Eu tenho um documento XML (caseiro) que possui uma estrutura como a seguinte:

<?xml version="1.0" encoding="utf-8"?>
    <wf:wf version="1.0a" xmlns:wf="http://example.com/workflow" xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://example.com/workflow">
  <wf:assemblies />
  <wf:dataDefinitions />
  <wf:processes />
  <wf:workflows>
    <wf:workflow id="g08615517-cdfd-4091-a053-217a965f7118">
      <wf:arguments />
      <wf:variables>
        <wf:variable id="g39ffecc9-f570-41c1-9ee0-b9358d63da3c" parameterType="Hidden">
          <wf:name>UIPTaskId</wf:name>
          <wf:dataDefinitionId>gc8f3715c-4a82-42d2-916c-51515083e7e5</wf:dataDefinitionId>
        </wf:variable>
        <wf:variable id="g46663a0c-7e60-4bd2-80df-16cd544087ad" parameterType="Hidden">
          <wf:name>UIPTaskName</wf:name>
          <wf:dataDefinitionId>g359FC555-9CC7-47D4-8ED3-EF973E7D74D7</wf:dataDefinitionId>
          <wf:value>Responsible Individual</wf:value>
        </wf:variable>
        <wf:variable id="gb32914d5-6761-4e82-b571-c8944a796fd9" parameterType="Hidden">
          <wf:name>Search?</wf:name>
          <wf:dataDefinitionId>g57201da8-62b4-46f2-9329-c71d86f39ffc</wf:dataDefinitionId>
          <wf:value>True</wf:value>
        </wf:variable>
    </wf:variables>
</wf:workflow>
</wf:workflows>
</wf:wf>

Eu tenho um utilitário para limpar os documentos XML e estou usando o XDocument para carregar o arquivo e depois percorrer determinados nós e substituir valores. Depois de concluído, estou chamando o método Save para salvar o arquivo em um novo local e, após uma inspeção mais aprofundada, o método Save está removendo meu prefixo wf em cada nó. Como posso preservar isso? Estou fazendo algo errado? Aqui está um exemplo do meu código:

string wf = "wf";
string wkfl = "C:\\MyFiles\\Temp\\myfile1.rrr";

XDocument xdoc = XDocument.Load(wkfl);
XElement variables= xdoc.Descendents(wf + "variables").Single();

foreach(XElement variable in variables.Elements(wf + "variable"))
{
    XElement name = variable.Element(wf + "name");
    name.Value = name.Value + "_MODIFIED";  
}

xdoc.Save(wkfl.Replace("\\Temp\\", "\\Modified\\"));

O método Save produz o seguinte XML:

<?xml version="1.0" encoding="utf-8"?>
        <wf version="1.0a" xmlns:wf="http://example.com/workflow" xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://example.com/workflow">
      <assemblies />
      <dataDefinitions />
      <processes />
      <workflows>
        <workflow id="g08615517-cdfd-4091-a053-217a965f7118">
          <arguments />
          <variables>
            <variable id="g39ffecc9-f570-41c1-9ee0-b9358d63da3c" parameterType="Hidden">
              <name>UIPTaskId</name>
              <dataDefinitionId>gc8f3715c-4a82-42d2-916c-51515083e7e5</dataDefinitionId>
            </variable>
            <variable id="g46663a0c-7e60-4bd2-80df-16cd544087ad" parameterType="Hidden">
              <name>UIPTaskName</name>
              <dataDefinitionId>g359FC555-9CC7-47D4-8ED3-EF973E7D74D7</dataDefinitionId>
              <value>Responsible Individual</value>
            </variable>
            <variable id="gb32914d5-6761-4e82-b571-c8944a796fd9" parameterType="Hidden">
              <name>Search?</name>
              <dataDefinitionId>g57201da8-62b4-46f2-9329-c71d86f39ffc</dataDefinitionId>
              <value>True</value>
            </variable>
        </variables>
    </workflow>
    </workflows>
    </wf>