In a medium pot, combine olive oil, onion, carrot and celery. Cook gently over medium heat until vegetables are soft and translucent.
Add sweet potatoes, coconut milk and water. Bring to a boil and then turn down; let the soup simmer until sweet potatoes are soft (approximately 10 minutes; test them by piercing with a fork). At this point the soup is ready to purée.
Pour into a blender,then add peanut butter, cayenne pepper and lime juice, and purée until smooth. If necessary to reach the desired consistency, add a little water and whirl in the blender again. Season with salt and pepper to taste.