De Yi Wu petitions for review of the Board of Immigration Appeals’ (BIA) decision affirming the Immigration Judge’s (IJ) order denying his application for asylum, withholding of removal, and relief under the United Nations Convention Against Torture (CAT). On appeal, Wu argues (1) his due process rights were violated because a malfunctioning tape recorder repeatedly interrupted his testimony during the removal proceeding, (2) the adverse credibility determination is not supported by substantial evidence, and (3) the BIA erred in finding he had not suffered past persecution and did not have a well-founded fear of future persecution. 1 *819 After review, we dismiss Wu’s petition in part and deny it in part. 2

I.

We review our subject matter jurisdiction de novo. Gonzalez-Oropeza v. U.S. Att’y Gen. 321 F.3d 1331, 1332 (11th Cir. 2003). We lack jurisdiction to, review claims that a petitioner fails to exhaust before the BIA. 8 U.S.C. § 1252(d)(1). A petitioner’s “allegation of a due process violation—that he was denied a full and fair hearing before a neutral factfinder—is precisely the kind of procedural error which requires exhaustion.” Amaya-Artunduaga v. U.S. Att’y Gen., 463 F.3d 1247, 1251 (11th Cir. 2006).

Wu failed to exhaust his claim that problems with the tape recorder deprived him of due process. Although Wu stated in his brief to the BIA that he had to answer certain questions repeatedly because of problems with the tape recorder, he did not argue this deprived him of due process. The BIA did not have an opportunity to address Wu’s due process argument, and we lack jurisdiction to review the claim. See Amaya-Artunduaga, 463 F.3d at 1251.

II.

We review credibility determinations under the substantial evidence test. Chen v. U.S. Att’y Gen., 463 F.3d 1228, 1230-31 (11th Cir. 2006). Under the substantial evidence test, we must affirm the BIA’s decision if it is “supported by reasonable, substantial, and probative evidence on the record considered as a whole.” Al Najjar v. Ashcroft, 257 F.3d 1262, 1284 (11th Cir. 2001). The BIA’s credibility determinations “can be reversed only if the evidence ‘compels’ a reasonable fact finder to find otherwise.” Chen, 463 F.3d at 1230-31.

The BIA “must offer specific, cogent reasons for an adverse credibility finding.” Forgue v. U.S. Att’y Gen., 401 F.3d 1282, 1287 (11th Cir. 2005). An adverse credibility determination may be based on “the inherent plausibility of the applicant’s or witness’s account, the consistency between the applicant’s or witness’s written and oral statements ..., the internal consistency of each such statement, [and] the consistency of such statements with other evidence of record.” 8 U.S.C. § 1158(b)(1)(B)(iii).

The BIA set forth specific, cogent reasons for its adverse credibility determination. Forgue, 401 F.3d at 1287. Substantial evidence supports the adverse credibility determination because the BIA (1) accurately identified discrepancies between Wu’s written account of his jailhouse beating and his testimony regarding the beating, and (2) found that Wu’s account of escaping from the hospital was inherently implausible. 8 U.S.C. § 1158(b)(1)(B)(iii). The record does not compel reversal of the BIA’s adverse credibility determination.

III.

An alien may establish eligibility for asylum if he shows he has suffered either “past persecution” or has a “well-founded fear” of future persecution based on a protected ground. Tang v. U.S. Att’y Gen., 578 F.3d 1270, 1277 (11th Cir. 2009). “To establish asylum based on past persecution, the applicant must prove (1) that [ ]he was persecuted, and (2) that the per *820 secution was on account of a protected ground.” Sanchez Jimenez v. U.S. Att’y Gen., 492 F.3d 1223, 1232 (11th Cir. 2007). A well-founded fear of future persecution may be established by showing, inter alia, (1) past persecution that creates a presumption of a “well-founded fear” of future persecution, or (2) a reasonable possibility of being singled out for persecution that cannot be avoided by relocating within the subject country. 8 C.F.R. § 208.13(b). 3

Wu submitted no credible evidence establishing how or why he was injured and thus failed to show he suffered past persecution on account of a protected ground. Because he did not establish past persecution, Wu is not entitled to a presumption of a well-founded fear of future persecution. 8 C.F.R. § 208.13(b). Wu also failed to show there was a reasonable possibility of him being singled out for future persecution that cannot be avoided by relocation. Although Wu offers some evidence that he belonged to a church in China, the only evidence that this church was unauthorized was Wu’s own testimony and written statements. Thus, the record does not compel the conclusion that Wu suffered past persecution or had a well-founded fear of future persecution. Because Wu failed to establish his eligibility for asylum, he necessarily failed to meet the higher burden of proof with respect to his claims for withholding of removal and CAT relief. See Al Najjar, 257 F.3d at 1292-93,1303.

PETITION DENIED IN PART AND DISMISSED IN PART.