Much of the crude oil from the North Slope is exported to Japan and broadly affects the Asian market. The loss of a major nuclear facility in Japan and the improving Asian economies must inevitably cause an increased demand for North Slope crude oil. In addition, the alternative source of crude for Asia — the Mid East — is cast into doubt by the ongoing unrest in the Persian Gulf.
Make that NONE, not much. It is far cheaper to send to the closer West Coast refineries.
Although Washington has no indigenous crude oil production, it is a principal refining center serving Pacific Northwest markets. Five refineries receive crude oil supply primarily by tanker from Alaska. However, because Alaskan production is in decline, Washington’s refineries are becoming increasingly dependent on crude oil imports from Canada and other countries.
http://www.eia.doe.gov/state/state-energy-profiles-analysis.cfm?sid=WA
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A network of crude oil pipelines connects production areas to refining centers in the Los Angeles area, the San Francisco Bay area, and the Central Valley. California refiners also process large volumes of Alaskan and foreign crude oil received at ports in Los Angeles, Long Beach, and the Bay Area. Crude oil production in California and Alaska is in decline and California refineries have become increasingly dependent on foreign imports.
http://www.eia.doe.gov/state/state-energy-profiles-analysis.cfm?sid=CA
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From Valdez, tankers ship the ANS crude oil primarily to refineries along the West Coast. Those refineries are designed to process the intermediate, sour (high-sulfur) crude oil from the ANS. Alaskan crude oil production has been in decline since 1988, when output peaked at over 2 million barrels per day.
http://www.eia.doe.gov/state/state-energy-profiles-analysis.cfm?sid=AK