I've had some success in printing with only one cartridge and I hope you will find the following helpful. If you want to use only one of the color cartridges (C,Y,M) you first have to convert the image to use only that color. Here are the RGB values that correspond to these inks:
C: Keep G,B = 255 and vary R. 0,255,255 (full cyan) to 255,255,255 (white)
Y: Keep R,G = 255 and vary B. 255,255,0 (full yellow) to 255,255,255 (white)
M: Keep R,B = 255 and vary G. 255,0,255 (full magenta) to 255,255,255 (white)
I use Gimp to do this for photos. If you want to print with only a black cartridge you don't have to worry about doing any of the above conversions.
Next when you do the actual printing you need to worry about three settings: Paper type, Color or Black/Grayscale, and Color Adjustment. The color adjustment options can be found by clicking the "Advanced" button when color printing is selected on the printers I use.
Here are the settings for a couple different Epson printers as a guideline:
1. The WF-2630 has 4 cartridges, BK, Y, M, and C. For this printer:
-To print using BK only, set to Black/Grayscale and Plain Paper. If you use any other paper setting the color cartridges will also be used to make the blacks and grays.
-To print using C, Y, or M only, make sure you image has only one of those colors as explained above, then set to Color and "No Adjustment" for color adjustment/correction. Paper type doesn't matter.
2. The XP-520, 610, 620, and 800 have 5 cartridges labeled BK, C, Y, M, and PBK. BK is the larger black cartridge used for most black and white text printing. PBK is a smaller black used for photos and color printing. For this printer:
-To print using BK only, set to Black/Grayscale and Plain paper. Again if you use the other paper settings the printer will use more than the BK ink cartridge.
-To print using C, Y, or M only, make sure you image has only one of those colors as explained above, then set to Color and "No Adjustment" for color adjustment/correction, and any paper setting.
-You can print pure black (0,0,0) with PBK. Set paper to anything but plain. Color settings don’t matter. You can only print pure black with PBK only. If you try to print grays using only PBK, the printer uses the other color cartridges to make the grays.