In several places around the world, notably the North Sea and the Middle East, carbonate reservoirs are being accessed with very long horizontal wells (2000 to 20,000 feet of reservoir section.) These wells are often acid stimulated to remove drilling fluid filter cakes and to overcome formation damage effects, or to create acid fractures or deep matrix stimulation to enhance productivity. Good acid coverage with a relatively small acid volume is required to economically obtain the desired broad reservoir access. We have developed a model to predict the placement of injected acid in a long horizontal well, and to predict the subsequent effect of the acid in creating wormholes, overcoming damage effects, and stimulating productivity. The model tracks the interface between the acid and the completion fluid in the wellbore, models transient flow in the reservoir during acid injection, considers frictional effects in the tubulare, and predicts the depth of penetration of acid as a function of the acid volume and injection rate at all locations along the completion. We have used this model to simulate treatments that are typical of those performed in the North Sea and in the Middle East. We present a hypothetical example of acid placement in a long horizontal section and an example of using the model to history match actual treatment data from a North Sea chalk well.