The answer to your question is no, simple membrane-like desalination removes total dissolved solids (TDS), or salt, from water. If there is a thermal component added to the process it can remove some metals, but usually not heavy metals like zinc, aluminum, barium, etc. Desalination does not treat volatile organics, like benzene. Nor radium, if it exists. You can understand this better just by asking what's-his-name, here:

There is NO way this water can pass whole effluent toxicity testing simply by reducing TDS. No way, not under EPA methodology using the right test organisms.

Desalination creates a waste stream, a brine like sludge that has to be disposed of in the ground, and its way worse that high TDS produced water.

www.epa.gov

Provides information about how the permit program interacts with other CWA programs to protect and improve water quality, and provides resources for professionals working in the program at the federal, state, local, and firm level, and concerned public.

There ARE standards for effluent discharges in Texas for an array of industry, including the oil and gas industry. The Permian tight oil sector does not like those standards (Texas Surface Water Quality Standards) because they can't pass them, so they want the Texas Commission on Environmental Quality to change the entire process. If they do they violate the Federal Clean Water Act and the EPA steps in and overrides the TCEQ.

If you are a landowner and want to put this produced water on your land or try to irrigate with it, knock yourself out. But if it then rains and that produced water or corresponding sediment washes down into a public water of the State, like the Pecos, that's my water as a Texan. And your water. And no aquatic life will live in the Pecos all the way down to Amistad.

That is against the law.

Yes, I am pissed about all this. The tight oil sector thinks its shit doesn't stink; its changed accounting definitions, definitions of terms in the Texas oil industry used for 100 years, can over-drill acreage on 330 foot spacing between wells, has burned thru 400 billion dollars of CAPEX, and counting, its demand on limited services and labor in the country has more than doubled ALL drilling and completion costs, it lied about EURs and reserves, flared billions of MCFs of gas (also against the law) and now wants to dump its water on the ground. CEO's make hundreds of millions of dollars off borrowed capital and if as an American consumer you think it lowered your gasoline prices at the pump the past 15 years you'd be really wrong.

For oil exports to Rotterdam, and/or Singapore?

Pissed is an understatement. So should every Texan be pissed.