Kanji itself is only a way to quickly visualise the multitude of similar sounding words in Japanese. Writing kanji is itself not a problem, only the multiple readings can throw me off. There are no real rules for using certain kana in place of kanji, only what is "acceptable" in daily use.

Generally speaking, if the sentence has too many hiragana words, I will try either to replace some of them with kanji, or katakana. However, I have seen authors use the same hiragana word in a single sentence, then switch over to its kanji equivalent mid sentence to make it clearer. 

Another example: pick up your Minna No Nihongo book, and the recommended word for "garbage" is ごみ。Head down to Tokyo and look around for a garbage bin (a little hard, but still possible), you may find either ゴミ箱 or ゴミバコ. It is a writing style that is both arbitrary, yet rigid. 

So I have given up trying to find a rule for it- if you are familiar with the hiragana/katakana word and its kanji equivalent, then use it however you like. I guess... it doesn't matter if I type "visualise" or "visualize" (or even "vizualize" [sic]), as long as it is readable (and fits the job on hand), I'll write as the situation demands.