First, $1.2 Billion is a drop in the bucket since this stock trades that value in a week at around current prices. So you are not going to last in the market very long. The stock will then just drop to its perceived value by the market.
Second, The idea of a buy back is not to support the stock, but to take shares off the market, thereby increasing the earnings per share and then the long term stock price.
The entire refining business is under pressure due to the closure in price between Brent and WTI and nothing is going to change that in the near term. In fact because of the ability to get more oil out of Cushing, OK, this situation may be more permanent.