Concept:
In a batch distillation process, the composition of the liquid in the reboiler (the "still") changes continuously as the more volatile component is removed.
Step 1: Analyze the dynamics of batch distillation.
As the distillation progresses, the concentration of the more volatile component ($x_W$) in the reboiler decreases. According to the vapor-liquid equilibrium, a weaker liquid in the reboiler produces a weaker vapor.
Step 2: Impact of a constant reflux ratio ($R$).
If the reflux ratio is kept constant, the separation power of the column remains relatively fixed. Since the "feed" (the reboiler liquid) is getting leaner in the volatile component over time, the resulting top product (distillate) will also become leaner. Therefore, the composition of the more volatile component in the distillate ($x_D$) will decrease as time passes.
Step 3: Contrast with constant distillate composition.
To maintain a constant distillate composition ($x_D$) in a batch process, one would have to continually increase the reflux ratio to compensate for the depleting concentration in the reboiler.