I'd like to go beyond your initial proposed solution, and encourage you to think about this opportunity a bit differently.
Right now you have an activity that could potentially be of value to your company, and it is not a part of your regular job. By seeking "financial consideration" for your activity, you would effectively be asking to make this part of your job, or otherwise you would be making the situation quite complicated. If it isn't part of your job, but you are being paid for it, are you then both an employee and a contractor? When you are blogging, are you now officially doing so as an employee of the company, and the company is liable for things you say (and/or promises you make) on your website? There is a lot of legal, accounting, and authority issues here, and it is unlikely that it will be easy for your company to say yes to you - which means you are far more likely to end in an awkward situation where not only do they need to tell you no, but might object to your current 'private' blogging as well.
Instead, here's what I would suggest you consider. Depending on the flexibility of your organization and your relationship with your manager, I'd consider having a meeting with your manager and discussing your interests. You appear to be interested in taking on some additional responsibilities, such as blogging, supporting the company publicly, and even helping generate sales leads, and if you just started "accidentally" producing leads then this is a good argument that you might be good at this sort of work in the future, so communicate your interest to your manager. Some workplaces strictly avoid this kind of thing (a culture of "that's not what we are paying you for"), while others are flexible and would jump at the chance to get a technical person more involved in building sales and public relations.
If you do this, you would either be trying to build a new (minimally tested and demonstrated) skill set, and expand your current role into more of a hybrid position. There are in fact lots of jobs for highly technical people with experience in sales, marketing, and public relations, and you would effectively be developing into having this as an opportunity for you in the future.
If you decide to take this track, you should not necessarily be concerned with an immediate pay raise, unless there is an existing role in your company that fits what you are suggested (combined developer/social media, etc) and that would have a higher pay rate than you currently make. If your company is interested in having you try out this role, you might ask if they would reconsider your salary for such an expanded role of responsibility and value, which could include a commission/bonus style of incentive that is more typical of sales-related workers (if that's what you really want, otherwise don't suggest it).
So in conclusion, just asking for money for something no one asked you to do probably wouldn't go well for anyone, and the complexity of paying an employee for things that they supposedly aren't doing as an employee (like generating leads in their personal time) makes this unlikely to be approvable, but your experiences and interests can absolutely be the basis for talking about changing and expanding your job roles and responsibility. This could even lead to a different career track, which may or may not increase your pay compared to your current track, but providing additional value to your organization (especially when it is easily measured in dollars) can often be a great negotiating point for increased pay.