How to zip / 7zip / or any other compress a list of files

I'm basically trying to do some basic log deleting operation by several steps.

1st - get all the files that are older then X days (7 in my case)
2nd - zip them to a different location
3rd - delete the zipped files
4th - go over the folder of zipped logs and delete older then 30 Days

1st - accomplished - I get the list of files
3rd - not a problem - I think
4th - same as 1st ...

2nd ... here I try to use the 7zip as it is already embedded in Windows we have strict policies regrading 3rd party tools so winrar is not an option

this is the code I have tried but I don't get any results it fails on the zip command

if ((Test-Path "$env:ProgramFiles\7-Zip\7z.exe") -eq $true){Set-Alias sz "$env:ProgramFiles\7-Zip\7z.exe" }
$DateStr = (Get-Date).ToString("dd-MM-yyyy")
$arcPath = "D:\SDDP\LOG_Archive_$DateStr.zip"

$limit = (Get-Date).AddDays(-7)
$path = "D:\SDDP\LOG"

$filesToBackUP = Get-ChildItem -Path $path -Recurse -Force | Where-Object { !$_.PSIsContainer -and $_.CreationTime -lt $limit }
ForEach ( $file in $filesToBackUP )
    {
        sz a -tzip $archPath $file.FullName
    }

the error I get is :

Open archive: D:\SDDP\LOG\DISTRIBUTOR(232)\04-09-2015\SDDP_DISTRIBUTOR(232)_04-09-2015_1.csv
sz : ERROR: D:\SDDP\LOG\DISTRIBUTOR(232)\04-09-2015\SDDP_DISTRIBUTOR(232)_04-09-2015_1.csv
At line:13 char:9
+         sz a -tzip $archPath $file.FullName
+         ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    + CategoryInfo          : NotSpecified: (ERROR: D:\SDDP\...4-09-2015_1.csv:String) [], RemoteException
    + FullyQualifiedErrorId : NativeCommandError

D:\SDDP\LOG\DISTRIBUTOR(232)\04-09-2015\SDDP_DISTRIBUTOR(232)_04-09-2015_1.csv
Open ERROR: Can not open the file as [zip] archive
ERRORS:
Is not archive
System ERROR:
Incorrect function.

Reference to the zip command I took from here
as I gone through the add reference there is nothing about creating a new 7zip file to add the files to, so I suppose it creates automatically but not so sure about it.

Please advice.
Thanks.

Solution

Try something along the lines of:

[string]$Zip = "C:\path to 7zip\7-zip\7z.exe"; 
[array]$args = "a", "-tzip", "-y", "-r", "$arcPath ";

ForEach ( $file in $filesToBackUP )
    { 
         $Zip $args $file;
    }

Sorry, I am currently on the move and unable to test this.