Houston is facing worsening historic flooding in the coming days as Tropical Storm Harvey dumps more rain on the city, swelling rivers to record levels and forcing federal engineers to release water from area reservoirs in hopes of controlling the rushing currents.

Harvey was the most powerful hurricane to strike Texas in more than 50 years when it came ashore on Friday near Corpus Christi, about 354 km south of Houston, and has killed at least two people. It has since lingered around Texas' Gulf Coast, where it is forecast to remain for several more days, drenching parts of the region with a year's worth of rain in the span of a week.

READ: Harvey has  rocked oil markets and hurt US producers

Rains have submerged cars and turned freeways into rivers, with more flooding expected when the storm shifts back in the direction of Houston. Harvey's centre was 148 km southwest of Houston on Monday morning and forecast to arc slowly toward the city through Wednesday, with the worst floods expected later that day and on Thursday.

Schools, airports and office buildings in the nation's fourth largest city were shut on Monday as chest-high water filled some neighbourhoods in the low-lying city that is home to about 2.3 million people.

The metropolitan area, home to 6.8 million people, also is the nation's refining and petrochemical hub, which has been crippled by the storm. Numerous refiners shut operations, likely for weeks.

Torrential rain also hit areas more than 240 km away, swelling rivers upstream and causing a surge that was heading toward the Houston area, where numerous rivers and streams already have been breached. Some areas have already seen as much as 76 cm of rain, according to the National Weather Service.

WATCH: Torrential rain comes pouring down on Houston 

By the end of the week in some Texas coastal areas the total precipitation could reach 127 cm, which is the average rainfall for an entire year, forecasters said.

Harvey is expected to produce an additional 38 to 63 cm of rain through Friday in the upper Texas coast and into southwestern Louisiana, the National Hurricane Center said.

Convention centre for displaced

More than 30,000 people are expected to be placed temporarily in shelters, FEMA Administrator Brock Long said at a news conference on Monday. The George Brown Convention Center in downtown Houston now has about 2,500 people, up from 1,000 last night, as people continue to arrive at the centre.

Wendy Rom, 24, was among those taking refuge at the centre with her husband and 1 1/2-year-old daughter.

"The water was high, entering our house," she said, "so we moved to the second floor but they started evacuating the neighbourhood so I came with my whole family."

Dallas, 386 km north of Houston, also was setting up a "mega shelter" at its convention centre to house 5,000 evacuees, the city said in a statement.

The US Army Corps of Engineers said Monday that it was releasing water from two nearby reservoirs into Buffalo Bayou, the primary body of water running through Houston.

"If we don’t begin releasing now, the volume of uncontrolled water around the dams will be higher and have a greater impact on the surrounding communities," said Colonel Lars Zetterstrom, Galveston district commander of the Corps.

The Harris County Flood Control District said it expected the release to start flooding homes around the Addicks and Barker reservoirs on Monday morning.

Authorities ordered more than 50,000 people to leave parts of Fort Bend County, about 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.

Houston did not order an evacuation, even a voluntary one, due to concerns about people being stranded on city highways now consumed by floods, Mayor Sylvester Turner said on Sunday.

FEMA's Long on Monday did not question the decision, saying the time frame "for evacuation of the city of Houston could take days, days, literally days."

Texas Governor Greg Abbott, who had suggested on Friday that people leave the area, on Monday told "CBS This Morning" that "the time for making that determination has passed, and (there's) no need to for us to relitigate that issue right now."

Trump visit

US President Donald Trump plans to go to Texas on Tuesday to survey the damage, a White House spokeswoman said on Sunday. On Monday he approved an emergency declaration for Louisiana.

Trump, facing the first big US natural disaster since he took office in January, had signed a disaster proclamation for Texas on Friday, triggering federal relief efforts. Abbott said on Sunday he planned to add 1,000 more National Guard personnel to the flood battle.

Almost half of the US refining capacity is in the Gulf region. Shutdowns extended across the coast, including Exxon Mobil's facility in Baytown, the nation's second largest refinery. More than 2.4 million barrels of capacity were offline as of Monday morning, about 13 percent of daily U.S. production.

The outages will limit the availability of US gasoline and other refined products and push prices higher, analysts said. Gasoline futures rose 3 percent on Monday.

Federal authorities predicted it would take years to repair the damage from Harvey. The expected rain conjured memories of Tropical Storm Allison, which lingered for days over South Texas in 2001, flooding 70,000 homes and causing $9 billion in damage.

Damages are not likely to be as extensive as Katrina in 2005, which killed 1,800 people in and around New Orleans, or Sandy, which hit New York in 2012, said a spokeswoman for Hannover Re, one of the world’s largest reinsurers. Those caused $80 billion and $36 billion in insured losses, respectively.

All Houston port facilities are closed on Monday because of the weather threat, a port spokeswoman said.

More than 263,000 customers in the Houston area were without power on Monday morning, utilities CenterPoint Energy, AEP Texas and TNMP said. CenterPoint warned, though, it could not update its figures due to limited access caused by flooding.

Jose Rengel, 47, a 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," he said.

"And it keeps raining. The water has nowhere to go."