Hi ron00nor,
It is difficult to tell why that would not work because the syntax all appears to be correct.
Have you tried enabling “Display SQL Queries” in the “Output and Debugging Preferences”? This will display all the queries used to display the data on the page, and you should be able to find a query for your weblog entries tag by searching on the page for “projecten” or possibly “DBPR_PEID”. You will then be able to see if the correct value for {logged_in_member_id} is being used in the query string.
Also, it may be worth placing some static text in the weblog entries loop, so that it is easier to tell if it is actually looping (because it may be looping, but ‘{DBPR_Plaats}’ could be empty?), for example:
{exp:weblog:entries weblog="projecten" search:DBPR_PEID="={logged_in_member_id}" disable="categories|pagination|trackbacks"}
DBPR_Plaats = "{DBPR_Plaats}"
{/exp:weblog:entries}