* At least two dead from storm
* Storm knocks out 11 percent of U.S. refining capacity
* Harvey now about 105 miles (170 km) from Houston
* Houston residents told to climb on roof if homes flood (Updates information on damage, flights, paragraphs 3, 11-12, 19, 21, 23)
By Ruthy Munoz and Gary McWilliams
HOUSTON, Aug 27 (Reuters) - Catastrophic flooding triggered by Tropical Storm Harvey inundated Houston on Sunday, forcing residents of the fourth most populous U.S. city to flee in boats or hunker down in anticipation of several more days of "unprecedented" rainfall.
Harvey came ashore late on Friday as the most powerful hurricane to hit Texas in more than 50 years and has killed at least two people. The death toll is expected to rise as the storm triggers additional tidal surges and tornadoes, with parts of the region expected to see a year's worth of rainfall in the span of a week.
The storm turned roads into rivers and caused chest-deep flooding on some streets in Houston as rivers and channels overflowed their banks. More than 26 inches (66 cm) of rain had fallen in parts of Houston in the past 48 hours, the National Weather Service said on Sunday, with more on the way.
Harvey struck at the heart of the country's oil and gas industry, forcing operators to close several refineries and evacuate and close offshore platforms. The massive flooding knocked out 11 percent of U.S. refining capacity and a quarter of oil production from the U.S. Gulf of Mexico.
"What we're seeing is the most devastating flood event in Houston's recorded history. We're seeing levels of rainfall that are unprecedented," said Steve Bowen, chief meteorologist at reinsurance firm Aon Benfield.
Total precipitation could reach 50 inches (127 cm) in some coastal areas of Texas by the end of the week, or the average rainfall for an entire year. The center of Harvey was about 105 miles (170 km) from Houston and forecast to arc slowly toward the city through Wednesday.
Floodwaters rose swiftly in Houston and emergency services told the city's 2.3 million inhabitants to climb onto the roofs of houses, if necessary.
"The water was right at our door," said Jasmine Melendez, a 23-year-old mother of three, including a week-old infant. "We were also worried about the kids, especially the baby."
U.S. President Donald Trump plans to go to Texas on Tuesday to survey damage from the storm, a White House spokeswoman said on Sunday.
Trump, facing the first big U.S. natural disaster since he took office in January, signed a disaster proclamation on Friday, triggering federal relief efforts. Texas Governor Greg Abbott said on Sunday 54 counties had been declared state disaster areas.
People in Houston and other areas of Texas were asked not to leave their homes, even if they were flooded, because roads were impassable.
Houston's George Bush Intercontinental Airport, one of the nation's busiest, and William P. Hobby airport halted all commercial flights on Sunday. Nearly 1,500 flights in and out of Houston were canceled due to the storm, tracking service FlightAware.com said.
The Gulf is home to almost half of the nation's refining capacity, and the reduced supply could affect gasoline supplies across the U.S. Southeast and other parts of the country. Shutdowns extended across the coast, including Exxon Mobil's Baytown refinery, the second largest U.S. refinery.
Gasoline futures rose as much as 7 percent in early trading on Sunday evening. Heating oil futures, a proxy for distillates like diesel fuel, were up as much as 3 percent, with supplies expected to be curtailed.
The outages will limit the availability of U.S. crude, gasoline and other refined products for global consumers and further push up prices, analysts said.
All Houston port facilities will be closed on Monday because of the weather threat, a port spokeswoman said on Sunday night.
Hundreds of people like Melendez and her children were sheltering at the downtown George Brown Convention Center, where they sought water, food and baby supplies. Some people were being brought to the center in city dump trucks.
The Harris County Sheriff's Office rescued more than 2,000 people in the greater Houston area using vehicles including motorboats, airboats and humvees on Sunday, a spokesman said.
The U.S. Coast Guard and Houston police rescued hundreds more as residents brought boats to staging centers to help.
Forecasters could only draw on a few comparisons to the storm, recalling Hurricane Katrina, which devastated New Orleans and killed 1,800 people in 2005, and Tropical Storm Allison.
Flood damage in Texas from Hurricane Harvey may equal that from Katrina, the costliest natural disaster in U.S. history, an insurance research group said on Sunday.
The Harris County Flood Control District said Harvey's impact would rival that of Allison, which dropped more than 40 inches (102 cm) of rain in Texas in June 2001, flooded 70,000 homes and caused $9 billion in damage.
Harvey hit Texas as a Category 4 hurricane with winds of 130 miles per hour (210 kph), the strongest storm to hit the state since 1961. About 70,000 customers were without power by Sunday evening, according to Centerpoint Energy.
Two deaths had been confirmed so far - one in Rockport, 30 miles (50 km) north of Corpus Christi, and one in west Houston on Saturday. The Twitter account for Harris County 911 said people should not call if their lives were not threatened.
Houston's schools were scheduled to close for the week, the school district said on Twitter. ConocoPhillips will close on Monday and Tuesday, the company said.
The Federal Emergency Management Agency said it had more than 400 rescue personnel in South Texas, and 500 others were in the state and expected to join rescue operations on Sunday night.
Jose Rengel, a 47-year-old construction worker who lives in Galveston, was helping with rescue efforts in Dickinson, southeast of Houston, where he saw water cresting the tops of cars.
"I am blessed that not much has happened to me, but these people lost everything. And it keeps raining," he said.
"The water has nowhere to go."
Additional reporting by Brian Thevenot in Corpus Christi, Texas, Sophia Kunthara, Dion Rabouin and Chris Michaud in New York, Timothy Gardner, Lisa Lambert, Jeff Mason and Mike Stone in Washington and Erwin Seba, Marianna Parraga, Nick Oxford and Ernest Scheyder in Houston; Writing by Simon Webb, David Gaffen and Jon Herskovitz; Editing by Andrew Hay, Peter Cooney and Paul Tait