(Adds shelter in Dallas, storm location)
HOUSTON, Aug 28 (Reuters) - Tropical Storm Harvey was set to dump more rain on Houston on Monday, worsening flooding that has paralyzed the country's fourth biggest city, forced thousands to flee surrounding counties and swollen rivers to levels not seen in centuries.
Harvey, the most powerful hurricane to hit Texas in more than 50 years, first hit land late on Friday and has killed at least two people. It has since stayed around Texas' Gulf of Mexico Coast where it is forecast to remain for several more days, drenching parts with a year's worth of rain in the span of a week.
Schools, airports and office buildings in Houston, home to about 2.3 million people, were ordered shut on Monday as scores of roads turned into rivers and chest-high water filled neighborhoods in the low-lying city.
Torrential rain also hit areas more than 150 miles (240 km) away, swelling rivers upstream and causing a surge that was heading toward the Houston area.
Authorities ordered more than 50,000 people to leave parts of Fort Bend County, about 35 miles (55 km) southwest of Houston as the Brazos River was set to crest at a record high of 59 feet (18 m) this week, 14 feet above its flood stage.
Brazos County Judge Robert Hebert told reporters the forecast crest represents a high not seen in at least 800 years.
"What we're seeing is the most devastating flood event in Houston's recorded history," 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, forecasters said. Nearly 24 inches fell in a span of 24 hours in Baytown, a city home to major refineries about 30 miles east of Houston, the National Weather Service said early on Monday.
"Water started flooding our house and by last night we were unable to leave," said Maria Davila, one of about 1,000 people in a makeshift shelter at Houston's sprawling convention center.
Dallas will set up a "mega shelter" it its convention center to house 5,000 evacuees, the city said in a statement.
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 he plans to add 1,000 more National Guard personnel to the flood battle.
Harvey is expected to produce an additional 15 inches to 25 inches of rain through Friday in the upper Texas coast and into southwestern Louisiana, the National Hurricane Center said.
The center of Harvey was 96 miles (154 km) southwest of Houston on Monday morning and forecast to arc slowly toward the city through Wednesday.
"The storm isnt moving much. If it doesnt move much, it keeps throwing rain into the same area," Steve Wistar, a senior meteorologist with AcuWeather, said in a telephone interview.
The Harris County Sheriff's Office used motorboats, airboats, humvees and other vehicles to rescue more than 2,000 people in the greater Houston area 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 and helicopters were deployed to save others stranded by the floods.
The National Weather Service has issued flood watches and warnings from near San Antonio to New Orleans, an area home to more than 13 million people.
Federal authorities predicted it would take years to repair the damage caused by Harvey.
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.
Katrina resulted in more than $15 billion in flood insurance losses in Louisiana and Mississippi.
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 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.
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.
More than 229,000 customers in the Houston area were without power on Monday morning, utilities CenterPoint Energy and AEP Texas said.
Houston's George Bush Intercontinental Airport, one of the nation's busiest, and William P. Hobby airport halted all commercial flights on Sunday. The airports remained closed to commercial traffic on Monday.
Jose Rengel, a 47-year-old construction worker who lives in Galveston, helped 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 Rockport, Kevin Drawbaugh and Jeff Mason in Washington, DC, Chris Michaud and Valerie Volcovici in New York, Erwin Seba, Marianna Parraga, Nick Oxford and Ernest Scheyder in Houston; Writing by Jon Herskovitz and David Gaffen; Editing by Paul Tait and Andrew Heavens)