I take my enemas down on my knees bent over the toilet with the lid down. Primarily, I take them this way because it is easier for me to brace myself with my left hand placed on the toilet lid whilst using my right hand to reach my anus and insert the colon tube since I can only self-administer because no one else in my family shares the same passion for enemas.
Certainly, positioning the torso in a horizontal configuration will encourage the enema water to penetrate deeper into the upper parts of the colon thus resulting in a more filling experience with a much deeper and thorough cleaning out - if that is the desired goal.
However, with reference to your question referring to standing up whilst taking an enema, I would like to state my personal experience.
I was introduced to enemas in a hospital in Rome when I was 4 years old. The first enema in my life was administered to me in the prone position (face down), but the rest of the enemas were administered in the standing position - which may seem as an unusual way to administer enemas.
In that Roman hospital, according to standard practice during the day prior to surgery the last meal was lunch and in the evening all the boys scheduled for surgery were required to line up outside a designated bathroom and wait standing patiently in line outside the door. Once the previous boy finished receiving an enema, he would exit the bathroom thus making way for the next boy in line. The next boy in line was then required to enter the bathroom and stand upright facing a bathtub, loosen and drop their pajama pants down to their ankles thus exposing their young bum, and lastly brace the edge of the bathtub with both hands. Once in that position, a nurse that was strategically seated on a chair behind the boy, and within reach of the his bare bum, would insert an orange rubber colon tube up into the his anus until she determined that the colon tube end with its one-eye side opening was sufficiently (12-16 inches) implanted high up to the start of the boy's descending colon. Next, a second nurse standing nearby next to an IV pole suspending an open-top glass cylindrical canister would flick open the hose clamp to let the enema liquid flow through the rubber hose attached to the colon tube. (It probably was one long single piece of tube.)
The rationale for administering those enemas in a standing position way was to allow the liquid gushing out of the colon tube opening to flow downwards (thanks to gravity) through the descending and sigmoid colons respectively, thus dislodging and forcing any faecal material into the rectum where it would be awaiting expulsion. This would ensure a good clean sweep of the colons which was the obvious intention of these pre-op enemas. However, as you can appreciate, taking an enema in the standing position produced such a strong intense ache inside my young small rectums (as it would have with all the other boys) as the accumulating liquid pressure forced it to expanded. All of which instinctively initiated an anal sphincters tightening response jerking the colon tube and resonating along all the way up to the fingers of nurse holding it. Perhaps that was the signal indicating to her that the enema liquid was flowing unhindered into my colon intended. She would have released that the enema was working! Anyway, if the liquid was not flowing, the second nurse standing by the canister would have said something.
I cannot say for certain what the enema liquid solution consisted of because none of us boys ever dared asked any questions, however since this was a hospital setting, it is safe for me to assume that the watery liquid would at the very least have include some kind of soap and perhaps a bit of salt to enhance the performance of the enema and ensure the best results possible.
Anyway, that second nurse in charge of the water flow would allow the liquid to flow until she determined that each boy was sufficiently supplied with a 200-250 ml dose. Such a measurement would have been easy to count off using the scale on the side of the glass canister. And if the canister capacity was 2 letres, then that should have allow between 8-10 boys to be serviced in that one enema session. Once the clamp was shut off, the sitting-down nurse would swiftly withdraw the colon tube and while each boy was busy refastening their pajama pants she would command the boy to pace the length of the corridor a few times before expelling - obviously so as to give the enema liquid extra time to slosh around and work its way in-and-out of the intestinal nooks and crannies. I can not speak for the other boys, but personally I only could manage a couple of rounds before the ache inside my pre-teen rectum would become so strong and intense forcing me to clinch my anal sphincters all the more tight. Honestly, it felt like I would loose my load there in the corridor, which was something I feared.
Thus, the process would be repeated for each boy in the line until the last boy was successful irrigated. As always, the bathroom door was left open for convenience, but unfortunately for us, this allowed the commuting public in the corridor to get a clear view of what was happening in the bathroom. As expressed by many other Zity members, privacy was not important back then.