Have butcher cut rib section lengthwise into serving pieces. Brown spare ribs slightly on both sides in shortening in a large skillet over medium heat. Drain well.
Sprinkle ribs on both sides with salt and pepper. Place ribs in a large Dutch oven; add water to cover, onion, and celery. Cover and cook over low heat 1 1/2 hours or until ribs are tender. Drain well.
Place sauerkraut , caraway seeds, and sugar in bottom of Dutch oven; stir well. Place ribs over sauerkraut; cover and cook over low heat 30 minutes. To serve, arrange sauerkraut on a serving platter, and place ribs over top.