Black bean and andouille sausage soup

Since I'm now working four doubles in a row each week (16-hour days Tuesday through Friday), naturally it's become imperative to do a bunch of cooking on my two days off. I started this week's lineup with an easy soup, using up a bag of dried beans and some leftover sausage.

1 bag of dried black beans, soaked overnight and pre-cooked in a CrockPot
1 onion, chopped
2 carrots, chopped
2 stalks of celery, chopped
1 red pepper (or green), chopped
1 package andouille sausage, sliced
2 cups tomato sauce, or one can diced tomatoes
1 1/2 quarts broth
Seasonings to taste: salt, pepper, chili powder, cumin, paprika, cayenne

In a big soup pot, add some olive oil (or bacon fat) over medium-high heat. Saute the onion, carrot, and celery until the onion is soft. Add the pepper and the sausage and saute for another couple of minutes. Add the beans, the tomatoes, and enough broth to float everything. Let cook down on medium-low heat, covered, until everything is cooked through. (If the beans are pre-cooked, 20-30 minutes; if not, 1-2 hours.) Season to taste and allow to simmer another five minutes or so.

Note: it would be very easy to add, say, a bag of frozen corn into this soup.