Income Taxes - Components of the Federal Deferred Tax Asset (Liability) (Details) - USD ($) $ in Thousands	Dec. 31, 2023	Dec. 31, 2022
Income Tax Disclosure [Abstract]
Prepaid and other insurance	$ (804)	$ (707)
Property	(12,559)	(15,208)
ROU assets	1,292	1,701
ROU liabilities	(1,293)	(1,701)
Amortization	(562)	(869)
Investment in unconsolidated affiliate	536	537
Valuation allowance related to investment in unconsolidated affiliate	(525)	(537)
Net operating loss	396	239
Other	571	1,168
Net long-term deferred tax liability	$ (12,948)	$ (15,377)

Deferred Tax Assets, Right-Of-Use Asset

No definition available.

Name:	ae_DeferredTaxAssetsRightOfUseAsset
Namespace Prefix:	ae_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Deferred Tax Liabilities, Amortization

+ References

No definition available.

+ Details

Name:	ae_DeferredTaxLiabilitiesAmortization
Namespace Prefix:	ae_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Deferred Tax Liabilities, Operating Income (Loss)

+ References

No definition available.

+ Details

Name:	ae_DeferredTaxLiabilitiesOperatingIncomeLoss
Namespace Prefix:	ae_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Noncurrent amount of deferred tax consequences attributable to taxable temporary differences derived from prepaid expenses.

+ References

No definition available.

+ Details

Name:	ae_DeferredTaxLiabilitiesPrepaidExpensesNoncurrent
Namespace Prefix:	ae_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Deferred Tax Liabilities, Right-Of-Use Liabilities

+ References

No definition available.

+ Details

Name:	ae_DeferredTaxLiabilitiesRightOfUseLiabilities
Namespace Prefix:	ae_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount before allocation of valuation allowances of deferred tax asset attributable to deductible temporary differences from equity method investments.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 6
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482685/740-10-50-6

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 8
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482685/740-10-50-8

+ Details

Name:	us-gaap_DeferredTaxAssetsEquityMethodInvestments
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount, before allocation of valuation allowance, of deferred tax asset attributable to deductible temporary differences, classified as other.

+ References

+ Details

Name:	us-gaap_DeferredTaxAssetsOther
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of deferred tax assets for which it is more likely than not that a tax benefit will not be realized.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482685/740-10-50-2

+ Details

Name:	us-gaap_DeferredTaxAssetsValuationAllowance
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount, after deferred tax asset, of deferred tax liability attributable to taxable differences without jurisdictional netting.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482685/740-10-50-2

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 45
-Paragraph 6
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482525/740-10-45-6

+ Details

Name:	us-gaap_DeferredTaxLiabilities
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of deferred tax liability attributable to taxable temporary differences from property, plant, and equipment.

+ References

+ Details

Name:	us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- References

No definition available.

+ Details

Name:	us-gaap_IncomeTaxDisclosureAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration