.Format("This is Row {0}, Cell {1}", rowNum, columnNum)));

                // write the end cell element
                writer.WriteEndElement();
            }

            // write the end row element
            writer.WriteEndElement();
        }

        // write the end SheetData element
        writer.WriteEndElement();
        // write the end Worksheet element
        writer.WriteEndElement();
        writer.Close();

        writer = OpenXmlWriter.Create(document.WorkbookPart);
        writer.WriteStartElement(new Workbook());
        writer.WriteStartElement(new Sheets());

        writer.WriteElement(new Sheet()
        {
            Name = "Large Sheet",
            SheetId = 1,
            Id = document.WorkbookPart.GetIdOfPart(workSheetPart)
        });

        // End Sheets
        writer.WriteEndElement();
        // End Workbook
        writer.WriteEndElement();

        writer.Close();

        document.Close();
    }
}

//A simple helper to get the column name from the column index. This is not well tested!
private static string GetColumnName(int columnIndex)
{
    int dividend = columnIndex;
    string columnName = String.Empty;
    int modifier;

    while (dividend > 0)
    {
        modifier = (dividend - 1) % 26;
        columnName = Convert.ToChar(65 + modifier).ToString() + columnName;
        dividend = (int)((dividend - modifier) / 26);
    }

    return columnName;
}