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As noted in the comment above, k1 etc must be called with its argument list. With this change the r1 etc equations become r1 = k1[r, ϕ] dens[r, ϕ]^2 nH[r] nOH[r]; r2 = k2[r, ϕ] dens[r, ϕ]^2 nH[r] nH2O[r]; r17 = k17[r, ϕ] dens[r, ϕ]^2 nH2[r] nO[r]; r18 = k18[r, ϕ] dens[r, ϕ]^2 nH2[r] nOH[r]; r62 = k62[r, ϕ] dens[r, ϕ]^2 nO[r] nOH[r]; r63 = k63[r, ϕ] ...


Take a look at X'[t]/Z'[t]: This is not the angle of rotation that you need. What you need is ArcTan[Z'[t],X'[t]], which looks like this If you change that in your code, you get the desired result.

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