Albers, who threw 30 pitches, was able to get loose quickly and said the session went well.
"It felt good, so I think I'm on track," Albers said.
Albers' first rehab appearance would be on Friday, and he expects to make at least two outings at Charlotte. One will likely be for an inning, with another lasting possibly two.
He started throwing bullpens around a week and a half ago, and he threw four of them before his simulated game on Tuesday.
Albers fractured his right pinkie finger in the White Sox fracas with the Royals in April. He subsequently underwent surgery and has not pitched in a game since April 19. He made four appearances out of the bullpen in April, recording a 1.59 ERA, before his injury.
• Alexei Ramirez was in the lineup on Tuesday after throwing a routine double-play ball into right field in Monday's loss. He has played in all but one game this season.
After an All-Star season in 2014, Ramirez has struggled both offensively and defensively this year.
"There's times when you do give him that day [off], and I don't think this is that time," manager Robin Ventura said. "He wants to get back in there as quick as he can and play."
• As the team's offensive output remains low, Ventura tossed around the idea of batting first baseman Jose Abreu second.
"You want him to hit as many times as you can," Ventura said, although they also want the potential for as many runners to be on base for their best run-producer.
When Ventura altered the lineup on June 19, he shifted right fielder Avisail Garcia to the two-hole and left fielder Melky Cabrera down.
• Target Field has not been kind to the White Sox this season. They are 0-5 against the Twins in Minnesota, with a 7.20 team ERA. They've been outscored 44-10 at the ballpark this season. Earlier this season they were swept in a four-game series, and they were also swept in four games at Target Field last June.