Acute exacerbations of Chronic Obstructive Pulmonary Disease (COPD) are a major source of morbidity and mortality for patients and cost to the society. In case of acute respiratory failure with hypercapnia and acidosis, Non Invasive Ventilation (NIV) is preferred as a first line treatment. NIV failures are not uncommon, from 15% in intensive care to 25 - 30% in emergency departments. They most often occur at the start of the NIV or in the hours that follow. There are many reasons for these failure. Among these are; dyspnea, discomfort, the pain related to the exacerbation and also to the NIV are frequently noted. The use of certain drugs with anxiolytic, hypnotic and/or analgesic properties could also be useful. Some sedatives and opioids have already been studied in this indication but without a therapeutic trial and satisfactory methodology. Among the molecules of interest, Morphine seems interesting . It's administration could reduce the ventilatory rate, intensity of dyspnea, pain and anxiety as well as dynamic hyperinflation. The investigators believe that morphine administration will decrease the rate of early NIV failure by improving comfort (decreased dyspnea and pain) and ventilation (decreased respiratory rate and increase in tidal volume) in patients with exacerbations of COPD. However, before considering a randomized phase III efficacy study, it is necessary to determine the optimal dose of morphine in this indication, through a phase I/II dose-finding study taking into accounts both the efficacy and toxicity of morphine. The main objective of this study, is to determine the optimal dose of morphine administered at the initiation of NIV in patient with acute Exacerbation of Chronic Obstructive Pulmonary Disease (COPD), which is defined as the maximum gain function combining the probability of dose-limiting toxicity with PaCO2.Therefore, the impact of morphine administration on the physiological parameters of NIV- COPD exacerbation patients will be assessed.